Overlay Multicast for Video On Demand on the Internet Kien A Hua Duc A Tran Roy Villafane School of Electrical Engineering and Computer Science University of Central Florida Orlando, FL 32816-2362, U.S.A School of Electrical Engineering and Computer Science University of Central Florida Orlando, FL 32816-2362, U.S.A School of Electrical Engineering and Computer Science University of Central Florida Orlando, FL 32816-2362, U.S.A kienhua@cs.ucf.edu dtran@cs.ucf.edu villafan@cs.ucf.edu Keywords ✁✄✂✆☎✞✝✠✟☛✡✌☞✎✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✌✛✢✜✄✕☛✣✢☎✞✤✥✤✆✦✧✣✢☎★✍✩✡✪✦✫✣✬✛✢✭✮✡✯✓✠✖✱✰✢✕☛✦✢✲✢✳ ABSTRACT ✭✮✡✯✓✠✖✱✰✢✕✗✦✒✲✴✕✗✘✵✡✙✦✶✡✯✓✷✓✷✝✸✡✙✖✞✓✠✕✗✂✹☎✮✓✠☎★✖✸✰✒✦✢✕☛✺✻✏✢☎✵✼✽✤✪✝✵✾✒✏✢✕✗✟✿✣❀✕✗✦✒✲❁☎✞❂❃✖✞✕☛☎✞✦✻✓❄✂✻✕✿✣❀☎★✤✙❅ ✙✤ ✦✢❅❆✣✢☎✞✍✩✡✙✦✫✣❇✘✚☞❀✘✚✓✠☎★✍❃✘★✳❃❈❉✤✯❊❋☎★✂✹☎✞✝✌✛●✘✷✕✗✦✒✖★☎✩✭✮✡✯✓✠✖✱✰✢✕✗✦✒✲❍✡✪✘✷✘✷✏✒✍❃☎★✘■✓✠✰✢☎ ☎✱❏✢✕✗✘✚✓✠☎★✦✢✖★☎❑✤✙✼❀▲✚✭❍▼✧✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✌✛✙✕☛✍❃◆✢✟✗☎★✍❃☎★✦❖✓✠✕✗✦✒✲✭✮✡✯✓✠✖✱✰✢✕✗✦✒✲✴✤✆✦■✓✠✰✢☎❑✖✞✏✢✝✷❅ ✝✠☎✞✦✻✓◗▲❘✦❖✓✠☎✞✝✠✦✢☎✞✓✥✕✗✘❃✡❇✖✱✰✒✡✙✟✗✟✗☎★✦✒✲✙✕✗✦✒✲❇✓✸✡✙✘✷❙❚✾❯☎★✖✌✡✪✏✒✘✷☎✎✓✠✰✒☎✎▲❘✦❖✓✠☎✞✝✠✦✒☎✱✓◗✕✗✘ ✾✒✡✙✘✷☎✌✣❱✤✙✦❲▲✚✭❨❳✄✦✒✕✗✖✌✡✪✘✚✓✧✤✙✦✒✟✔☞❖✳❩▲❘✦❬✓✠✰✢✕☛✘✎◆✫✡✪◆❯☎✞✝✌✛✴❊☎❇◆✢✝✠✤✙◆❯✤✆✘✷☎❭✡✙✦ ✤✯✂✹☎✱✝✠✟✿✡★☞❪✓✠☎★✖✱✰✢✦✒✕☛✺❖✏✒☎❫✖★✡✙✟✗✟✗☎✌✣❵❴✵❛✠❜✙❝✠❞✄✼❡✤✙✝❢☎★✦✫✡✪✾✒✟✗✕✗✦✒✲❚✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❢✘✷☎✞✝✷❅ ✂✻✕✗✖★☎★✘✄✤✆✦❍✓✠✰✒☎✑✡✙◆✢◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✆✦❭✟☛✡★☞❖☎✞✝✌✛✬✡✙✘■✡✩❊✡✌☞✧✓✠✤✎✘✷✏✢◆✒◆❯✤✪✝✷✓✄✓✠✰✒☎❣✕✗✍✥❅ ◆✢✟✗☎★✍❃☎★✦❖✓✸✡✪✓✠✕✗✤✆✦❤✤✙✼✴✭✮✡✯✓✠✖✱✰✢✕☛✦✢✲✢✳❢❳✄✦✢✟☛✕✗❙✹☎❃☎★✡✪✝✠✟✗✕✗☎✞✝◗✤✯✂✹☎✱✝✠✟✿✡★☞✐✍◗✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓ ✘✷✖✸✰✒☎✞✍❃☎★✘★✛❄✜❉✖✌✡✙✘✚✓❥✣✢✤❖☎★✘✶✦✒✤✪✓❥✕✗✦❖✓✷✝✠✤✻✣✢✏✒✖✞☎✥✡✙✦❖☞❇✲✙✟☛✤✙✾✫✡✪✟❑✓✠✤✙◆❯✤✆✟✗✤✆✲✪☞✐✼❡✤✙✝ ✓✠✰✢☎◗✤✯✂✹☎✞✝✠✟☛✡★☞❭✡✙✦✒✣❫✓✠✰✒☎✞✝✠☎✞✼❡✤✙✝✠☎❃✡✌✂✹✤✙✕☛✣✢✘■✖★✤✙✦❖✓✷✝✠✤✆✟❦✤✯✂✹☎✞✝✠✰✒☎★✡✆✣❍✓✠✤❢✍✩✡✪✕☛✦❀❅ ✓✸✡✪✕✗✦✥✕✔✓✌✳❦✜✄✖✌✡✪✘✚✓❧✖★✡✙✦✥✖★✤✙✦✢♠✒✲✆✏✢✝✠☎❁✕✔✓✠✘✷☎★✟✔✼✬✡✙✣✒✡✙◆❀✓✠✕✗✂✹☎★✟✔☞✑✓✠✤❉✓✠✰✒☎✖✸✰✫✡✪✦✒✲✆✕✗✦✢✲ ✦✢☎✞✓❘❊❋✤✙✝✠❙❫✓✷✝✸✡✯❂❃✖✆✛●✡✙✦✒✣❇✕✗✘■✓✠✤✙✟☛☎✱✝✸✡✙✦❖✓■✓✠✤✩✼♥✡✙✕✗✟✗✏✢✝✠☎✞✘❥◆✢✝✠✤✆✦✢☎✑✓✠✤✎✰✫✡✪◆✒◆❯☎★✦ ✼✿✝✠☎✌✺❖✏✒☎★✦❖✓✠✟✔☞♦✕✗✦❱✣❀☞❀✦✒✡✙✍❃✕✗✖✧☎★✦✻✂✻✕✔✝✠✤✆✦✢✍❃☎★✦❖✓✠✘✥✘✷✏✒✖✸✰❱✡✪✘✩✓✠✰✢☎❍▲❘✦❖✓✠☎✞✝✠✦✢☎✞✓✌✳ ▲❆✦❤✡✙✣✒✣❀✕✗✓✠✕✗✤✙✦●✛●✜✄✖✌✡✪✘✚✓❥◆✢✝✠✤✯✂✻✕☛✣✢☎★✘❥✟✗✤✹✡✙✣✐✾✒✡✙✟☛✡✙✦✢✖★✕✗✦✒✲❫✡✪✍❃✤✆✦✢✲❢✦✢☎✞✓❘❊❋✤✙✝✠❙ ✦✢✤✻✣✢☎★✘❉✾❖☞❫☎★✍❃◆✢✟☛✤✌☞❀✕✗✦✒✲✥✓✠✰✢☎✑♣q✤✆✏✢✦✫✣❀❅r✝✠✤✙✾✒✕✗✦❍✡✙◆✢◆✢✝✠✤✆✡✙✖✸✰❭✕✗✦❇✘✷☎★✟✗☎★✖✞✓✠✕✗✦✢✲ ✣❀☎★✟✗✕✗✂✹☎✞✝✷☞❢◆✫✡✪✓✠✰✢✘✼✽✤✪✝✄✖★✟✗✕✗☎★✦❖✓✠✘★✳ ✡✪✝✠☎❁✕✗✦❖✓✠☎✞✝✠☎★✘✚✓✠☎★✣✑✕✗✦◗✓✠✰✒☎❋◆✢✝✠✤✆✾✢✟✗☎★✍t✤✙✼✫✘✚✓✷✝✠☎✌✡✙✍❃✕✗✦✒✲✄✾✫✡✙✦✒✣❀❊✴✕☛✣❀✓✠✰❀❅ s ☎❁INTRODUCTION ✕✗✦❖✓✠☎★✦✢✘✷✕☛✂✆☎✍❃☎✌✣✢✕☛✡✴✤✆✦◗✣✢☎★✍✩✡✪✦✫✣❥✼❡✝✠✤✆✍✉✡q✘✷✤✆✏❀✝✠✖★☎✓✠✤■✡q✟✿✡✯✝✠✲✆☎✴✺❖✏✫✡✪✦❖✓✠✕✗✓❆☞ ✤✪✼✈✝✠☎★✖★☎★✕✗✂✹☎✞✝✠✘❧✤✆✦✥✓✠✰✢☎q▲❆✦❖✓✠☎✞✝✠✦✒☎✞✓✌✳✵✇✰✒☎✴✘✷✕✗✍❃◆✒✟✗☎★✘✚✓❧✘✷✤✆✟✗✏✢✓✠✕✗✤✙✦❢✣❀☎✌✣✢✕✗✖✌✡✯✓✠☎★✘ ✡✪✦❤✕✗✦✫✣❀✕✗✂❀✕☛✣❀✏✫✡✙✟✮✖✞✤✆✦✒✦✢☎★✖✞✓✠✕✗✤✆✦❭✓✠✤❢✘✚✓✷✝✠☎★✡✙✍①✓✠✰✢☎◗✖★✤✙✦✻✓✠☎✞✦✻✓✄✓✠✤✧☎✌✡✪✖✱✰❇✝✠☎✞❅ ✖✞☎★✕✗✂✹☎✞✝✌✳②✇✰✢✕☛✘❍✍❃☎✱✓✠✰✒✤✻✣③✖★✤✆✦✢✘✷✏✒✍❃☎★✘❍✡♦✓✷✝✠☎★✍❃☎★✦✫✣❀✤✆✏✢✘❫✡✙✍❃✤✙✏✒✦❖✓❍✤✪✼ ✖✞✤✆✘✚✓✠✟✔☞❲✾✫✡✪✦✫✣✻❊✴✕✿✣✻✓✠✰③✡✙✦✒✣❱✟☛☎★✡✆✣✢✘✎✓✠✤♦✡✙✦❲✕✗✦✢✼❡☎✞✝✠✕✗✤✙✝❇✺❖✏✫✡✪✟✗✕✗✓❆☞❱✘✚✓✷✝✠☎✌✡✪✍ ✼❡✤✙✝❃✓✠✰✢☎❢✝✠☎★✖★☎✞✕☛✂✆☎✞✝✌✛✍✩✡✪❙❀✕✗✦✢✲❭✕✔✓✩✦✢☎✌✡✪✝✠✟✔☞④✕✗✍❃◆❯✤✆✘✷✘✷✕✗✾✒✟✗☎✧✼❡✤✙✝✎✡❇✘✷☎✞✝✠✂✻✕✗✖★☎ ◆❀✝✠✤✯✂❀✕☛✣❀☎✞✝✓✠✤❣✘✷☎✞✝✠✂✹☎■✺❖✏✒✡✙✟✗✕✔✓❘☞✩✘✚✓✷✝✠☎✌✡✪✍❃✕☛✦✢✲❣✓✠✤❣✟☛✡✪✝✠✲✙☎❥✡✙✏✒✣✢✕✗☎★✦✒✖✞☎★✘❊✴✰✒✕✗✟✗☎ ✲✙☎★✦✒☎✱✝✸✡✪✓✠✕✗✦✒✲❍◆❀✝✠✤✙♠✒✓✠✘★✳✩▲❘✭t▼✧✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓✧⑤ ⑥✯⑦❋✖★✤✙✏✒✟☛✣❤✾❯☎✥✓✠✰✢☎✥✾❯☎★✘✚✓✶❊❁✡★☞ ✓✠✤❃✤✯✂✹☎✱✝✠✖★✤✆✍❃☎❥✓✠✰✒✕✗✘❉✣❀✝✸✡★❊✴✾✫✡✪✖✱❙✎✘✷✕✗✦✒✖★☎❣✕✔✓❉❊✡✙✘❉✣✢☎★✘✷✕✗✲✙✦✒☎✌✣✧✼❡✤✙✝■✲✪✝✠✤✆✏✢◆✢❅ ✤✪✝✠✕✗☎★✦❖✓✠☎✌✣✥✡✙◆✢◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✙✦✒✘★✳❧⑧✒✤✙✝❑✖★✟✗✕✗☎★✦❖✓✠✘❦✝✠☎✌✺❖✏✒☎★✘✚✓✠✕✗✦✒✲❉✓✠✰✒☎❁✘✠✡✙✍❃☎❋✂❀✕☛✣❀☎★✤✢✛ ✇✰✒✕✗✘❄✝✠☎★✘✷☎✌✡✯✝✠✖✱✰❣✕✗✘✮◆✫✡✯✝✷✓✠✕✿✡✪✟✗✟✗☞✶✘✷✏✢◆✒◆❯✤✪✝✷✓✠☎✌✣❥✾✻☞■❳❥⑨■⑩■✡✯✓✠✕☛✤✙✦✫✡✪✟✒⑨✻✖★✕✗☎★✦✒✖✞☎ ⑧✢✤✆✏✒✦✒✣✒✡✯✓✠✕☛✤✙✦❫✏✒✦✒✣✢☎✞✝✲✙✝✸✡✙✦❖✓❉❶❉⑩❉▲❆❅❆❷✆❷✙❸✆❸✙❷✹❹✙⑥ Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee SAC 2003 Melbourne, Florida, USA Copyright 2003 ACM 1-58113-624-2/03/03 5.00 ❺ ✓✠✰✒☎q✘✷☎✞✝✠✂✹☎✱✝✖✞✝✠☎✌✡✯✓✠☎★✘❁✡❥✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓❁✡✙✣✒✣✻✝✠☎★✘✷✘❁✡✙✦✒✣✥✘✷☎★✦✫✣❀✘❁✡❥✘✚✓✷✝✠☎✌✡✙✍❻✤✙✼ ✓✠✰✒☎✶✂✻✕☛✣✢☎★✤✥✓✠✤✎✡✪✟☛✟❄✤✙✼❦✓✠✰✒☎★✍❼✤✙✦❇✡✩✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓q✓✷✝✠☎★☎✆✳q❶q✦❇✡✆✣❀✂✆✡✪✦✻✓✸✡✪✲✆☎ ✕✗✘✓✠✰✒☎❉✤✆◆✢✓✠✕✗✍✩✡✪✟❯✏✒✘✷☎✄✤✪✼✵✦✢☎✞✓❘❊❋✤✙✝✠❙❃✾✫✡✪✦✫✣✻❊✴✕✿✣✻✓✠✰❢✘✷✕✗✦✢✖★☎■✡❣✘✷✕☛✦✢✲✆✟✗☎■✖★✤✙◆❖☞ ✤✙✼✄✂✻✕✿✣❀☎★✤✐✣✒✡✪✓✸✡❇✕✗✘✩✣✢☎★✟✗✕✗✂✹☎✞✝✠☎★✣♦✤✙✦❪☎✌✡✪✖✱✰♦◆✒✰❖☞❀✘✷✕✗✖✌✡✙✟✴✟✗✕✗✦✒❙❽✓✠✤✐✡✙✟✗✟❁✓✠✰✒☎ ✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓■✖✞✟☛✕✗☎★✦❖✓✠✘★✳❣❶q✦✒✤✙✓✠✰✢☎✞✝✄✡✆✣✢✂✙✡✙✦❖✓✸✡✪✲✆☎◗✕✗✘✄✓✠✰✒✡✪✓❉✓✠✰✒☎✞☞❇✡✪✟✗✟✮✘✷✰✫✡✪✝✠☎ ✡❫✘✷✕✗✦✒✲✙✟☛☎✎✘✚✓✷✝✠☎✌✡✪✍❾☎✞✍✩✡✙✦✫✡✯✓✠☎✌✣✐✼✿✝✠✤✆✍❿✓✠✰✒☎✩✘✷☎✞✝✠✂✹☎✱✝✌✛✮✰✒☎★✦✢✖★☎✩✡❫✘✷✕✗✲✆✦✢✕✗♠✢❅ ✖✌✡✪✦✻✓✑✘✠✡✌✂✻✕☛✦✢✲❫✤✆✦❽✓✠✰✢☎❃✘✷☎✞✝✠✂✹☎✞✝✑✾✫✡✪✦✫✣✻❊✴✕✿✣✻✓✠✰●✳❫✁✄✦❤✓✠✰✒☎❃✤✪✓✠✰✒☎✞✝✑✰✫✡✪✦✫✣✈✛ ✘✷✕✗✦✒✖★☎✩✖★✟✗✕✗☎★✦❖✓✠✘❣◆✫✡✪✝✷✓✠✕✗✖★✕✗◆✒✡✪✓✠✕✗✦✒✲❍✕✗✦❚✡❫✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❣✲✙✝✠✤✙✏✒◆❤✝✠☎✞✖★☎★✕✗✂✹☎❃✓✠✰✒☎ ✘✠✡✙✍❃☎q✣✢✡✪✓✸✡❥✡✪✓✡✙✦❖☞✑◆❯✤✆✕✗✦❖✓❋✤✪✼✬✓✠✕✗✍❃☎✆✛✙✓✠✰✒☎✴✘✷☎✞✝✠✂✹☎✱✝❋✰✒✡✙✘❦✓✠✤❣✖✱✝✠☎✌✡✪✓✠☎✴✦✒☎✱❊ ✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✶✡✙✣✒✣❀✝✠☎✞✘✷✘✷☎★✘■✼✽✤✪✝✶✟✿✡✯✓✠☎✞❅➀✖★✤✆✍❃✕✗✦✢✲✧✖★✟✗✕✗☎★✦❖✓✠✘❥✕✗✦✐✤✪✝✸✣✢☎✞✝■✓✠✤❢◆✢✝✠✤✪❅ ✂✻✕☛✣✢☎◗✓✠✰✢☎★✍➁❊✴✕✔✓✠✰✐✓✠✰✢☎◗✼✽✏✢✟✗✟❑✖✞✤✆✦❖✓✠☎★✦❖✓✶✤✙✼❧✓✠✰✒☎◗✝✠☎✌✺❖✏✢☎★✘✚✓✠☎✌✣❇✂❀✕☛✣❀☎★✤✢✳◗▲❘✦ ✝✠☎✌✡✪✟☛✕✔✓❆☞❖✛✵✖★✟✗✕✗☎★✦❖✓✑✝✠☎★✺✻✏✢☎★✘✚✓✠✘❥✏✒✘✷✏✒✡✙✟✗✟✔☞✐✝✠☎★✡✙✖✸✰❤✓✠✰✒☎✥✘✷☎✱✝✠✂✹☎✞✝✑✡✪✓✑✣✢✕✔➂✈☎✞✝✠☎✞✦✻✓ ✓✠✕✗✍❃☎★✘★✳❦✇✰✢☎q✘✷☎✱✝✠✂✹☎✞✝❧✍✩✡✌☞✑✰✫✡✌✂✹☎✓✠✤❥✖✱✝✠☎✌✡✪✓✠☎❉✡■✟☛✡✪✝✠✲✆☎q✦✻✏✒✍✑✾❯☎✞✝❦✤✙✼✬✘✷☎★◆❀❅ ✡✪✝✸✡✯✓✠☎❫✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✠✘★✛❧✡✙✦✒✣④✓✠✰✢☎✞✝✠☎✞✼✽✤✪✝✠☎✆✛❋✓✠✰✢☎❢✾✒✡✙✦✒✣❀❊✴✕☛✣❀✓✠✰④✾❯✤✙✓✷✓✠✟✗☎★✦✢☎★✖✸❙ ✝✠☎★✍✩✡✪✕☛✦✢✘✴✘✷☎★✂✹☎✞✝✠☎✆✳ ✭✮✡✪✓✠✖✸✰✒✕✗✦✢✲❢⑤ ❸❀✛✢➃✯⑦✈✕☛✘✴✡❥✝✠☎★✍❃☎✌✣✻☞◗✼❡✤✙✝❁✓✠✰✒☎❉✡✪✼❡✤✙✝✠☎★✍❃☎✞✦✻✓✠✕✗✤✙✦✒☎✌✣✩✟✗✕☛✍❃✕✔✓✸✡✯❅ ✓✠✕✗✤✆✦✐✤✙✼❁▲❘✭➄▼✧✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓✌✳❃▲❘✦❇✓✠✰✒✕✗✘■✓✠☎★✖✸✰✒✦✢✕☛✺✻✏✢☎✆✛✈❊✴✰✒☎★✦❤✡❢✦✢☎✞❊✉✖★✟✗✕✗☎★✦❖✓ ✝✠☎✌✺❖✏✒☎✞✘✚✓✠✘■✡✩✂❀✕☛✣❀☎★✤✢✛✈✕✔✓❋➅❘✤✆✕✗✦✒✘❉✓✠✰✒☎❣✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓■✲✙✝✠✤✙✏✒◆❍✓✠✰✫✡✯✓✄❊✡✙✘■✖✞✝✠☎✱❅ ✡✪✓✠☎★✣❬✍❃✤✆✘✚✓✩✝✠☎★✖★☎✞✦✻✓✠✟✔☞④✼✽✤✪✝❢✓✠✰✢☎❍✘✠✡✙✍❃☎❍✂✻✕☛✣✢☎★✤❀✛q✡✙✦✒✣❪✝✠☎★✖★☎★✕✗✂✹☎✞✘❢✣✢✡✪✓✸✡ ✣✢☎✞✘✚✓✠✕☛✦✢☎✌✣❫✼✽✤✪✝✄✓✠✰✒✕✗✘❉✲✙✝✠✤✆✏✢◆●✳✄⑨❀✕✗✦✢✖★☎◗✡❃◆❯✤✪✝✷✓✠✕☛✤✙✦❇✤✙✼❧✾❯☎★✲✆✕✗✦✒✦✢✕✗✦✒✲✩✂✻✕✿✣❀☎★✤ ✣✒✡✯✓✸✡■✖✌✡✙✦✢✦✒✤✪✓❧✾❯☎✴✣❀☎★✟✗✕✗✂✹☎✞✝✠☎✌✣✑✼✿✝✠✤✆✍➆✓✠✰✫✡✯✓❑✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓✌✛✆✓✠✰✒☎❋✖★✟✗✕☛☎✞✦✻✓❧✲✆☎✱✓✠✘ ✕✔✓✼❡✝✠✤✙✍❻✓✠✰✢☎❉✘✷☎✞✝✠✂✆☎✞✝✤✯✂✹☎✞✝✡❣✏✢✦✒✕✗✖✌✡✪✘✚✓✌✛✻✤✙✝✴✡❇➇❘◆✒✡✪✓✠✖✸✰✒✕✗✦✒✲✙➈✑✘✚✓✷✝✠☎✌✡✪✍❫✳❦❶ ◆✢✝✠✤✙◆❯☎✞✝✶✾✒✏❀➂✈☎✞✝✠✕✗✦✒✲✧✡✙✟✗✲✆✤✪✝✠✕✗✓✠✰✢✍②✕☛✘❥◆✢✏✢✝✠✘✷✏✢☎✌✣❤✡✯✓❥✓✠✰✒☎✥✖★✟✗✕✗☎★✦❖✓❥✓✠✤❫✘✚☞❀✦✢❅ ✖✸✰✢✝✠✤✆✦✢✕✗➉★☎✑✓✠✰✢☎✑◆✢✟✿✡★☞❀✾✫✡✪✖✱❙✧✤✙✼❑✓✠✰✒☎★✘✷☎❣✓❘❊✤❢✣✒✡✯✓✸✡❃✘✚✓✷✝✠☎✌✡✙✍❃✘✥➊♥✕♥✳ ☎✆✳✗✛✬✍◗✏✢✟✗❅ ✓✠✕✗✖✌✡✙✘✚✓✄✘✚✓✷✝✠☎✌✡✙✍➁✡✙✦✒✣❫◆✫✡✯✓✠✖✱✰✢✕☛✦✢✲✩✘✚✓✷✝✠☎✌✡✙✍✎➋✱✳q❶q✦❫✤✆✾✻✂✻✕✗✤✆✏✒✘✄✡✆✣❀✂✆✡✪✦✻✓✸✡✪✲✆☎ ✤✙✼✄✭✮✡✪✓✠✖✸✰✒✕✗✦✢✲❭✕✗✘❣✓✠✰✫✡✪✓◗✕✗✦✒✘✚✓✠☎✌✡✙✣④✤✪✼q✖✞✝✠☎✌✡✪✓✠✕✗✦✢✲❤✡❍✟✗✤✆✦✢✲✙❅➀✟☛✡✙✘✚✓✠✕✗✦✒✲❭✍◗✏✢✟✗❅ ✓✠✕✗✖✌✡✙✘✚✓✎✘✚✓✷✝✠☎✌✡✪✍➌✼✽✤✪✝✩✓✠✰✒☎✧✦✢☎✞❊❼✖★✟✗✕✗☎★✦❖✓✌✛❋✓✠✰✢☎❫✘✷☎✞✝✠✂✹☎✞✝❥➅❘✏✒✘✚✓✩✖✞✝✠☎★✡✪✓✠☎★✘✩✡ ✘✷✰✒✤✪✝✷✓✷❅r✓✠☎✞✝✠✍❻✏✢✦✒✕✗✖✌✡✪✘✚✓❋✘✚✓✷✝✠☎✌✡✪✍❫✳❑✇✰✒☎✞✝✠☎✱✼✽✤✙✝✠☎✙✛✒✭✮✡✯✓✠✖✱✰✢✕✗✦✒✲✶✕✗✘❋✰✒✕✗✲✙✰✒✟✔☞✥☎✞✼✿❅ ♠✫✖✞✕☛☎✞✦✻✓✑✕✗✦❽✝✠☎✌✣✢✏✢✖★✕✗✦✒✲❫✓✠✰✢☎❢✣❀☎★✍✩✡✙✦✒✣❤✤✆✦❚✘✷☎✱✝✠✂✹☎✞✝✑✾✫✡✙✦✒✣❀❊✴✕☛✣❀✓✠✰❽❊✴✰✢✕✗✟☛☎ ◆✢✝✠✤✯✂✻✕☛✣✢✕✗✦✒✲✥✓✷✝✠✏✢☎❥✜❉✁✄➍t✘✷☎✞✝✠✂✻✕✗✖★☎★✘❉✓✠✤✥✓✠✰✢☎❥✖★✟✗✕✗☎★✦❖✓✠✘★✳❁➍■✏✒☎■✓✠✤❃✕✔✓✠✘q✘✷✕✗✍✥❅ ◆✒✟✗✕✗✖★✕✔✓❘☞④✕✗✦♦✖★✤✆✦✢✖★☎★◆❀✓✩✡✙✦✒✣♦☎✞❂✥✖★✕✗☎★✦✒✖✞☞④✕✗✦♦◆❯☎✞✝✷✼✽✤✪✝✠✍✩✡✙✦✢✖★☎✆✛❋✭✮✡✪✓✠✖✸✰✒✕✗✦✒✲ ✰✫✡✪✘✴✾❯☎★☎★✦❫✏✢✘✷☎✌✣✧✕✗✦❍✡◗✟☛✡✪✝✠✲✙☎✶✦❀✏✢✍◗✾❯☎✞✝✤✙✼✮❊✤✪✝✠❙✻✘✑➊♥☎✆✳ ✲❀✳☛✛❄⑤✔➎★➏✢✛❯➐✻✛●➎✆✛✈❹❖✛ ➎✌➃✯⑦❡➋❣✓✠✰✫✡✯✓✥✣❀☎✌✡✙✟❋❊✴✕✔✓✠✰④✂✙✡✪✝✠✕✗✤✆✏✢✘✑✼✽✏✢✦✫✣✢✡✙✍❃☎★✦❖✓✸✡✙✟❧✕✗✘✷✘✷✏✒☎★✘❣✝✠☎★✟✗☎★✂✆✡✪✦❖✓✑✓✠✤ ✜❉✁✄➍t✘✚☞❀✘✚✓✠☎★✍❃✘★✳ s ☎❉✡✪✝✠☎✄✕☛✦❖✓✠☎✞✝✠☎✞✘✚✓✠☎✌✣✎✕✗✦✎✕✗✍❃◆✒✟✗☎★✍❃☎★✦❖✓✠✕✗✦✒✲❣✭✮✡✪✓✠✖✸✰✒✕✗✦✢✲✑✤✙✦✎✓✠✰✢☎✄▲❘✦❖✓✠☎✞✝✷❅ ✦✒☎✱✓✌✳❥⑨✻✕☛✦✢✖★☎❣✭✮✡✪✓✠✖✸✰✒✕✗✦✒✲✎✡✪✘✷✘✷✏✒✍❃☎★✘q✓✠✰✒☎❣☎✞❏❀✕☛✘✚✓✠☎✞✦✒✖★☎❣✤✙✼❑▲✚✭③▼✧✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✌✛ ✓✠✰✒☎q✍✩✡✙✕✗✦❃✾✒✡✪✝✷✝✠✕✗☎✞✝✕✗✦✩✤✆✏❀✝◆❀✝✠✤✆✾✒✟✗☎★✍❨✕✗✘✣❀✏✒☎❁✓✠✤❥✓✠✰✒☎✴✕✗✦✢✼✽☎★✡✙✘✷✕✗✾✒✕✗✟✗✕✔✓❘☞✎✤✙✼ ✣✢☎✞◆✒✟✗✤✌☞✢✕✗✦✢✲✎▲❘✭③▼✧✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✶✤✙✦❍✓✠✰✒☎❣✖★✏✢✝✷✝✠☎★✦❖✓✄▲❘✦❖✓✠☎✞✝✠✦✒☎✱✓✌✳■✇✰✢☎✞✝✠☎✞✼✽✤✪✝✠☎✆✛ ❊☎❢☎✞❏✢✡✙✍❃✕✗✦✒☎✩✾✢✏✒✕✗✟☛✣✢✕✗✦✒✲❭✍◗✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓✥✘✷☎✞✝✠✂✻✕✗✖★☎★✘◗✤✆✦❚✓✠✰✒☎❢✡✙◆✢◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✆✦ ✟☛✡★☞❖☎✞✝✌✛✻❊✴✰✒✕✗✖✸✰✧✡✪✘✷✘✷✏✒✍❃☎★✘❁✤✙✦✒✟✔☞❃✓✠✰✒☎❉▲✚✭❚❳✄✦✢✕☛✖★✡✙✘✚✓❁◆❀✝✠✤✙✓✠✤❖✖★✤✙✟r✳❋✇✰✒☎❉✾✫✡✯❅ ✘✷✕✗✘✑✼❡✤✙✝✥✤✙✏✢✝❣❊✤✪✝✠❙❽✕✗✘✑✓✠✤❍✕✗✦✒✘✚✓✸✡✪✟☛✟✡❇✦✻✏✢✍◗✾❯☎✞✝✶✤✪✼❉✍✩✡✪✖✱✰✢✕✗✦✒☎★✘✑✡✪✓❣✓✠✰✒☎ ☎★✦✒✣❀❅➀✘✚☞❀✘✚✓✠☎★✍❿✦✒✤✻✣❀☎★✘★✛✵❊✴✰✒✕✗✖✸✰❽◆✒✟☛✡★☞❚✡✪✘◗✡✪◆✒◆✢✟☛✕✗✖✌✡✯✓✠✕✗✤✆✦✢❅➀✟☛✡★☞❖☎✞✝❣✝✠✤✆✏❀✓✠☎✞✝✠✘★✳ ✇✰✒☎✞✘✷☎q✦✢✤✻✣✢☎★✘❑✡✪✦✫✣✑✓✠✰✢☎✘✷☎✞✝✠✂✹☎✞✝❧✡✯✝✠☎q✤✪✝✠✲✹✡✪✦✒✕✗➉★☎✌✣✥✕✗✦❖✓✠✤❥✡✄✟✗✤✆✲✙✕✗✖✌✡✙✟✫✤✯✂✹☎✱✝✷❅ ✟☛✡★☞❽❊✴✰✒✤✙✘✷☎✎✓✠✤✙◆❯✤✆✟✗✤✆✲✪☞④✕☛✘✑✾✒✏✢✕☛✟✔✓◗✤✆✦❚✓✠✤✆◆❚✤✪✼❉✓✠✰✢☎✎▲❆✦❖✓✠☎✞✝✠✦✒☎✞✓✌✳❇✜❉✕☛✣✢☎★✤ ✣✒✡✯✓✸✡✐✡✯✝✠☎❢✓✷✝✸✡✪✦✒✘✷✍❃✕✔✓✷✓✠☎✌✣❚✤✆✦♦✏✒✦✢✕☛✖★✡✙✘✚✓❃◆✒✡✪✓✠✰✒✘✑✕✗✦❀✂✆✤✆✟✗✂✻✕☛✦✢✲❭✓✠✰✢☎❢✤✯✂✹☎✱✝✷❅ ✟☛✡★☞❫✦✒✤✻✣❀☎★✘q✤✆✦✒✟✔☞❖✳❋❶➄✦✒☎✱❊➄✖★✟✗✕✗☎★✦❖✓❑➅✚✤✆✕✗✦✢✘■✡✙✦✧☎✞❏❀✕☛✘✚✓✠✕✗✦✢✲❃✂❀✕☛✣❀☎★✤❃✘✚✓✷✝✠☎✌✡✙✍ ✾❖☞✩✖★✤✙✦✒✦✢☎★✖✞✓✠✕✗✦✒✲◗✓✠✤◗✡✙✦❢✤✪✂✆☎✞✝✠✟☛✡✌☞✎✦✢✤✻✣✢☎❥✡✪◆✒◆❯☎✌✡✯✝✠✕☛✦✢✲✥✤✆✦✎✓✠✰✒☎❥✣❀☎★✟✗✕✗✂✹☎✞✝✷☞ ◆✒✡✪✓✠✰✎✓✠✤✥✡✙✦✧☎✌✡✪✝✠✟✗✕✗☎✞✝q✖★✟✗✕✗☎★✦❖✓✌✳❋✇✰✢✕✗✘❉✡✪◆✒◆❀✝✠✤✹✡✙✖✸✰✧✕✗✘q✡✑❙✻✕✗✦✫✣✎✤✙✼✴➑✪➒✙➓✱➔✞→✗❜✙➣ ↔✑↕ → ❞♥➙r❛✠❜✙❝✠❞❀❊✴✰✢✕✗✖✱✰✑✰✫✡✙✘✮✘✷◆✢✏✢✝✷✝✠☎✌✣❣✍✩✡✙✦❖☞■✝✠☎★✖✞☎★✦❖✓✮❊✤✙✝✠❙✻✘✮✤✙✦◗◆✢✝✠✤✯✂✻✕☛✣✢✕✗✦✒✲ ✲✪✝✠✤✆✏✢◆✢❅➀✤✙✝✠✕✗☎★✦❖✓✠☎✌✣❇✘✷☎✞✝✠✂✻✕✗✖★☎★✘✶✤✆✦❇✓✠✰✒☎✑▲❘✦❖✓✠☎✞✝✠✦✒☎✱✓✥⑤ ➏✢✛✵➛✻✛❄➜❀✛❑➎✯❹❖✛❧➎★❷❀✛❋➎✙➎✆✛ ➎✌➛✻✛●➎✯➐✯⑦r✳ ✁✄✦✢☎✥✰✫✡✪✘❣✓✠✤✧✖★✤✆◆❯☎✥❊✴✕✔✓✠✰❽✘✷☎★✂✆☎✞✝✸✡✙✟❧✕☛✘✷✘✷✏✢☎★✘❣✕☛✦❽✣✢☎★✘✷✕✗✲✆✦✢✕✗✦✒✲❍✡❫✲✙✤❖✤✻✣ 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✓✠✕✗✤✙✦♦➏❀✛✮❊☎❃✝✠☎★◆❯✤✪✝✷✓✥◆❯☎✞✝✷✼❡✤✙✝✠✍✩✡✙✦✢✖★☎❃✝✠☎★✘✷✏✒✟✔✓✠✘❣✼❡✝✠✤✆✍❾✤✆✏❀✝◗✘✷✕✗✍✑✏✒✟☛✡✪✓✠✕✗✤✆✦ ✘✚✓✠✏✒✣❀☞❖✳❦⑧✵✕✗✦✒✡✙✟✗✟✔☞❖✛✒❊☎❥✲✙✕✗✂✹☎❥✖★✤✆✦✢✖★✟✗✏✫✣❀✕☛✦✢✲◗✝✠☎★✍✩✡✯✝✠❙❀✘❁✕✗✦❫⑨❀☎★✖✞✓✠✕✗✤✙✦❇➛✻✳ ✇ ✰✢☎❋VCAST ✜❉✖✌✡✙✘✚✓✮✘✚☞❀✘✚OVERLAY ✓✠☎★✍❩✕✗✘✮✡✙✦✶✤✯✂✹☎✞✝✠✟☛✡★MODEL ☞✶✦✒☎✞✓❆❊✤✪✝✠❙❥✖★✤✆✦✢✘✷✕☛✘✚✓✠✕✗✦✢✲❉✤✪✼✒✓✠✰✢✝✠☎✞☎ ✖✞✤✆✍❃◆❯✤✆✦✢☎★✦❖✓✠✘★➥✴✘✷☎✞✝✠✂✹☎✞✝✄✦✒✤✻✣❀☎✆✛✈✖★✟✗✕✗☎★✦❖✓❥✦✒✤✻✣❀☎★✘★✛✬✡✙✦✒✣❇✕✗✦❖✓✠☎✞✝✠✦✒✡✙✟✵✦✢✤✻✣✢☎★✘★✳ ✇✰✢☎✑❝✞➓✱➔✸➒✙➓✱➔■➦❯➑✌➧❖➓❑✕☛✘❧✓✠✰✒☎q✘✷✤✆✏✢✝✠✖✞☎✄✤✙✼❄✂✻✕✿✣❀☎★✤✶✘✚✓✷✝✠☎✌✡✙✍❃✘❋✡✙✦✒✣✎✡✪✘✷✘✷✏✒✍❃☎✌✣ ✓✠✤✶✝✠☎★✍✩✡✪✕☛✦✩✏✢◆✩✡✙✟✗✟✫✓✠✰✒☎✴✓✠✕✗✍❃☎✆✳■➢❦→ ➙➀➓✱➦✢❞❑➦✫➑✌➧❖➓✱❝❑✡✪✝✠☎q✓✠✰✒☎q✦✒✤✻✣❀☎★✘❧❊✴✰✢☎✞✝✠☎ ✖✞✟☛✕✗☎★✦❖✓✠✘❑✝✠☎✌✺❖✏✒☎★✘✚✓❑✼✽✤✪✝❁✘✷☎✞✝✠✂✻✕✗✖★☎✆✳❑✇✰✒☎✱☞✥✖✌✡✪✦✎✾❯☎q✡✪✦✻☞✻❊✴✰✢☎✞✝✠☎✴✤✆✦❃✓✠✰✒☎✴▲❘✦❀❅ ✓✠☎✱✝✠✦✒☎✞✓✌✳❑❶③✖★✟✗✕✗☎★✦❖✓q✡✙✟✔❊❁✡★☞❀✘✴✘✷☎★✦✫✣❀✘❁✕✗✓✠✘✝✠☎★✺✻✏✢☎★✘✚✓✓✠✤❣✓✠✰✒☎✄✘✷☎✱✝✠✂✹☎✞✝❁✦✢✤✻✣✢☎✆✳ ➨ ➦✢❞❆➓✱➔✱➦✫❜✆→●➦✫➑✌➧❖➓✱❝❁✡✯✝✠☎❥✍✩✡✙✖✸✰✒✕✗✦✒☎✞✘❁✕☛✦✢✘✚✓✸✡✙✟✗✟✗☎✌✣❫✡✪✖✞✝✠✤✆✘✷✘✴✓✠✰✒☎■▲❆✦❖✓✠☎✞✝✠✦✒☎✞✓❁✓✠✤ ✡✪✖✞✓✄✡✙✘❁✓✠✰✒☎❥✾✒✡✙✖✸❙❀✾❯✤✙✦✒☎❥✦✢✤✻✣✢☎★✘✴✤✙✼✮✓✠✰✢☎■✤✯✂✹☎✞✝✠✟☛✡★☞❖✳✇✰✢☎✞☞❢✡✪✝✠☎❥✝✠☎★✘✷◆❯✤✙✦✢❅ ✘✷✕✗✾✢✟☛☎✶✼✽✤✪✝■✝✠☎★✟☛✡★☞❀✕☛✦✢✲✩✂❀✕☛✣❀☎★✤❃✘✚✓✷✝✠☎✌✡✙✍❃✘✴✓✠✤❃✓✠✰✒☎✶✖★✟✗✕✗☎★✦❖✓✠✘★✳❉✇✰✒☎❣✦❀✏✢✍◗✾❯☎✞✝ ✤✪✼❁✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟❑✦✢✤✻✣✢☎★✘❥✍✩✡★☞❇✖✸✰✫✡✪✦✒✲✆☎◗✤✪✂✆☎✞✝■✓✠✕✗✍❃☎❃✣✢✏✢☎✑✓✠✤✧✡✆✣✒✣❀✕✔✓✠✕☛✤✙✦❤✤✪✼ ✦✢☎✞❊③✦✒✤✻✣❀☎★✘❁✤✙✝❁✝✠☎✞✍❃✤✪✂✙✡✙✟❯✤✪✼✵☎✞❏❀✕✗✘✚✓✠✕✗✦✒✲✥✦✢✤✻✣✢☎★✘★✳❦▲❆✦❖✓✠☎✞✝✠✦✫✡✪✟❯✦✒✤✻✣✢☎✞✘✴✡✙✦✫✣ ✓✠✰✢☎❥✘✷☎✞✝✠✂✹☎✞✝✴✦✢✤✻✣✢☎✶✡✯✝✠☎❥✖✌✡✙✟✗✟✗☎✌✣❚➑✙➒✙➓✱➔✱→✗❜✙➣❃➦❯➑✌➧✹➓✱❝✸✳ ▲➀✼❑✦✒✤✩✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟❄✦✒✤✻✣✢☎❣✕✗✘■✕✗✦✒✘✚✓✸✡✪✟☛✟✗☎✌✣✈✛✬✏✒✘✷✕✗✦✒✲✎✡✩✣✢☎✌✣❀✕✗✖✌✡✪✓✠☎✌✣❍✘✚✓✷✝✠☎✌✡✪✍ ✼❡✤✙✝❣☎✌✡✪✖✱✰❇✝✠☎✌✺❖✏✒☎★✘✚✓✠✕✗✦✢✲✧✖★✟✗✕✗☎★✦❖✓✶✘✷☎★☎★✍❃✘✄✓✠✤❢✾❯☎✑✓✠✰✢☎◗✤✆✦✢✟✔☞✐✘✷✕✗✍❃◆✢✟☛☎❣❊❁✡★☞ ✓✠✤❇✕✗✍❃◆✒✟✗☎★✍❃☎✞✦✻✓✑✭✮✡✯✓✠✖✱✰✢✕☛✦✢✲❇✤✆✦❚✓✠✰✒☎✩▲❘✦❖✓✠☎✞✝✠✦✢☎✞✓✌✳❭✇✰✒✕✗✘✥✕✗✘✑✤✆✾✻✂✻✕☛✤✙✏✒✘✷✟✔☞ ✦✢✤✙✓❋✡❥✣✢☎★✘✷✕✔✝✸✡✪✾✒✟✗☎❉✘✷✤✙✟✗✏✢✓✠✕✗✤✆✦✬✳❑➩❧☞◗☎✞✍❃◆✒✟✗✤✌☞✢✕✗✦✢✲■✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟✢✦✒✤✻✣❀☎★✘❧✕✗✦✥✓✠✰✢☎ ✦✢☎✞✓❘❊❋✤✙✝✠❙✥✼✽✡✙✾✢✝✠✕✗✖✆✛❀✜❉✖✌✡✙✘✚✓❁✤✪➂✈☎✞✝✠✘❁✡✶✾❯☎✞✓✷✓✠☎✞✝❋✘✷✤✆✟✗✏✢✓✠✕✗✤✆✦✬✳❑▲❘✦✫✣❀☎★☎✌✣✈✛✹❊✴✰✒☎★✦ ✡✶✖★✟✗✕✗☎★✦❖✓✝✠☎✌✺❖✏✒☎✞✘✚✓✠✘✡✶✂❀✕☛✣❀☎★✤✶✘✚✓✷✝✠☎✌✡✙✍❫✛❖✓✠✰✢☎✄✣✢✡✪✓✸✡✶✍✩✡✌☞◗◆✫✡✪✘✷✘❋✓✠✰✢✝✠✤✙✏✒✲✆✰ ✡■✦✻✏✢✍◗✾❯☎✞✝✮✤✪✼✈✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟❀✦✒✤✻✣❀☎★✘❦✾❯☎✞✼✽✤✪✝✠☎❁♠✫✦✫✡✪✟✗✟✗☞❣✝✠☎✌✡✪✖✱✰✢✕☛✦✢✲■✓✠✰✒☎✖✞✟☛✕✗☎★✦❖✓✌✳ ❶q✦❤✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟❦✦✒✤✻✣✢☎◗✕☛✦✻✂✹✤✙✟✗✂❀✕✗✦✢✲❫✕✗✦❽✡✧✣❀☎★✟✗✕✗✂✹☎✞✝✷☞❭✤✙✼✴✡❢✂❀✕☛✣❀☎★✤✧✘✚✓✷✝✠☎✌✡✪✍ ✕✗✘✎✖✌✡✙✟✗✟✗☎✌✣❲✡❬➔✷➓✞→✗❜✙➣❽➦❯➑✌➧✹➓✩✤✪✼❥✓✠✰✫✡✪✓✎✘✚✓✷✝✠☎✌✡✪✍❫✳➆⑨✻✏✒✾✢✘✷☎✌✺❖✏✒☎★✦❖✓❃✖★✟✗✕✗☎★✦❖✓✠✘ ✕✗✦✢✘✚✓✠☎✌✡✆✣❽✤✪✼❉✲✙☎✞✓✷✓✠✕✗✦✒✲❇✡❫✂✻✕☛✣✢☎★✤✧✘✚✓✷✝✠☎✌✡✙✍②✼❡✝✠✤✙✍②✓✠✰✢☎✩✘✷☎✞✝✠✂✹☎✞✝✑✡✪✝✠☎✎✡✪✾✒✟✗☎ ✓✠✤✐✲✆☎✞✓✥✕✗✓❃✼✿✝✠✤✆✍➌✓✠✰✢☎★✘✷☎❢✝✠☎✞✟✿✡★☞④✦✢✤✻✣✢☎★✘★✳❬➤❋✟✗☎✌✡✪✝✠✟✔☞❖✛❁✦✢✤✐✍❃✤✪✝✠☎✧✘✷☎✞✝✠✂✆☎✞✝ ✾✒✡✙✦✒✣❀❊✴✕☛✣❀✓✠✰❫✕✗✘❉✖★✤✆✦✢✘✷✏✒✍❃☎✌✣✧✕✗✦✧✓✠✰✢✕✗✘❉✖✌✡✪✘✷☎✆✳❉✁✄✦✒☎✶✍❃✕✗✲✆✰❖✓❉✡✪✝✠✲✙✏✒☎❥✓✠✰✫✡✯✓ ✓✠✰✢☎✄✖★✤✙✍❃◆✒✟✗☎✞❏❀✕✔✓❘☞✥✡✙✦✫✣❃✖★✤✙✘✚✓q✡✪✝✠✕✗✘✷☎❉✼✿✝✠✤✆✍➫✣❀☎★◆✒✟✗✤✌☞❀✕✗✦✒✲❣✡✙✦✒✣✎✍✩✡✪✕☛✦❖✓✸✡✪✕☛✦❀❅ ✕✗✦✢✲✥✓✠✰✒☎■✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟●✦✢✤✻✣✢☎★✘★✳⑨❀✰✒✡✪✝✠✕✗✦✒✲✑✓✠✰✒☎■✘✠✡✪✍❃☎❥✕☛✦✢✘✷✕✗✲✆✰❖✓q✕☛✦❤⑤✗➎★❷✪⑦r✛✒❊❋☎ ✾❯☎✞✟☛✕✗☎★✂✆☎✶✓✠✰✒✡✪✓q✤✆✦✢☎✞❅r✓✠✕✗✍❃☎❥✰✫✡✪✝✸✣✻❊❁✡✯✝✠☎❣✖✞✤✆✘✚✓✠✘❉✣✢✤❃✦✒✤✪✓❉✣❀✝✠✕✗✂✹☎■✓✠✰✒☎■✓✠✤✪✓✸✡✙✟ ✖✞✤✆✘✚✓❑✤✙✼✫✓✠✰✢☎✘✚☞❀✘✚✓✠☎★✍❫✳❦▼❫✡✪✕✗✦✻✓✠☎✞✦✫✡✙✦✢✖★☎❁✖★✤✙✘✚✓✠✘❧✡✯✝✠☎✖★✏❀✓❦✾✻☞❣✘✷✕✗✍❃◆✒✟✗✕✔✼❡☞❀✕✗✦✒✲ ✦✢✤✻✣✢☎✑✣✢☎★◆✢✟✗✤✯☞❀✍❃☎★✦❖✓✌✳❶❉✘q✘✷✰✒✤✌❊✴✦❇✟✿✡✯✓✠☎✞✝❉✕☛✦❍✓✠✰✢☎✶✝✠☎✞✘✚✓✄✤✪✼❑✓✠✰✢✕✗✘❉◆✒✡✙◆❯☎✞✝✌✛ ✜❉✖✌✡✙✘✚✓✑◆✢✝✠✤✯✂✻✕☛✣✢☎★✘✑✡✧✰✢✕☛✲✙✰✒✟✔☞❽✘✷✖★✡✙✟☛✡✙✾✢✟☛☎✎✘✷✤✆✟✗✏❀✓✠✕☛✤✙✦❽❊✴✰✒✕✗✟✗☎❢✾❯☎✞✕☛✦✢✲❍❙✹☎★◆❀✓ ✘✷✕✗✍❃◆✢✟☛☎✶✡✪✦✫✣✎✟☛✕✗✲✙✰✻✓❆❊☎★✕✗✲✙✰✻✓✌✳ s ☎✥✣❀✤❢✦✢✤✙✓■☎✞✘✚✓✸✡✙✾✒✟✗✕✗✘✷✰❽✡✪✦❖☞❍✓✠✤✆◆❯✤✆✟✗✤✙✲✙☞❇✼✽✤✪✝✶✖★✤✆✦✢✦✒☎★✖✞✓✠✕✗✦✢✲❢✤✯✂✹☎✞✝✠✟☛✡★☞ ✦✢✤✻✣✢☎★✘★✳❪✇✰✢☎❍✣✢☎★✟✗✕✗✂✹☎✞✝✷☞❽◆✫✡✪✓✠✰④✼✽✤✪✝✎✡❭✖✞✟☛✕✗☎★✦❖✓✩✕✗✘✥✾✢✏✒✕✗✟✔✓❃✤✆✦❪✣✢☎★✍✩✡✪✦✫✣ ➭➯✢➲✮➳❡➵❽➸✫➺❣➻✬➵✻➼✪➽●➾✽➚✆➵❭➭➯✢➲✮➳❡➵ ✚✘ ✓✷✝✠☎★✡✙✍❃▲❘➍ ◆✫✡✯✝✠☎★✦❖✓ ✖✸✰✒✕✗✟☛✣✒➟✬✕☛✘✚✓ ⑨❀◆❯✤✪✝✷✓q⑩✄☎✞❊✴✘ ➩ ➪❁✛❯⑧❋✛✫➶ ✇✕✔✓✸✡✪✦✒✕✗✖ ❈ ➩❉✛❯➪❁✛✒❶❣✛❀➹ ✇●✤✆✦✒✕✗✲✙✰✻✓✄⑨✻✰✒✤✌❊ ❶ ➤ ✝✸✡✪✓✠☎ ➎✌❷✙❷ ➏✆❷ ❹✙❷✪➏✹❸ ✡✙✦✒✣❍✡✆✣✯➅✚✏✒✘✚✓✸✡✪✾✒✟✗☎◗✤✯✂✹☎✱✝❉✓✠✕✗✍❃☎✶✾✫✡✪✘✷☎✌✣❍✏✒◆❯✤✆✦❫✓✠✰✢☎✶✏✒✦✫✣❀☎✞✝✠✟✔☞❀✕☛✦✢✲✥✓✷✝✸✡✪❂❃✖ ✤✙✝✥✦✒✤✻✣✢☎✩✼♥✡✪✕✗✟☛✏❀✝✠☎✆✳④✇✰✢✕☛✘◗◆✫✡✪✓✠✰❚✖★✡✙✦♦✾❯☎✧✡❇✣✢✕✔✝✠☎★✖✱✓✥◆✫✡✯✓✠✰❚✼❡✝✠✤✆✍❾✓✠✰✒☎ ✘✷☎✞✝✠✂✹☎✱✝❉✤✪✝❉✡◗◆✫✡✯✓✠✰✧✖★✤✙✦✒✘✷✕✗✘✚✓✠✕✗✦✒✲❃✤✙✼✵✘✷☎★✂✹☎✞✝✸✡✪✟❄✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟●✦✢✤✻✣✢☎★✘★✳ ❶❉✦❍✤✯✂✹☎✱✝✠✟✿✡★☞✧✦✒✤✻✣✢☎✶➘❾✕✗✘■✡✙✘✷✘✷✕✗✲✙✦✒☎✌✣❭✡❃✏✒✦✒✕☛✺❖✏✒☎❥✕☛✣❀☎★✦❖✓✠✕✗♠✒☎✞✝❉✾✻☞❢✓✠✰✒☎ ✘✷☎✞✝✠✂✹☎✱✝❃❊✴✰✒☎★✦♦♠✒✝✠✘✚✓✎✡✆✣✢✣✢☎✌✣④✓✠✤✐✓✠✰✢☎❫✤✯✂✹☎✞✝✠✟☛✡★☞❖✳③▼❫✡✙✕✗✦❖✓✸✡✙✕✗✦✢☎✌✣❱✡✪✓✩➘ ✡✪✝✠☎✎✡✐➦✫➑✌➧❖➓❢→ ➙✽❝✠❞❧✡✙✦✒✣❽✡✐❝✞➓✱➔✸➒✌➙r❛✸➓✎❞➀❜✹➴★→☛➓✱✳❍✇✰✢☎✩✦✒✤✻✣✢☎❃✟✗✕✗✘✚✓✑✖★✤✆✦❖✓✸✡✙✕✗✦✢✘ ✓✠✰✒☎✩▲❆➍➷✤✪✼✄☎✞✂✹☎✞✝✷☞✐✤✙✓✠✰✒☎✱✝✥✤✯✂✹☎✞✝✠✟☛✡★☞❽✦✢✤✻✣✢☎✆✳❤✇✰✒✕✗✘◗✕✗✘✑✏✒◆✈✣✒✡✯✓✠☎✌✣❽✤✆✦✢✟✔☞ ❊✴✰✒☎✞✦❪✡✪✦④✕☛✦❖✓✠☎✞✝✠✦✒✡✙✟✦✢✤✻✣✢☎✎✕✗✘◗✝✠☎★✍❃✤✯✂✹☎✌✣❤✤✪✝✩✡❍✦✒☎✞❊➠✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟❁✦✢✤✻✣✢☎ ✕✗✘✶✡✆✣✢✣✢☎✌✣✈✳◗✇✰✢☎✥✘✷☎✞✝✠✂✻✕✗✖★☎◗✓✸✡✪✾✒✟✗☎◗✰✒✡✙✘■✼✽✤✙✏✢✝❣✡✯✓✷✓✷✝✠✕☛✾✢✏✢✓✠☎★✘❥➬★➮❘➱✆✃✌❐✻❒✧❮✻❰✧✛ Ï ❐✻➱✙✃✯Ð❯➮✱✛❧Đ✞Ị✒Ĩ➀Ơ❡Õ✻Ư❦Ĩ❘➬✞➮✱✛✡✪✦✫✣❚➱✙❐❖➮✚✃❖✳❽➪❧✡✪✖✱✰④✝✠✤✌❊➫✖★✤✪✝✷✝✠☎★✘✷◆❯✤✆✦✒✣✢✘✥✓✠✤✐✡✙✦ ✡✙✖✱✓✠✕☛✂✆☎❣✘✚✓✷✝✠☎★✡✙✍➁➬✞➮✚➱✙✃✯❐✻❒❢❮✻❰❼×❨Ø✉✖★✏✢✝✷✝✠☎✞✦✻✓✠✟✔☞❢✖★✤✆✍❃✕✗✦✢✲◗✓✠✤❃✦✒✤✻✣❀☎❥➘❤✳ ➘Ù✝✠☎★✖★☎✞✕☛✂✆☎★✘❃✓✠✰✒✕✗✘❃✘✚✓✷✝✠☎✌✡✙✍Ú✼✿✝✠✤✆✍Û✦✒✤✻✣❀☎ Ï ❐✻➱✙✃✯Ð❯➮✞➊♥➘❤✛✴Ø❣➋✥✡✙✦✒✣♦✼✽✤✪✝✷❅ ❊❁✡✯✝✸✣✢✘❁✕✔✓✓✠✤◗✡✙✟✗✟✈✦✒✤✻✣✢☎✞✘❁✕☛✦✎Đ★Ị✢Ĩ❆Ơ✿Õ✻Ư❑Ĩ❆➬✞➮★➊♥➘❤✛✒Ø❣➋❧✤✆✦✎✓✠✰✒☎q✖★✤✙✝✷✝✠☎✞✘✷◆❯✤✆✦✫✣✻❅ ✕✗✦✒✲❣✏✒✦✢✕☛✖★✡✙✘✚✓◆✒✡✪✓✠✰✢✘★✳❑✇✰✒☎q✂✆✡✪✟☛✏✢☎❉✤✪✼❄➱✪❐❖➮✷✃❖➊♥➘❤✛❀Ø❣➋❑✕✗✘❋✓✠✰✢☎❉☎✞✘✚✓✠✕☛✍✩✡✯✓✠☎✌✣ ✡✪✝✷✝✠✕✗✂✻✕✗✦✒✲❍✣✢✡✪✓✸✡✩✝✸✡✪✓✠☎❍➊♥✕✗✦✐➹✶➩➡✪✘✸➋❥✡✪✓✶✦✢✤✻✣✢☎✥➘Û✡✪✦✫✣❇✖★✤✆✍❃◆✢✏✢✓✠☎✌✣❍✼✽✤✪✝ ✡❫◆✫✡✯✝✷✓✠✕✗✖★✏✒✟☛✡✪✝◗✘✚✓✷✝✠☎✌✡✙✍➞Ø✥✳❇✇✰✒✕✗✘❣✂✆✡✪✟✗✏✒☎✆✛❦✕✗✦✒✕✔✓✠✕☛✡✙✟✗✟✔☞❚✘✷☎✞✓❣✓✠✤❍➉★☎✞✝✠✤❀✛❦✕✗✘ ✤✆✾✢✘✷☎✞✝✠✂✹☎✌✣✥✟✗✤❖✖✌✡✪✟✗✟✗☞❃✡✙✦✫✣✥✏✢◆✈✣✒✡✯✓✠☎✌✣◗◆❯☎✞✝✠✕✗✤✻✣✢✕✗✖✌✡✪✟✗✟✗☞◗❊✴✕✗✓✠✰✢✤✆✏❀✓✡✪✦✻☞◗✖★✤✆✍✥❅ ✍◗✏✢✦✒✕✗✖✌✡✯✓✠✕☛✤✙✦✎✡✙✖✞✝✠✤✙✘✷✘✴✓✠✰✢☎✄✦✢☎✞✓❘❊❋✤✙✝✠❙❯✳❑✇✵✡✙✾✢✟✗☎✑➎■✲✙✕✗✂✹☎★✘❁✡❣✘✠✡✙✍❃◆✒✟✗☎❉✟☛✤❖✤✙❙ ✤✙✼✮✓✠✰✢✕✗✘✓✸✡✙✾✒✟✗☎✆✳ ➶✄✕✗✂✹☎★✦◗✓✠✰✢☎❁✡✙✾❯✤✯✂✹☎❁✘✚✓✷✝✠✏✢✖✞✓✠✏✢✝✠☎✙✛❖✡✙✦◗✤✪✂✆☎✞✝✠✟☛✡✌☞✑✦✒✤✻✣❀☎❁✤✆✦✢✟✗☞✑❙✻✦✒✤✌❊✴✘❦✕✔✓✠✘ ◆✫✡✯✝✠☎★✦❖✓✠✘★✛✒☎★✡✙✖✸✰❢✼✽✤✪✝❉✡✙✦✧✕✗✦✒✣✢✕✗✂✻✕✿✣❀✏✫✡✪✟✬✘✚✓✷✝✠☎★✡✙✍❫✛✢✡✙✦✒✣✎✓✠✰✒☎❉✖★✤✙✝✷✝✠☎✞✘✷◆❯✤✆✦✫✣✻❅ ✕✗✦✒✲✥✖✸✰✒✕✗✟☛✣❀✝✠☎✞✦●✳❧➪❑✂✆☎★✦❢✓✠✰✢✤✆✏✒✲✙✰✧✖★✤✙✍❃◆✒✏❀✓✠☎✌✣✎✟✗✤❖✖✌✡✪✟✗✟✗☞❖✛✢✓✠✰✒☎❥✘✷☎✞✝✠✂✻✕✗✖★☎■✓✸✡✯❅ ✾✒✟✗☎❣✝✠☎✞Ü✫☎★✖✱✓✠✘✄✓✠✰✒☎❣✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲✩✦✒☎✞✓❆❊✤✪✝✠❙✧✓✷✝✸✡✪❂❃✖❣❊☎★✟✗✟♥✳✑➩❧☞❍✟✗✤❖✤✆❙✻✕✗✦✒✲ ✡✪✓❦✓✠✰✢☎☎★✦❖✓✷✝✷☞✶✖★✤✙✝✷✝✠☎✞✘✷◆❯✤✆✦✫✣❀✕✗✦✒✲✄✓✠✤❥✡❉✂❀✕☛✣❀☎★✤✄✘✚✓✷✝✠☎✌✡✪✍❨Ø❃✛✹✡❉✰✢✕☛✲✙✰✥✂✙✡✙✟✗✏✒☎ ✤✙✼❋➱✙❐❖➮✚✃✻➊♥➘✐✛✵Ø❣➋❉✕✗✦✫✣❀✕✗✖✌✡✪✓✠☎★✘■✓✠✰✒✡✪✓✶➘➞✘✷✰✒✤✆✏✢✟☛✣✐❙✹☎★☎✞◆❭✕✔✓✠✘❥✖★✤✙✦✒✦✢☎★✖✞✓✠✕✗✤✆✦ ❊✴✕✔✓✠✰✥✓✠✰✒☎✴◆✫✡✯✝✠☎★✦❖✓ Ï ❐✻➱✆✃✌Ð❯➮★➊♥➘❤✛❖Ø✑➋✱✳❦✁✄✦✥✓✠✰✒☎❁✖★✤✙✦✻✓✷✝✸✡✯✝✷☞❖✛✻✡■✟✗✤✌❊❱✂✙✡✙✟✗✏✒☎ ✕✗✦✫✣❀✕☛✖★✡✪✓✠☎★✘❃✖★✤✙✦✒✲✙☎★✘✚✓✠✕✗✤✆✦❱✤✪✝✩✣✢✕✗✘✷✖★✤✙✦✒✦✒☎✞✖✞✓✠✕✗✤✆✦❬✕✗✦④✓✠✰✒☎❢✏✒◆✒✘✚✓✷✝✠☎★✡✙✍❫✳♦❶ íí ịòỏ ị òỏ õótọõ q ọồổ q q ➩❧☞❇➅✚✤✙✕✗✦✒✕✗✦✒✲❚✡✪✦❬☎✞❏❀✕✗✘✚✓✠✕✗✦✒✲❽✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❃✓✷✝✠☎✞☎✆✛✴✡✐✖✞✟☛✕✗☎★✦❖✓✩✖✌✡✪✦❱✤✆✦✢✟✔☞ ❊❁✡✯✓✠✖✱✰❭✓✠✰✒☎✑✂❀✕☛✣❀☎★✤❢✼✿✝✠✤✆✍①✓✠✰✢☎◗◆❯✤✆✕✗✦❖✓❥❊✴✰✒☎✞✦❭✓✠✰✢☎✑✝✠☎✌✺❖✏✒☎✞✘✚✓❥✕✗✘❣✲✙☎★✦✒☎✱✝✷❅ ✡✪✓✠☎★✣✬✳❚⑧✢✤✙✝✥✓✠✰✢☎❢✍❃✕✗✘✷✘✷✕✗✦✒✲❇◆❯✤✙✝✷✓✠✕✗✤✙✦●✛❑✓✠✰✒☎✎✖★✟✗✕☛☎✞✦✻✓✥✲✆☎✞✓✠✘✑✕✗✓◗✼❡✝✠✤✆✍❾✓✠✰✒☎ ✘✷☎✞✝✠✂✹☎✱✝✑✤✙✦❽✡❫✣❀✕✔✝✠☎★✖✞✓✶✏✒✦✢✕✗✖✌✡✙✘✚✓❣◆✫✡✯✓✠✰❽✡✪✘❣✕✗✦❤✓✠✰✢☎✥✤✙✝✠✕✗✲✙✕☛✦✒✡✙✟❋✭✮✡✪✓✠✖✸✰✒✕✗✦✒✲ ✣✢☎✞✘✷✕☛✲✙✦③⑤ ❸✯⑦r✳❚⑧✒✤✪✝✑✓✠✰✢☎✎✝✠☎★✘✚✓◗✤✙✼✴✓✠✰✒☎✩◆✒✡✙◆❯☎✞✝✌✛❦❊☎✩✼✽✤❖✖✞✏✒✘✥✤✙✦❚✰✒✤✌❊➠✓✠✤ ✍✩✡✙✕✗✦❖✓✸✡✙✕✗✦❱✤✯✂✹☎✱✝✠✟✿✡★☞❬✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓✎✓✷✝✠☎✞☎★✘★✛✴❊✴✰✒✕✗✖✱✰❬✕☛✘✩✓✠✰✒☎❇✍❃✤✙✘✚✓❢✖✸✰✫✡✪✟✔❅ ✟✗☎★✦✒✲✙✕✗✦✒✲✩✓✸✡✙✘✷❙❫✓✠✤✌❊❁✡✯✝✸✣❭✤✙✏✢✝■◆✢✏✢✝✠◆❯✤✙✘✷☎✑✤✪✼❋✕✗✍❃◆✒✟✗☎★✍❃☎✞✦✻✓✠✕✗✦✢✲✩✭✮✡✪✓✠✖✸✰✒✕✗✦✒✲ ✤✆✦❢✓✠✰✒☎■▲❆✦✻✓✠☎✱✝✠✦✒☎✞✓✌✳ VCAST PROTOCOL DESCRIPTION ▲❘✦❽✓✠✰✢✕✗✘✑✘✷☎★✖✱✓✠✕☛✤✙✦●✛❑❊☎❢✣✢☎★✘✷✖✱✝✠✕☛✾❯☎✎✰✒✤✌❊➠✜✄✖✌✡✪✘✚✓✑✼❡✏✒✦✒✖✱✓✠✕☛✤✙✦✒✘✑✤✆✦❚✓✠✰✒☎ ✼✽✤✙✟✗✟☛✤✌❊✴✕✗✦✒✲♦☎★✂✹☎✞✦✻✓✠✘★➥❤✡❽✖★✟✗✕✗☎★✦❖✓❢✝✠☎★✺✻✏✢☎★✘✚✓✠✘❢✡❽✂❀✕☛✣❀☎★✤✢✛❉✡❽✖★✟✗✕✗☎★✦❖✓❫✺❖✏✢✕✗✓✠✘ ➊♥◆✒✏❀✝✠◆❯✤✆✘✷☎★✟✔☞♦✤✙✝✎✡✪✖★✖★✕☛✣✢☎✞✦✻✓✸✡✪✟✗✟✗☞✒➋✱✛✴✡❭✦✒☎✞❊❼✕✗✦❖✓✠☎✞✝✠✦✒✡✙✟✴✦✒✤✻✣❀☎❫✕✗✘✩✡✆✣✒✣❀☎✌✣ ✓✠✤✩✓✠✰✒☎✶✤✯✂✹☎✞✝✠✟☛✡★☞❖✛✬✡✙✦❇✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟✮✦✢✤✻✣✢☎❣✕✗✘■◆✒✏❀✝✠◆❯✤✆✘✷☎★✟✔☞❫✝✠☎★✍❃✤✯✂✹☎★✣✧✼❡✝✠✤✆✍ ✓✠✰✒☎q✤✯✂✹☎✞✝✠✟☛✡★☞❖✛❀✡✙✦✒✣✎✡✪✦✩✕☛✦❖✓✠☎✞✝✠✦✒✡✙✟❯✦✢✤✻✣✢☎✴✼♥✡✙✕✗✟✗✘★✳ s ☎❉✡✙✟✗✘✷✤✑◆❀✝✠☎★✘✷☎★✦❖✓✰✢✤✌❊ ✜✄✖★✡✙✘✚✓❃✕✗✘✥✘✷☎★✟✔✼✿❅❆✤✪✝✠✲✹✡✪✦✒✕✗➉★☎✌✣④✓✠✤✐✡✙✣✒✡✪◆✢✓✥❊✴✕✔✓✠✰④✖✱✰✒✡✙✦✢✲✆✕✗✦✒✲❭✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲ ✦✒☎✱✓❘❊✤✪✝✠❙✎✓✷✝✸✡✯❂❃✖✆✳ 3.1 A New Client Requests ⑨❀☎✱✝✠✂❀✕✗✖★✕✗✦✢✲✐✡❇✖★✟✗✕✗☎★✦❖✓◗✝✠☎✌✺❖✏✢☎★✘✚✓✥✰✒✡✙✘✑✓❆❊✤❭◆✒✰✒✡✙✘✷☎★✘★➥❭➊✚➎✯➋❥♠✫✦✒✣✢✕✗✦✒✲❇✡ New Client (1) req (2) Join A (3) Join D (4) Join B (5) Join A E E D B F G F G C C ỗ ốộờởỡớợùộớờủũú ụ ➼✪➵❀ï ✝✠☎✌✺❖✏✢☎★✘✚✓ ✓✠✤❭✓✠✰✒☎❢✘✷☎✞✝✠✂✹☎✞✝✩✦✢✤✻✣✢☎✧❊✴✰✢✕☛✖✸✰♦✕☛✘❃✓✠✰✢☎✧✤✆✦✢✟✔☞④✦✒✤✻✣✢☎✧✤✆✦❪✓✠✰✢☎✧✤✯✂✹☎✞✝✠✟☛✡★☞ ơ❿✕✗✘✎✡✌❊✡✪✝✠☎❭✤✙✼❆✳t▲❘✦❪✝✠☎★✘✷◆❯✤✆✦✢✘✷☎✆✛❁✓✠✰✒☎❍✘✷☎✞✝✠✂✆☎✞✝❢✝✠☎✱✓✠✏✢✝✠✦✒✘❃✓✠✰✢☎❫▲❘➍❿✤✪✼ ✡✪✦④✕☛✦❖✓✠☎✞✝✠✦✒✡✙✟❁✦✢✤✻✣✢☎✎➘õ✓✠✤❍✓✠✰✒☎✎✖★✟✗✕✗☎★✦❖✓✌✳❚✇✰✢✕☛✘◗✦✒✤✻✣✢☎✎✕✗✘◗✖✌✡✪✟✗✟☛☎★✣④✓✠✰✢☎ ➔✷➓❆ư✫➔✠➓✱❝✞➓✱➦✢❞➀❜✙❞♥➙✽➒✙➓❧✤✪✼✫✓✠✰✒☎✖✞✟☛✕✗☎★✦❖✓✌✳❦✇✰✢☎❁✘✷☎★✟✗☎★✖✞✓✠✕✗✤✆✦◗✤✙✼✈✡❉✝✠☎✞◆✢✝✠☎★✘✷☎★✦❖✓✸✡✯✓✠✕☛✂✆☎ ✼❡✤✆✟✗✟✗✤✌❊✴✘✩✡❤➔✷➑ ↕ ➦❯➧✙÷➀➔✚➑✹➴✞➙✽➦✐◆❯✤✆✟✗✕✗✖✞☞❖✳❭⑨❀◆❯☎✞✖★✕✔♠✫✖✌✡✪✟☛✟✔☞❖✛❦✕✔✼✴✦✒✤✻✣❀☎✩ø❵✕✗✘❣✓✠✰✢☎ ✝✠☎✞◆✢✝✠☎★✘✷☎★✦❖✓✸✡✯✓✠✕☛✂✆☎■✼✽✤✙✝q✓✠✰✒☎✄✟✿✡✪✘✚✓❉✝✠☎★✺✻✏✢☎★✘✚✓✠✕✗✦✒✲✥✖✞✟☛✕✗☎★✦❖✓✌✛✢✦✒✤✻✣❀☎❥➘❵❊✴✕☛✟✗✟●✾❯☎ ✓✠✰✢☎❁✦✒☎✞❏✻✓❑✦✒✤✻✣❀☎❁✤✙✼✈ø❩✕☛✦✑✓✠✰✒☎❁✦✒✤✻✣❀☎❁✟✗✕☛✘✚✓❧✍✩✡✙✕✗✦❖✓✸✡✙✕✗✦✢☎✌✣✥✡✪✓❑✓✠✰✒☎❋✘✷☎✞✝✠✂✹☎✞✝✌✳ ▲❆✦❢✓✠✰✢☎❥✘✷☎★✖★✤✆✦✒✣✧◆✒✰✒✡✙✘✷☎✆✛✢✓✠✰✒☎❥✖★✟✗✕✗☎★✦❖✓✄ôt✖★✤✆✦❖✓✸✡✙✖✱✓✠✘q✕✔✓✠✘✴✝✠☎★◆✢✝✠☎✞✘✷☎★✦❖✓✸✡✪❅ ✓✠✕✗✂✹☎✎➘ù✡✙✦✫✣❚✡✪✘✷❙✻✘✥✕✔✓✑✓✠✤❍♠✫✦✒✣❚✡❫✝✠☎★✟☛✡✌☞❽✦✒✤✻✣✢☎✩✼✽✤✪✝✎ô❼✓✠✤❃➅❘✤✆✕✗✦♦✡✙✦✫✣ ✲✙☎✞✓✶✣✢✡✪✓✸✡❇➊♥✘✷☎★☎❃⑨✻☎★✖✞✓✠✕✗✤✆✦✐➃✩✼❡✤✙✝❣✣❀☎✞♠✫✦✢✕✗✓✠✕✗✤✙✦❭✤✪✼❋✝✠☎★✟☛✡★☞❇✦✒✤✻✣❀☎✯➋✱✳❥▲➀✼❧✓✠✰✢☎ ✖✞✤✆✦❖✓✸✡✙✖✞✓❁✼✽✡✙✕✗✟✗✘✶➊♥☎✆✳ ✲✢✳✗✛✫✣❀✏✒☎✴✓✠✤✑✓✠✰✢☎q✼✽✡✙✕✗✟✗✏✢✝✠☎❥✤✙✼❄➘❇➋✱✛✻✓✠✰✒☎❉✖★✟✗✕☛☎✞✦✻✓✰✫✡✙✘✓✠✤ ✝✠✤✙✟✗✟❑✾✒✡✙✖✸❙✧✓✠✤✎◆✒✰✫✡✪✘✷☎✎➎◗✡✙✦✒✣❍✖★✤✆✦❖✓✸✡✙✖✱✓✠✘✄✓✠✰✒☎✑✘✷☎✞✝✠✂✹☎✞✝■✡✙✲✹✡✪✕✗✦✐✓✠✤✎✲✆☎✞✓■✡ ✦✢☎✞❊④✝✠☎★◆✢✝✠☎✞✘✷☎★✦❖✓✸✡✪✓✠✕✗✂✹☎✆✳ s ✕✗✓✠✰✢✤✆✏❀✓❦✟☛✤✙✘✷✘❧✤✪✼✈✲✆☎★✦✢☎✞✝✸✡✙✟✗✕✔✓❘☞❖✛✆✘✷✏✒◆✢◆❯✤✆✘✷☎✓✠✰✫✡✯✓ qq ớỳ ứổ rỷ qứ ỷ ớỳỹ ýỵ úỡ ứỵ úỡ qq q q rq ì qq ứứ ỵ úỡ ỵ úỡ q ớộỳ q ỵ úỡ ớộỳ q q ❶q✦❽☎✞❏✢✡✙✍❃◆✢✟✗☎✎✕✗✟✗✟✗✏✒✘✚✓✷✝✸✡✯✓✠✕☛✦✢✲❍✓✠✰✒☎❃✝✠☎✌✺❖✏✒☎★✘✚✓✠✕✗✦✢✲❍☎★✂✹☎★✦❖✓❣✕✗✘◗✲✆✕✗✂✹☎✞✦❚✕☛✦ ⑧✵✕✗✲❀✳✫➎✆✳❑✇✰✢☎q✟✗☎✞✼✿✓✷❅➀✘✷✕✿✣❀☎✌✣❃✣✢✕☛✡✪✲✙✝✸✡✙✍❨✘✷✰✒✤✌❊✴✘❦✓✠✰✒☎✴✖★✤✙✦✒✘✚✓✷✝✠✏✒✖✱✓✠✕☛✤✙✦❃✤✙✼❯✓✠✰✢☎ ✣❀☎★✟✗✕✗✂✹☎✞✝✷☞♦◆✫✡✯✓✠✰❱✡✙✦✒✣♦✓✠✰✢☎✧✝✠✕✗✲✆✰❖✓✷❅➀✘✷✕✿✣❀☎✌✣❬✣❀✕☛✡✙✲✙✝✸✡✪✍➝✘✷✰✒✤✌❊✴✘✩✓✠✰✒☎❫✦✢☎✞❊ ✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❦✓✷✝✠☎★☎✙✳✮▲❘✦❣✓✠✰✒✕✗✘✮☎✞❏✢✡✙✍❃◆✢✟☛☎✙✛✙✓✠✰✢☎❁✘✷☎✞✝✠✂✹☎✞✝❦✕✗✘❦✖★✏✢✝✷✝✠☎✞✦✻✓✠✟✔☞✑✣✢☎✞✟☛✕✗✂❖❅ ☎✱✝✠✕☛✦✢✲■✓❘❊❋✤❥✂❀✕☛✣❀☎★✤❥✘✚✓✷✝✠☎✌✡✙✍❃✘★✛❖✁Ø à✝✆ ✡✙✦✒✣❃Ø ✆☎✞ ✠✟☛✡ ổqq ỉ ỵ úỡ ỉ ỵ úỡ r ỵ úỡ ỵ úỡ Ø ✂☎✄ ✏à ✆ ✛✢✓✠✰✒☎❣✣✢☎✞✟☛✕✗✂✹☎✱✝✷☞✧◆✒✡✪✓✠✰ ✔✗✖✘✒✙✖✐✚ ❰ ✖✛☞➆✕✗✘✴✖✞✝✠☎✌✡✪✓✠☎★✣❫✣✢☎★✘✚✓✠✕✗✦✢☎✌✣❢✼✽✤✪✝✴✓✠✰✒☎■✦✢☎✞❊æ✖★✟✗✕☛☎✞✦✻✓✌✳ ▲❘✦✶✤✙✏✢✝✮✘✷✖✸✰✒☎★✍❃☎✙✛✪✓✠✰✢☎❧✘✷☎✞✟☛☎✞✖✞✓✠✕✗✤✆✦◗✤✪✼✒✓✠✰✢☎❧✝✠☎★◆❀✝✠☎★✘✷☎★✦❖✓✸✡✪✓✠✕✗✂✹☎❧✡✙✦✒✣❣◆✒✡✪✓✠✰ ✦✒✤✻✣❀☎★✘❣✕☛✘✶✾✒✡✙✘✷☎✌✣❽✤✙✦❤✝✠✤✆✏✢✦✫✣❀❅r✝✠✤✙✾✒✕✗✦❤✍✩✡✪✦✒✦✒☎✱✝✌✳❫➤❋✤✙✦✒✘✷☎✌✺❖✏✢☎★✦❖✓✠✟✗☞❖✛●✓✠✰✒☎ ✦✒☎✱✓❘❊✤✪✝✠❙✩✟☛✤✆✡✆✣✎✕☛✘✴☎★✂✆☎★✦✒✟✔☞✎✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠☎✌✣✎✡✙✍❃✤✆✦✢✲✑✓✠✰✢☎■✤✯✂✹☎✞✝✠✟☛✡★☞✩✦✒✤✻✣✢☎✞✘ ✡✙✦✒✣■✕✗✦✻✓✠☎✱✝✷❅❆✦✢✤✻✣✢☎❦◆✫✡✯✓✠✰✒✘★✳❄✇✰✒✕✗✘❄✰✢☎★✟✗◆✒✘✬◆✢✝✠☎★✂✆☎★✦❖✓●✦✢☎✞✓❘❊❋✤✙✝✠❙❉✖★✤✆✦✢✲✆☎★✘✚✓✠✕✗✤✆✦ ✡✙✦✒✣❽✤✯✂✹☎✞✝✠✟☛✡★☞❽✦✒✤✻✣❀☎✩✾❯✤✙✓✷✓✠✟✗☎★✦✒☎✞✖✱❙❯✳❭✁✄✏❀✝✑◆❯☎✱✝✷✼✽✤✙✝✠✍✩✡✪✦✒✖★☎✩☎★✂✙✡✙✟✗✏✒✡✪✓✠✕✗✤✆✦ ✝✠☎★✘✷✏✢✟✗✓✠✘★✛✆✓✠✤✄✾❯☎❁◆✢✝✠☎✞✘✷☎★✦❖✓✠☎✌✣✑✕✗✦❃⑨✻☎★✖✞✓✠✕✗✤✆✦❃➛✻✛✹✘✷✰✢✤✌❊♦✓✠✰✒✡✪✓❑✦✒☎✱✓❘❊✤✪✝✠❙✶✟☛✤✆✡✆✣ ✕✗✘q✡✙✟✗✘✷✤❃✾✫✡✪✟✿✡✪✦✒✖★☎★✣❫✡✙✍❃✤✙✦✒✲✥✏✢✦✫✣✢☎✱✝✠✟✗☞❀✕✗✦✒✲✑✦✒☎✞✓❆❊✤✪✝✠❙✎✦✢✤✻✣✢☎★✘★✳ 3.2 A Client Quits ▲❆✼●✡❥✖★✟✗✕✗☎★✦❖✓✴ô❲❊❁✡✪✓✠✖✸✰✒✕✗✦✢✲❣✂✻✕☛✣✢☎✞✤❣✘✚✓✷✝✠☎★✡✙✍➫Ø③❊❁✡✙✦❖✓✠✘❑✓✠✤❣✖★✡✙✦✒✖✞☎★✟✫✓✠✰✒☎ ✆✤ ✦❀❅➀✲✆✤✆✕✗✦✢✲❢✘✷☎✞✝✠✂✻✕✗✖★☎❣◆✒✏❀✝✠◆❯✤✆✘✷☎★✟✔☞❖✛❯✕✔✓■☎✱❏✢◆✢✟✗✕☛✖✞✕✗✓✠✟✔☞❢✝✠☎★◆❯✤✙✝✷✓✠✘✄✓✠✰✢☎❥❊✴✕☛✘✷✰❍✓✠✤ ✕✔✓✠✘✑✝✠☎★◆❀✝✠☎★✘✷☎★✦❖✓✸✡✪✓✠✕✗✂✹☎✩➘❤✳❭▲➀✼q✡❇✖✞✟☛✕✗☎★✦❖✓✥✺✻✏✢✕✔✓✠✘❣✓✠✰✢☎✎✘✷☎✱✝✠✂❀✕✗✖★☎❢✡✙✖✞✖★✕☛✣✢☎★✦❀❅ ✓✸✡✙✟✗✟✔☞❖✛✈➘❾✍◗✏✒✘✚✓q✰✒✡✯✂✆☎✑✘✷✤✙✍❃☎✶❊✡★☞❫✓✠✤✎✣✢☎✞✓✠☎★✖✱✓✌✳✄✜❉✖✌✡✙✘✚✓✄☎★✦✫✡✪✾✒✟✗☎★✘❉✓✠✰✢✕✗✘ ✣✢☎✱✓✠☎★✖✞✓✠✕✗✤✆✦❚✾❖☞❭✏✒✘✷✕✗✦✒✲❇✡❪➇❘✰✒☎★✡✪✝✷✓✠✾❯☎✌✡✯✓✠➈❭✍❃☎✞✖✱✰✒✡✙✦✒✕✗✘✷✍❿✡✯✓✑✓✠✰✢☎✥✝✠☎★◆✢✝✠☎✱❅ ✘✷☎★✦❖✓✸✡✪✓✠✕✗✂✹☎✶✓✠✤✎✖✱✰✢☎★✖✱❙✎✓✠✰✒☎✑✡✙✟✗✕✗✂✹☎★✦✢☎★✘✷✘❥✤✙✼❧✕✔✓✠✘✄✖★✟✗✕✗☎★✦❖✓✠✘★✳ s ✕✔✓✠✰✒✤✙✏✢✓✄✟☛✤✙✘✷✘ ✤✙✼✵✲✆☎★✦✢☎✞✝✸✡✙✟✗✕✔✓❘☞❖✛✒✘✷✏✒◆✒◆❯✤✙✘✷☎■✓✠✰✫✡✯✓✴➘❿❙❀✦✢✤✌❊✴✘❁✦✒✤✙✓✴✓✠✤◗✼❡✤✙✝✷❊✡✪✝✸✣❍✣✒✡✯✓✸✡❣✓✠✤ ✖★✟✗✕✗☎★✦❖✓qơ➄✡✪✦✻☞❀✍❃✤✪✝✠☎✆✳❦✇✰✒☎✱✝✠☎❥✡✪✝✠☎q✓❘❊✤❣◆❯✤✆✘✷✘✷✕✗✾✢✕☛✟✗✕✔✓✠✕✗☎★✘✴✼✽✤✙✝✦✒✤✻✣✢☎❉➘➁✓✠✤ ✖★✤✙✦✒✘✷✕☛✣✢☎✞✝✌➥ ë❣➯✒ð★➵❭➸ ➥❑❶✓❋✟☛☎★✡✙✘✚✓q✡✙✦✢✤✙✓✠✰✢☎✞✝✴✣✢✤✌❊✴✦✢✘✚✓✷✝✠☎✌✡✙✍➁➊♥✖★✟✗✕☛☎✞✦✻✓✤✙✝❁✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟✿➋ ✦✒✤✻✣❀☎❇✡✪✝✠☎❍✝✠☎★✖★☎✞✕☛✂✻✕✗✦✒✲❚✂✻✕☛✣✢☎✞✤❽✘✚✓✷✝✠☎✌✡✙✍õØ✥➥❤✇✰✒✕✗✘✩✖✌✡✙✘✷☎❇✕✗✘❢✰✒✡✙✦✒✣✢✟✗☎✌✣ ✘✷✕✗✍❃◆✒✟✔☞❫✾❖☞❢✝✠☎★✍❃✤✯✂❀✕✗✦✢✲✎ơ✉✼❡✝✠✤✙✍①Đ✞Ị✒Ĩ➀Ơ❡Õ✻Ư❑Ĩ❆➬✞➮★➊♥➘✐✛●Ø✑➋✴✕☛✦❍✓✠✰✢☎❣✘✷☎✱✝✠✂❀✕✗✖★☎ ✓✸✡✙✾✢✟✗☎✆✳❧❶❉✘✴✡✑✝✠☎★✘✷✏✢✟✔✓✌✛✒✼✽✏❀✓✠✏✢✝✠☎❥✣✢✡✪✓✸✡✑❊✴✕✗✟✗✟❄✦✢✤✙✓q✾❯☎■✘✷☎★✦❖✓✴✓✠✤✥✖★✟✗✕✗☎★✦❖✓❉ơ✑✳ ë❣➯✒ð★➵♦ü ➥❥⑩✄✤✧✣✢✤✌❊✴✦✒✘✚✓✷✝✠☎★✡✙✍❿✦✒✤✻✣❀☎✥✕✗✘❥✝✠☎★✖★☎★✕✗✂✻✕✗✦✒✲❫✂✻✕☛✣✢☎★✤❢✘✚✓✷✝✠☎✌✡✙✍ Ø✥➥✵▲❘✦❣✓✠✰✒✕✗✘❦✖✌✡✙✘✷☎✙✛❖✦✒✤✻✣❀☎❁➘➫✕☛✘❑✦✒✤❉✟✗✤✆✦✒✲✙☎✞✝❧✦✒☎★☎✌✣❀☎✌✣◗✤✙✦✑✓✠✰✒☎❁✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓ ✓✷✝✠☎★☎✴✼✽✤✪✝❁✂✻✕✿✣❀☎★✤◗Øt✡✙✦✫✣✥✖★✡✙✦✎✾❯☎q✝✠☎★✍❃✤✯✂✹☎★✣◗✼❡✝✠✤✆✍❨✓✠✰✒☎❁✓✷✝✠☎★☎✆✳❑⑧✢✤✙✝❋✓✠✰✢✕✗✘ ◆✒✏❀✝✠◆❯✤✆✘✷☎✆✛✪➘➆✝✠☎★✍❃✤✯✂✹☎★✘✈✓✠✰✒☎❦☎★✦❖✓✷✝✷☞✄✖★✤✙✝✷✝✠☎★✘✷◆❯✤✙✦✫✣❀✕☛✦✢✲❁✓✠✤q✂✻✕☛✣✢☎✞✤qØ❪✼❡✝✠✤✆✍ ✓✠✰✒☎◗✘✷☎✞✝✠✂✻✕☛✖✞☎✥✓✸✡✙✾✒✟✗☎✆✛✵✡✙✦✒✣✐✘✷☎★✦✒✣✢✘✶✡ ï✬é✵➾❡í ◆✒✡✙✖✸❙✹☎✞✓❥✓✠✤✧✕✔✓✠✘✶◆✫✡✯✝✠☎★✦❖✓✶ø ✤✆✦✩✓✠✰✒☎✴✓✷✝✠☎★☎✆✳❦øt✝✠☎✞✍❃✤✪✂✆☎★✘❧➘➷✼❡✝✠✤✙✍➠Đ★Ị✢Ĩ❆Ơ✿Õ✻Ư❑Ĩ❆➬✞➮★➊♥ø✎✛✢Ø✑➋❑✡✙✦✫✣❃✖✌✡✯✝✷✝✠✕✗☎★✘ ✤✆✏❀✓✴✓✠✰✒☎■✘✠✡✪✍❃☎✄✓✠☎✌✡✪✝✷❅➀✤✪➂✐◆❯✤✙✟✗✕☛✖✱☞❫✡✪✘❉✦✢✤✻✣✢☎■➘②✣❀✤❖☎★✘★✳ ➤❋✟✗☎✌✡✪✝✠✟✔☞❖✛●✓✠✰✒☎✥✡✪✾❯✤✯✂✹☎◗✘✚✓✷✝✸✡✯✓✠☎★✲✙☞❭✘✠✡✌✂✹☎★✘❥✦✢☎✞✓❘❊❋✤✙✝✠❙❇✾✫✡✪✦✫✣❀❊✴✕☛✣✻✓✠✰●✳❣▲❆✼ ✡✙✦✎✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟❯✦✒✤✻✣✢☎❉✕✗✘❁✦✒✤✙✓✦✒☎★☎✌✣❀☎✌✣✥✓✠✤❣✼❡✤✙✝✷❊✡✪✝✸✣❫✣✢✡✪✓✸✡❥✓✠✤◗✡✪✦✻☞✩✤✪✓✠✰✒☎✞✝ ✦✒✤✻✣❀☎✆✛✈☎✞❏❀✖★✟✗✏✫✣❀✕✗✦✒✲❃✕✔✓✄✼✿✝✠✤✆✍➁✓✠✰✢☎✶✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓✄✓✷✝✠☎★☎✑✡✌✂✹✤✆✕☛✣✢✘q✓✷✝✸✡✙✦✢✘✷✍❃✕✗✓✷❅ ✓✠✕✗✦✒✲✎✝✠☎✌✣✢✏✢✦✫✣✒✡✪✦❖✓✄✕✗✦✢✼❡✤✙✝✠✍✩✡✯✓✠✕☛✤✙✦●✳◗❶❨✦✢✤✻✣✢☎◗❊✴✰✢☎★✦❭✦✒✤✙✓■◆✫✡✪✝✷✓■✤✙✼❁✡✪✦❖☞ ✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✄✓✷✝✠☎✞☎✑✾❯☎★✖✞✤✆✍❃☎★✘q✕☛✣✢✟✗☎✥✡✪✦✫✣❫✕✗✘■✦✒✤✪✓✄✕✗✦✻✂✹✤✙✟☛✂✆☎✌✣❫✕✗✦✐✡✪✦❖☞❫✦✒☎✱✓✷❅ ❊✤✪✝✠❙❃✖★✤✆✍❃✍✑✏✒✦✢✕☛✖★✡✪✓✠✕✗✤✆✦✬✳✮✇❄✤✶✓✠✰✒✕✗✘☎✞❏✻✓✠☎★✦❖✓✌✛❖✜❉✖✌✡✙✘✚✓✕☛✘✣✢✕✗✘✚✓✠✕✗✦✒✲✆✏✢✕✗✘✷✰✒☎✌✣ ✼❡✝✠✤✙✍➄☎✌✡✯✝✠✟✗✕☛☎✱✝✮✤✯✂✹☎✞✝✠✟☛✡★☞■✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓●✘✷✖✱✰✢☎★✍❃☎★✘❄✕✗✦■❊✴✰✢✕☛✖✸✰✶☎★✂✹☎✞✝✷☞✄✤✯✂✹☎✞✝✠✟☛✡★☞ ✦✒✤✻✣❀☎❃✡✙✟✔❊✡✌☞❀✘❣✦✒☎★☎★✣✢✘■✓✠✤❫✖★✤✙✍❃✍◗✏✢✦✒✕✗✖✌✡✪✓✠✕✗✦✢✲✎✓✠✰❀✝✠✤✆✏✒✲✙✰✐✓✠✰✢☎✥✦✒☎✞✓❆❊✤✪✝✠❙ ✓✠✤◗✝✠☎✞❅➀☎★✂✙✡✙✟✗✏✒✡✪✓✠☎❥✕✔✓✠✘✴◆❯✤✆✘✷✕✔✓✠✕✗✤✆✦❫✤✙✦✧✓✠✰✒☎■✤✯✂✹☎✱✝✠✟✿✡★☞❖✳ 3.3 Addition of An Internal Node ✇✰✒✕✗✘q◆✢✝✠✤❖✖★☎★✣✢✏✢✝✠☎✶✕✗✘✄✘✷✕✗✍❃◆✢✟☛☎❥✕✗✦❍✜❉✖✌✡✙✘✚✓✌✳ s ✰✒☎★✦❍✡✥✦✢☎✞❊❩✍✩✡✙✖✸✰✒✕✗✦✒☎ ❊❁✡✪✦❖✓✠✘❉✓✠✤✩✾❯☎❣✡✙✦❇✤✯✂✹☎✞✝✠✟☛✡★☞❍✦✒✤✻✣❀☎✆✛❯✕✔✓■✘✷☎★✦✒✣✢✘❉✡✙✦ ó❯ì ✝✠☎✌✺❖✏✒☎★✘✚✓q✓✠✤❃✓✠✰✒☎ ✘✷☎✞✝✠✂✹☎✱✝✌✳✵▲❘✦❥✝✠☎★✘✷◆❯✤✙✦✒✘✷☎✆✛✪✓✠✰✒☎❑✘✷☎✞✝✠✂✹☎✱✝✮✘✷☎★✦✫✣❀✘❄✾✒✡✙✖✸❙❥✡q✦✢☎✞❊❚✏✢✦✒✕☛✺❖✏✒☎❦✕☛✣✢☎★✦❀❅ ✓✠✕✔♠✫☎✞✝❁✼❡✤✙✝q✓✠✰✒☎■✦✢☎✞❊③✦✒✤✻✣❀☎✄✓✠✤✆✲✙☎✞✓✠✰✒☎✱✝q❊✴✕✔✓✠✰✧✓✠✰✢☎■✟✗✕✗✘✚✓❉✖✞✤✆✦❖✓✸✡✙✕✗✦✒✕✗✦✢✲◗✓✠✰✒☎ ▲❘➍❻✤✙✼❋☎★✂✹☎✞✝✷☞❇☎✞❏❀✕✗✘✚✓✠✕✗✦✒✲❢✤✪✂✆☎✞✝✠✟☛✡✌☞❭✦✢✤✻✣✢☎✆✳◗✇✰✒☎✥✘✷☎✱✝✠✂✹☎✞✝❣✡✙✟✗✘✷✤❢✕☛✦❀✼✽✤✪✝✠✍❃✘ ☎★✂✹☎✱✝✷☞✶✤✙✓✠✰✒☎✱✝❦✕☛✦❖✓✠☎✞✝✠✦✒✡✙✟❀✦✒✤✻✣❀☎❋✤✙✼✒✓✠✰✒✕✗✘✮✦✒☎✞❊④✕☛✣❀☎★✦❖✓✠✕✗♠✒☎✞✝✌✳❦✇✰✢✕☛✘✮☎✞✦✒✘✷✏✢✝✠☎✞✘ ✓✠✰✫✡✯✓✴✡✙✦❖☞✩✤✯✂✹☎✞✝✠✟☛✡★☞✩✦✒✤✻✣❀☎✄✕✗✘✴✡★❊❁✡✯✝✠☎■✤✙✼●✓✠✰✒☎✄☎✱❏✢✕✗✘✚✓✠☎★✦✢✖★☎✄✤✪✼✮✡✪✦✻☞✩✤✪✓✠✰✒☎✞✝ ✦✒✤✻✣❀☎✆✳ 3.4 Removal of An Internal Node ❶❉✦✄✕☛✦❖✓✠☎✞✝✠✦✒✡✙✟✹✦✢✤✻✣✢☎❦➘✉❊❁✡✙✦❖✓✠✘✈✓✠✤❁✝✠☎★✍❃✤✯✂✹☎✮✕✔✓✠✘✷☎★✟✔✼✢✼✿✝✠✤✆✍③✓✠✰✒☎❦✤✯✂✹☎✞✝✠✟☛✡★☞ ✾❖☞❽✘✷☎★✦✒✣✢✕✗✦✒✲❭✡✪✦ ó✢✜ ✍❃☎★✘✷✘✠✡✙✲✙☎✎✓✠✤❇☎★✂✆☎✞✝✷☞❽✤✪✓✠✰✒☎✞✝◗✤✪✂✆☎✞✝✠✟☛✡✌☞❽✦✒✤✻✣✢☎❃✓✠✤ ✕✗✦✢✼❡✤✙✝✠✍❩✓✠✰✢☎✮✝✠☎★✍❃✤✯✂✆✡✪✟✆✤✙✼❀➘❤✳❄▲❘✦■✝✠☎★✘✷◆❯✤✙✦✒✘✷☎✆✛✙☎✌✡✪✖✱✰❥✝✠☎★✖★✕✗◆✢✕☛☎✞✦✻✓✬✝✠☎★✍❃✤✯✂✹☎★✘ ➘ ✼✿✝✠✤✆✍Ú✕✔✓✠✘✥✦✢✤✻✣✢☎❫✟✗✕✗✘✚✓✌✳❬▲❆✦④◆✫✡✪✝✷✓✠✕✗✖★✏✢✟☛✡✪✝✌✛❁☎✌✡✪✖✱✰♦◆✫✡✯✝✠☎★✦❖✓❃ø②✤✙✼✄➘❤✛ ✡✙✖✞✖★✤✙✝✸✣❀✕☛✦✢✲❢✓✠✤❢✘✷✤✆✍❃☎◗✤✙✦✢❅➀✲✆✤✙✕✗✦✒✲✧✂✻✕☛✣✢☎✞✤❢✘✚✓✷✝✠☎✌✡✪✍❫✛✈✝✠☎★✍❃✤✯✂✹☎★✘✄➘➞✼❡✝✠✤✆✍ A E D B F A D E B G ✝✠☎★✖★✤✙✦✒✦✢☎★✖✞✓✶✓✠✤❢✓✠✰✢☎❃✲✙✝✸✡✙✦✒✣✢◆✒✡✪✝✠☎★✦❖✓✶✦✒✤✻✣❀☎❫➊♥✕✗✦✒✘✚✓✠☎✌✡✙✣❤✤✙✼❋✓✠✰✒☎✥✘✷☎✞✝✠✂✆☎✞✝✱➋✱✳ ❶❉✟✔✓✠✰✢✤✆✏✒✲✙✰❍✓✠✰✒✕✗✘■✡✪◆✒◆✢✝✠✤✆✡✙✖✸✰❇✘✠✡✯✂✆☎★✘✄✘✷☎✞✝✠✂✆☎✞✝■✾✒✡✙✦✫✣✻❊✴✕☛✣❀✓✠✰●✛✫☎✌✡✙✖✸✰✐✦✢✤✻✣✢☎ ❊✤✙✏✒✟☛✣✶✰✫✡✌✂✹☎✮✓✠✤❉❙✆☎★☎★◆❥✍❃✤✙✝✠☎❑✕✗✦✢✼❡✤✙✝✠✍✩✡✪✓✠✕✗✤✙✦◗✡✪✦✫✣■✓✠✰✒☎❑◆✢✝✠✤✪✓✠✤❖✖★✤✆✟✹❊❋✤✆✏✒✟☛✣ ✾❯☎★✖★✤✙✍❃☎✍❃✤✙✝✠☎❧✖★✤✆✍❃◆✢✟✗☎✞❏✈✳❦⑨❀✕✗✦✢✖★☎❁✡❉✦✢✤✻✣✢☎❁✣❀✤❖☎★✘✮✦✒✤✪✓✮✼♥✡✪✕☛✟✻✼❡✝✠☎★✺✻✏✢☎★✦❖✓✠✟✔☞❖✛ ❊☎✧✤✆◆✢✓❃✼❡✤✙✝❃✓✠✰✢☎✧✘✷✕✗✍❃◆✒✟✗☎✞✝❃✘✚✓✷✝✸✡✯✓✠☎★✲✙☞❪✣❀☎★✘✷✖✞✝✠✕✗✾❯☎✌✣❪◆❀✝✠☎★✂✻✕✗✤✆✏✒✘✷✟✔☞❖✳ s ☎ ✘✷✰✫✡✪✟✗✟❁✣✢✕✗✘✷✖★✏✢✘✷✘◗✘✷✰✒✤✪✝✷✓✠✟✔☞❚✰✒✤✌❊❨✓✠✤❇✝✠☎★✣✢✏✒✖✞☎✩✓✠✰✢☎✩✘✷☎✞✝✠✂✹☎✞✝◗✟☛✤✆✡✆✣❚✘✷✰✒✤✙✏✒✟☛✣ ✓✠✰✒☎❭✘✷☎✞✝✠✂✹☎✱✝❫✰✫✡✪◆✒◆❯☎★✦❱✓✠✤④✘✷☎✞✝✠✂✆☎❭✓✠✤❖✤♦✍✩✡✙✦❖☞♦✝✠☎★✖★✤✆✦✢✦✒☎★✖✱✓✠✕☛✦✢✲④✦✒✤✻✣✢☎✞✘ ✣✢✕✔✝✠☎★✖✱✓✠✟✗☞❖✳ G C C Client Client Before adjustment 3.6 Dynamic Change of Delivery Paths After adjustment ỗ ốộỹợúúờỡỡớỡúũ A B A E D F D E B G G C C Client Before adjustment Client After adjustment ỗ ốộ ỗ ộúờỡỡớỡúũ q ✓✠☎✞✟☛✟✗✘❧✕✗✓✠✘❧✖★✤✙✝✷✝✠☎✞✘✷◆❯✤✆✦✫✣❀✕✗✦✒✲✶✖✱✰✢✕✗✟✿✣✻✝✠☎★✦✥✓✠✤■✝✠☎★✖★✤✙✦✒✦✢☎★✖✞✓❑✓✠✤✶✓✠✰✢☎❁◆✫✡✯✝✠☎★✦❖✓❋ø ✤✪✼✒➘✉✓✠✤✴✲✆☎✞✓●✓✠✰✒☎❦✝✠☎★✍✩✡✙✕✗✦✢✕☛✦✢✲✴✣✒✡✯✓✸✡❀✳❦❶q✦❥☎✞❏✢✡✙✍❃◆✒✟✗☎❦✕✗✘❄✲✙✕☛✂✆☎★✦✶✕☛✦✶⑧✵✕✗✲❀✳✙❹ ✓✠✤❥✕✗✟✗✟✗✏✒✘✚✓✷✝✸✡✯✓✠☎q✓✠✰✢☎✝✠☎★✍❃✤✯✂✆✡✪✟✢◆❀✝✠✤❖✖★☎✌✣✢✏❀✝✠☎✆✳❦✇✰✢☎✞✝✠☎q✡✪✝✠☎q✖★✏✢✝✷✝✠☎★✦❖✓✠✟✔☞✶✓❘❊❋✤ ✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❋✓✷✝✠☎★☎★✘■➊r✣✢✡✙✘✷✰✒☎★✣✎✡✪✦✫✣❃✘✷✤✆✟✗✕☛✣✫➋❧✼❡✤✙✝✓❆❊✤✑✣✢✕✔➂✈☎✞✝✠☎★✦❖✓❋✘✚✓✷✝✠☎✌✡✙✍❃✘★✳ ⑨✻✕✗✦✒✖★☎✩✦✒✤✻✣❀✭ ☎ ✒➷✣❀☎★✖★✕☛✣✢☎✞✘✑✓✠✤❍✾❯☎❃✤✙➂✮✛❦✦✢✤✻✣✢☎❢ơ❼✡✙✦✫✣❤✡❇✖✞✟☛✕✗☎★✦❖✓✑✦✒✤✻✣❀☎ ✰✒✡✌✂✹☎❭✓✠✤❚✝✠☎★✖✞✤✆✦✒✦✢☎★✖✞✓❫✓✠✤④✦✢✤✻✣✢☎✐❰õ❊✴✰✒✕✗✖✸✰ỉ❊✡✙✘❫◆❀✝✠☎★✂✻✕✗✤✆✏✒✘✷✟✔☞❱✓✠✰✢☎★✕✔✝ ✲✪✝✸✡✙✦✒✣✢◆✫✡✯✝✠☎★✦❖✓✌✳❨⑩✄✤✻✣✢☎✐❰ù✕✗✘✧✡✙✟✗✘✷✤❬✡❚✖✸✰✒✕✗✟☛✣❱✤✙✼❣✦✒✤✻✣❀✘ ☎ ✒◗✛❉❰ù✡✙✟✗✘✷✤ ✦✢☎★☎✌✣❀✘✴✓✠✤✑✝✠☎★✖★✤✆✦✢✦✒☎★✖✱✓q✓✠✤✑✕✔✓✠✘q✖✞✤✙✝✷✝✠☎★✘✷◆❯✤✙✦✫✣✢✕✗✦✢✲❃✲✙✝✸✡✙✦✒✣✢◆✒✡✪✝✠☎★✦❖✌✓ ✔❃✳ ⑧✢✤✆✟✗✟✗✤✯❊✴✕✗✦✢✲q✓✠✰✢☎❦✝✠☎✞✍❃✤✪✂✙✡✙✟✪✘✚✓✷✝✸✡✪✓✠☎✞✲✙☞❖✛✯✓✠✰✒☎✮✲✪✝✸✡✙✦✫✣❀◆✫✡✯✝✠☎★✦❖✓❋➊♥☎✆✳ ✲❀✳☛✛✪✦✢✤✻✣✢☎ ❰✩➋❑✍❃✕☛✲✙✰❖✓❋✾❯☎★✖✞✤✆✍❃☎❉✡❣✾❯✤✪✓✷✓✠✟☛☎✞✦✒☎★✖✸❙✥✕✔✼✵✡✪✖★✖★☎★◆❀✓✠✕✗✦✒✲✶✓✠✤❖✤✑✍✩✡✪✦✻☞✑✝✠☎★✖★✤✙✦✢❅ ✦✢☎★✖✞✓✠✕✗✦✒✲✧✦✒✤✻✣✢☎✞✘★✳❫✇✰✢✕☛✘❣✖✌✡✪✦❽✾❯☎✥✝✠☎★✘✷✤✆✟✗✂✹☎★✣❤✟☛✡✪✓✠☎✞✝✑✾❖☞❭✝✠☎✞✖★✤✆✦✢✦✒☎★✖✞✓✠✕✗✦✢✲ ✘✷✤✙✍❃☎❉✤✪✼✬✕✗✓✠✘❧✖✱✰✢✕✗✟✿✣✥✦✢✤✻✣✢☎★✘❑✓✠✤❥✤✙✓✠✰✢☎✞✝❋✝✠☎★✟☛✡★☞❃✦✢✤✻✣✢☎★✘★✳ s ☎❁❊✴✕☛✟✗✟✈✣❀✕☛✘✷✖✞✏✒✘✷✘ ✓✠✰✢✕✗✘q✕✗✦❇⑨✻☎★✖✞✓✠✕✗✤✆✦✧➃❀✳ ⑥❀✳ 3.5 Failure of An Internal Node ➤❋✰✢✕✗✟✿✣✻✝✠☎★✦❭✤✙✼❋✡✎✦✢✤✻✣✢☎◗➘➞✖✌✡✙✦❭✣❀☎✞✓✠☎★✖✞✓❥✕✔✓✠✘✄✼✽✡✙✕✗✟✗✏✢✝✠☎✥✾❖☞✧✤✆✾✒✘✷☎✱✝✠✂❀✕✗✦✢✲ ✓✠✰✢☎❧☎✞✘✚✓✠✕☛✍✩✡✯✓✠☎✌✣❣✡✪✝✷✝✠✕✗✂✆✡✪✟✻✣✒✡✯✓✸✡❁✝✸✡✯✓✠☎★✘✮✤✙✼❀✓✠✰✒☎❑✂✻✕☛✣✢☎★✤✴✘✚✓✷✝✠☎✌✡✪✍❃✘❄✼❡✝✠✤✙✍➄➘❤✳ s ✰✒☎★✦❃✡■✖✸✰✒✕✗✟☛✣◗✦✢✤✻✣✢☎✴✣✢☎✱✓✠☎★✖✞✓✠✘❦✓✠✰✒☎★✘✷☎✴✣✢✡✪✓✸✡✄✝✸✡✪✓✠☎✞✘❋✣✻✝✠✤✆◆◗✓✠✤✶✡✪✦✫✣◗✘✚✓✸✡★☞ ✡✯✓✄✓✠✰✢☎❣➉✞☎✞✝✠✤❢✟✗☎★✂✆☎★✟●✼❡✤✙✝✶✡❃◆❯☎✞✝✠✕✗✤✻✣❍✤✙✼❦✓✠✕✗✍❃☎✆✛✫✓✠✰✢✕☛✘❉✦✒✤✻✣❀☎✶✝✠☎★✺✻✏✢☎★✘✚✓✠✘❉✓✠✤ ✖✞✤✆✦✒✦✢☎★✖✞✓❁✕✔✓✠✘✷☎★✟✔✼✵✓✠✤✶✓✠✰✒☎❉✘✷☎✞✝✠✂✹☎✞✝✌✳❦▲❆✦❃✝✠☎★✘✷◆❯✤✆✦✢✘✷☎✆✛✢✓✠✰✢☎✄✘✷☎✞✝✠✂✆☎✞✝❁◆✒✕✗✖✸❙✻✘✏✒◆ ✓✠✰✢☎❥✘✷☎✞✝✠✂✻✕✗✖★☎✶✟☛☎✱✼❡✓❉✤✙➂❭✾❖☞❢➘✐✛❯✡✙✦✒✣✧✕✗✦✢✼❡✤✙✝✠✍❃✘q✡✙✟✗✟●✓✠✰✢☎❥✕✗✦✻✓✠☎✱✝✠✦✫✡✙✟●✦✒✤✻✣❀☎★✘ ✓✠✤✎✝✠☎★✍❃✤✯✂✹☎◗➘➞✼❡✝✠✤✆✍❵✓✠✰✢☎★✕✔✝❥✦✒✤✻✣❀☎✥✟✗✕✗✘✚✓✌✛✮✡✙✦✒✣❭✖✞✤✙✝✷✝✠☎★✘✷◆❯✤✙✦✫✣✢✕✗✦✢✲❫✖✱✰✢✕✗✟✿✣ ✟✗✕✗✘✚✓✠✘✮✕✔✼✢✓✠✰✢☎❧✕✗✦❖✓✠☎✞✝✠✦✒✡✙✟❖✦✒✤✻✣❀☎★✘✮✡✯✝✠☎❧◆✒✡✪✝✠☎★✦❖✓✠✘✵✤✪✼✒➘❻✘✷✤q✓✠✰✒✡✪✓✵✘✷✏✢✾✒✘✷☎✌✺❖✏✢☎★✦❖✓ ✣✢✡✪✓✸✡❥❊✴✕✗✟☛✟❯✦✢✤✙✓❋✾❯☎q✼❡✤✙✝✷❊❁✡✯✝✸✣✢☎✌✣❃✓✠✤❥✓✠✰✒✕✗✘❧✼✽✡✙✕✗✟✗☎✌✣✩✦✒✤✻✣✢☎✙✳ s ☎q✕☛✟✗✟✗✏✒✘✚✓✷✝✸✡✯✓✠☎ ✓✠✰✢✕✗✘❧◆❀✝✠✤❖✖★☎✌✣✢✏❀✝✠☎✴✕☛✦✩⑧✵✕✗✲❀✳✻➃❀✳✮▲❆✦◗✓✠✰✒✕✗✘❑☎✞❏✢✡✙✍❃◆✢✟☛☎✙✛✹✦✒✤✻✣❀✌☎ ✒ỉ✲✙✤❖☎★✘✣❀✤✯❊✴✦ ✡✪✖★✖★✕☛✣✢☎✞✦✻✓✸✡✪✟✗✟✗☞❖✳➠❶❉✟✗✟q✓✠✰✢✝✠☎★☎❭✤✙✼❣✕✔✓✠✘✧✖✸✰✒✕✗✟☛✣❀✝✠☎★✦ỉơ✑✛✄❰ ✡✪✦✫✣❲✡❽✖★✟✗✕✗☎★✦❖✓ ✦✢✤✻✣✢☎✎✰✫✡✌✂✹☎✥✓✠✤❍✝✠☎★✖★✤✙✦✒✦✢☎★✖✞✓❣✓✠✤❇✓✠✰✢☎✩✘✷☎✞✝✠✂✹☎✞✝❣✼✽✤✪✝◗✓✠✰✒☎❃✝✠☎★✍✩✡✪✕✗✦✫✣✢☎✱✝◗✤✪✼ ✓✠✰✢☎✑✘✷☎✱✝✠✂❀✕✗✖★☎✙✳ s ✰✒✕✗✟✗☎◗✦✢✤✻✣✢☎✑❰➁✝✠☎★✖★✤✙✦✒✦✢☎★✖✞✓✠✘❉✓✠✰❀✝✠✤✆✏✢✲✆✰❭✡✎✘✷✤✙✟✗✕✿✣❇✟✗✕✗✦✒☎✆✛ ơ➫✡✪✦✫✣❭✓✠✰✢☎❃✖★✟✗✕✗☎★✦❖✓❣✝✠☎✞✖★✤✆✦✢✦✒☎★✖✞✓❥✓✠✰❀✝✠✤✆✏✢✲✆✰❚✡❫✣✢✡✙✘✷✰✢☎✌✣✐✟✗✕✗✦✒☎✆✳❢✇✰✢✕☛✘✶✕✗✘ ✣❀✏✒☎✶✓✠✤❃✓✠✰✒☎✶✼♥✡✙✖✱✓■✓✠✰✫✡✯✓❥❰➷❊✡✙✘■✖✞✤✆✦✒✦✢☎★✖✞✓✠☎✌✣❫✓✠✤✩✓✠✰✒☎✶✘✷✤✆✟✗✕☛✣❀❅➀✟✗✕✗✦✒☎◗✓✷✝✠☎✞☎ ✾❯☎✱✼✽✤✙✝✠✮☎ ✒❬✼✽✡✙✕✗✟✗☎✌✣✬✛✙❊✴✰✒✕✗✟✗☎qô❱✡✙✦✒✣✶✓✠✰✢☎✖★✟✗✕✗☎★✦❖✓✮❊☎✞✝✠☎✖✞✤✆✦✒✦✢☎★✖✞✓✠☎✌✣✶✓✠✤❉✓✠✰✢☎ ✣✢✡✙✘✷✰✢☎✌✣❀❅➀✟✗✕✗✦✒☎❃✓✷✝✠☎★☎✆✳ s ☎✥✝✠☎★✖✌✡✙✟✗✟❋✓✠✰✒✡✪✓❣❊☎✩✏✒✘✷☎✎✡❍✘✷✤✆✟✗✕☛✣❚✟✗✕☛✦✢☎✎✡✙✦✫✣❤✡ ✣✢✡✙✘✷✰✢☎✌✣✥✟✗✕☛✦✢☎q✓✠✤❣✣❀☎★✦✒✤✪✓✠☎q✂✻✕☛✣✢☎✞✤❥✘✚✓✷✝✠☎✌✡✙✍❃✘❦✼✽✤✪✝✓❘❊❋✤✶✣✢✕✔➂✈☎✞✝✠☎★✦❖✓❧✂❀✕☛✣❀☎★✤✆✘★✳ s ☎❢✦✢✤✙✓✠☎✎✓✠✰✫✡✪✓◗❊✴✰✒☎★✦❪✡❭✦✢✤✻✣✢☎✎✼♥✡✙✕✗✟✗✘★✛❁✕✔✓✠✘✥✖✸✰✒✕✗✟☛✣❀✝✠☎★✦④✖★✤✙✏✒✟☛✣♦✡✙✟✗✘✷✤ ⑨❀✕✗✦✢✖★☎❫✡✪✟☛✟❉✣✢☎✞✟☛✕✗✂✹☎✱✝✷☞❪◆✒✡✪✓✠✰✢✘❃✡✪✝✠☎❫✤✯✂✹☎✱✝✠✟✿✡★☞♦◆✫✡✯✓✠✰✒✘★✛❧✓✠✰✒☎★✕✔✝✎✺❖✏✫✡✪✟☛✕✔✓❆☞ ✍✩✡★☞✎✖✱✰✒✡✙✦✒✲✙☎✶✤✪✂✆☎✞✝✴✓✠✕☛✍❃☎✙✳⑧✒✤✪✝q✕☛✦✢✘✚✓✸✡✙✦✢✖★☎★✘★✛❯✖★✤✙✦✒✲✙☎★✘✚✓✠✕✗✤✆✦❍✤✙✼❑✡✥◆✢✰❖☞✢✘✚❅ ✕✗✖✌✡✙✟✮✟✗✕✗✦✒❙✧✦✒☎★✲✆✡✪✓✠✕✗✂✹☎★✟✔☞❇✡✯➂✈☎★✖✞✓✠✘✄☎✞✂✹☎✞✝✷☞❫◆✒✡✪✓✠✰❇✖★✤✙✦✻✓✸✡✪✕✗✦✒✕✗✦✒✲✩✕✔☛✓ ✯✬✡✎✦✢✤✻✣✢☎ ✕✗✦æ✡♦✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✎✓✷✝✠☎★☎❤✍✩✡★☞❪✾❯☎★✖★✤✙✍❃☎❤✡❚✾❯✤✙✓✷✓✠✟✗☎★✦✢☎★✖✸❙❲✡✙✘❍✡❽✝✠☎★✘✷✏✢✟✔✓ ✤✙✼❉✝✠☎★✍❃✤✯✂✻✕☛✦✢✲❭✡✙✦④✤✯✂✹☎✞✝✠✟☛✡★☞④✦✒✤✻✣✢☎❭➊r✡✙✘✩✣❀✕✗✘✷✖★✏✒✘✷✘✷☎✌✣④✕✗✦❪⑨❀☎★✖✞✓✠✕✗✤✙✦✒✘✩➃❀✳ ➏ ✡✙✦✒✣❲➃❀✳ ➛✆➋✱✳❨✜❉➤✡✙✘✚✓❢✕✗✘❫✡✪✾✒✟✗☎❍✓✠✤❪✡✙✣✪➅❘✏✒✘✚✓✎✓✠✰✒☎❍✓✠✤✆◆❯✤✙✟☛✤✙✲✙☞❲✤✪✼✑✣✢☎★✟✗✕✗✂❖❅ ☎✞✝✷☞❤◆✫✡✪✓✠✰✢✘✑✓✠✤❭✡✆✣✢✣❀✝✠☎★✘✷✘✑✘✷✏✒✖✸✰❚◆✢✝✠✤✙✾✒✟✗☎★✍❃✘★✳✐▲❘✦❚◆✫✡✯✝✷✓✠✕✗✖★✏✒✟☛✡✪✝✌✛❦✓✠✰✢✕☛✘✑✕✗✘ ✡✙✖✸✰✒✕✗☎★✂✆☎✌✣❽❊✴✕✗✓✠✰✢✤✆✏❀✓◗✓✠✰✒☎✩✤✯✂✹☎✞✝✠✰✢☎✌✡✆✣❽✤✪✼✄☎✱❏✢✖✸✰✫✡✪✦✒✲✙✕☛✦✢✲❇✘✚✓✸✡✪✓✠✏✒✘✑✕✗✦✢✼✽✤✪✝✷❅ ✍✩✡✪✓✠✕✗✤✙✦❢✡✪✍❃✤✆✦✢✲❣✓✠✰✢☎❉✤✯✂✹☎✞✝✠✟☛✡★☞❃✦✢✤✻✣✢☎★✘❁✡✪✘✕✗✦❢✍❃✤✙✘✚✓☎✞❏❀✕✗✘✚✓✠✕✗✦✒✲❣✤✯✂✹☎✞✝✠✟☛✡★☞ s q ỉ ỉ ỉ ị òỏ ✛❋✦✒✤✻✣❀☎❫➘Ù✖★✤✙✦✒✘✷✕☛✣✢☎✞✝✠✘✥✓✠✰❀✝✠☎★☎❫◆❯✤✙✘✷✘✷✕☛✾✢✕✗✟☛✕✔✓✠✕✗☎★✘★➥ ➊✚➎✯➋■✓✠✰✒☎❃◆✒✡✪✝✠☎★✦❖✓❣ø➌➊♥✕♥✳ ☎✆✳✗✛❦ø②× Ï ❐✻➱✙✃✯Ð❯➮✞➊♥➘❤✛❦Ø❣➋✷➋✄✼♥✡✙✕✗✟✗✘★✛q➊➀❹✆➋❥✘✷✤✆✍❃☎ ◆✒✰❖☞❀✘✷✕✗✖✌✡✙✟✴✟✗✕✗✦✒❙❚✤✙✦♦✓✠✰✢☎✧◆✫✡✯✓✠✰♦✼✿✝✠✤✆✍Úø❿✓✠✤✐➘ ✕✗✘❃✖★✤✆✦✢✲✆☎★✘✚✓✠☎★✣✬✛✴✡✪✦✫✣ ➊r➃✹➋❑✘✷✤✆✍❃☎q◆✒✰❖☞❀✘✷✕☛✖★✡✙✟❯✟✗✕✗✦✒❙✥✤✙✦✩✓✠✰✢☎✄✏✢◆✒✘✚✓✷✝✠☎✌✡✪✍❻◆✒✡✪✓✠✰✒✘❉➊♥✾❯☎✞✼✽✤✪✝✠☎✄✝✠☎✌✡✪✖✱✰❀❅ ✕✗✦✒✲❇ø◗➋✶✕✗✘◗✖✞✤✆✦✒✲✙☎★✘✚✓✠☎✌✣✈✳ s ☎❢✣❀✕✗✘✷✖★✏✒✘✷✘✑✰✒✤✌❊ ✜❉✖✌✡✙✘✚✓◗✰✫✡✙✦✒✣✢✟✗☎★✘✶✓✠✰✒☎★✘✷☎ ✘✷✕✔✓✠✏✫✡✯✓✠✕☛✤✙✦✒✘q✾❯☎★✟✗✤✌❊❥✳ ⑧✵✕✔✝✠✘✚✓✌✛■✦✢✤✻✣✢☎❭➘ ✘✷☎★✦✒✣✢✘✧✡♦✍❃☎★✘✷✘✠✡✪✲✆☎❇✓✠✤❪ø➞✝✠☎★◆❯✤✙✝✷✓✠✕✗✦✒✲❪✺❖✏✫✡✪✟☛✕✔✓❆☞ ✣✢☎✞✲✙✝✸✡✆✣✢✡✪✓✠✕✗✤✆✦✬✳❑✇✰✒☎q✍❃☎★✘✷✘✠✡✙✲✙☎✴✕☛✦✢✖★✟✗✏✫✣❀☎★✘❑✓✠✰✢☎✴✂✆✡✪✟☛✏✢☎✴✤✙✼✬➱✙❐❖➮✚✃✻➊♥➘✐✛✻Ø✶➋✱✳ ▲❆✼✒ø③✕☛✘❦✣❀☎✌✡✆✣✈✛✪➘➠❊✴✕✗✟☛✟❀✦✒✤✪✓✵✝✠☎★✖★☎✞✕☛✂✆☎❁✡✙✦❖☞❥✝✠☎★◆✢✟✗☞❖✳●▲❘✦✶✓✠✰✒✕✗✘✮✖✌✡✪✘✷☎✆✛✹➘❻✰✫✡✪✘ ✓✠✤❉♠✒✦✫✣❣✡❉✦✢☎✞❊④◆✫✡✯✝✠☎★✦❖✓✮✦✒✤✻✣❀☎❋✓✠✤❉✝✠☎★✖✞✤✆✦✒✦✢☎★✖✞✓✮✕✔✓✠✘✷☎★✟✔✼❯✓✠✤q✓✠✰✒☎❋✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓ ✓✷✝✠☎★☎✆✳❍✇✰✒✕✗✘✑◆❀✝✠✤❖✖★☎✌✣❀✏✢✝✠☎✩✕✗✘❣✓✠✰✢☎✎✘✠✡✪✍❃☎✩✡✙✘❣✕✗✦❽✓✠✰✒☎❃✖✌✡✪✘✷☎❢✤✪✼✄✡❫✦✢✤✻✣✢☎ ✲✆✤✙✕✗✦✒✲✩✣✢✤✌❊✴✦❍✡✪✖★✖★✕☛✣✢☎✞✦✻✓✸✡✪✟✗✟✗☞✧✡✙✘q✣❀✕☛✘✷✖✞✏✒✘✷✘✷☎✌✣✧✕✗✦❇⑨✻☎★✖✞✓✠✕✗✤✆✦❫➃❀✳ ứỉ ỷr qỷì ẽ éứỉứ ứỉ ịòỏ ë❣➯✒ð★➵t➸ ➥❍➱✪❐✻➮✚✃❖➊♥ø✥✛qØ✶✱ ✓✠✰✫✡✯✓❁✤✆✦✢✟✔☞✎✓✠✰✢☎✄◆✒✡✪✓✠✰✩✼❡✝✠✤✆✍➫ø➆✓✠✤✑➘①✕✗✘✴◆❯✤❖✤✙✝❁❊✴✰✒✕✗✟✗☎✄✓✠✰✢☎■✏✒◆✢✘✚✓✷✝✠☎✌✡✙✍ ◆✫✡✯✓✠✰✒✘q✡✪✝✠☎❣✡✪✖★✖★☎★◆❀✓✸✡✙✾✒✟✗☎✆✳❧▲❘✦❢✓✠✰✒✕✗✘✴✖✌✡✙✘✷☎✆✛✒➘②✘✷☎★✦✫✣❀✘❉✡ ï●é✵➾✿í ✍❃☎✞✘✷✘✠✡✙✲✆☎ ✓✠✤❇✕✗✦✢✼✽✤✪✝✠✍➞ø➁✓✠✤❫✝✠☎★✍❃✤✯✂✹☎❃➘õ✼✿✝✠✤✆✍❾✕✔✓✠✘◗✖✸✰✒✕✗✟☛✣❽✟☛✕✗✘✚✓✌✛❑Đ★Ị✢Ĩ❆Ơ✿Õ✻Ư❑Ĩ❆➬✞➮★➊♥ø✩✛ Ø❣➋✱✳❱⑧✒✏❀✝✷✓✠✰✒☎✞✝✠✍❃✤✪✝✠☎✆✛❧➘Ù✡✪✓✷✓✠☎✞✍❃◆✢✓✠✘◗✓✠✤❇✝✠☎★✖★✤✙✦✒✦✒☎✞✖✞✓❃✓✠✤✐✓✠✰✢☎✧✍◗✏✢✟✔✓✠✕✗❅ ✖✌✡✪✘✚✓✥✓✷✝✠☎★☎✩✓✠✰✢✝✠✤✆✏✢✲✆✰❚✕✔✓✠✘◗✲✪✝✸✡✙✦✒✣✢◆✫✡✯✝✠☎★✦❖✓✩û■✳❽✇✰✢✕✗✘✥◆❯✤✆✟✗✕✗✖✞☞❚✰✒✡✙✘✑✓❆❊✤ ✕✗✍❃◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✙✦✒✘★✳✴⑧✵✕✔✝✠✘✚✓✌✛✫✕✔✼✮✓✠✰✢☎❥✟☛✤✌❊➄✕☛✦✢✖★✤✆✍❃✕✗✦✢✲❃✣✒✡✯✓✸✡◗✝✸✡✪✓✠☎✶✡✪✓❉➘❿❊❁✡✪✘ ứ ứổ qứ ị òỏ ỷổỷ ởỹ ứỉ ịòỏ q ỷổứứ ứỉỷ ứ ứỉ tị òỏ q ỉ ✠✟☛✡ ✆ ✡✙✦✒✣✩Ø ✂☎✄ ✝à ✆ ✛✹✝✠☎✞✘✷◆❯☎★✖✞✓✠✕✗✂✹☎★✟✔☞❖✳❑⑨✻✏✒◆✒◆❯✤✙✘✷☎❁✓✠✰✫✡✪✓ A E D B F E A D G B F C G C Before adjustment After adjustment ỗ ốộỡởỡốúốỡớúỡ é❄ú❃❂❣➯✒➼✪ị❬➼✯➵❀➚✆ó❯ì❄ì❄➵❀➚✆í✌➾❡ó❯ì❅❄ A E D B F C Before adjustment A G E D B F G C After adjustment ỗ ❡➾ è✫é❄➼✯➵✍❆✬➺✕✷✱✸●ì❄➯✹✣❤➾❡➚✎ë✻✺❄➯✫ì●è✫➵✧ó✁✥✮✼✥➽❯➵✻➼✪➳❡➯✽✸✾✼◗➼✯è✫➯✒ì✵➾❀✿✹➯✢í✌➾❡ó❯ì ❁ ị❄ó✤❂✥ì✑❂❣➯✒➼✪ị❬➼✯➵❀➚✆ó❯ì✵ì●➵✢➚✙í✌➾❡ó❯ì❇❄ ✦✢✤✻✣✢❈ ☎ ✒❨✣✢☎✞✓✠☎★✖✱✓✠✘✄✡❃✣❀☎★✲✙✝✸✡✙✣✒✡✪✓✠✕✗✤✙✦❭✕✗✦❫✓✠✰✢☎❥☎★✘✚✓✠✕✗✍✩✡✪✓✠☎✌✣❍✡✯✝✷✝✠✕☛✂✙✡✙✟✵✣✒✡✪✓✸✡ ✝✸✡✯✓✠☎❍✖★✤✙✝✷✝✠☎✞✘✷◆❯✤✆✦✫✣❀✕✗✦✒✲❤✓✠✤✐✾❯✤✙✓✠✰❬✘✚✓✷✝✠☎★✡✙✍❃✘✎Ø✁ ✂☎✄ à✏✆ ✡✪✦✫✣❪Ø ✆❉✞ ✠✟☛✡ ✆ ✛✮✒ ✝✠☎✞◆❯✤✙✝✷✓✠✘❦✓✠✰✒✕✗✘❧✖✞✤✆✦✫✣❀✕✔✓✠✕☛✤✙✦✥✓✠✤■✦✒✤✻✣❀☎q❰✧✳✮⑩✄✤✻✣❀☎❉❰➆✖★✏❀✝✷✝✠☎★✦❖✓✠✟✔☞✑✝✠☎★✖✞☎★✕✗✂✹☎★✘ ✁Ø à✏✆ ✼❡✝✠✤✙✍➠✦✢✤✻✣✢✕ ☎ ✔✉✡✪✦✫✣✎Ø ✆❉✞ ✠✟☛✡ ✆ ✼❡✝✠✤✙✍➠✦✒✤✻✣❀✕ ☎ ☞✥✳❦⑩✄✤✻✣❀☎✄❰➠♠✒✦✫✣❀✘ ✓✠✰✒✂❉✡✪✄ ✓✧✕✗✓✠✘✧➱✙❐❖➮✷✃❖➊r❰✧✛■✁Ø ịòỏ rỉ ị òỏ ✦ ✔❃✛✮❰❿✝✠☎★✖★✤✙✦✒✦✒☎✞✖✞✓✠✘❥✓✠✤❍✦✒✤✻✣✢✎ ☎ ❋✉✼✽✤✪✝◗✘✚✓✷✝✠☎✌✡✪✍ ✁Ø ✂❉✄ à✏✆ ✯❁✾✒✏❀✓✥✦✢✤✻✣✢✱ ☎ ✒➷✝✠☎★✍✩✡✪✕☛✦✢✘✥✖★✤✙✦✒✦✒☎✞✖✞✓✠☎✌✣❽✓✠✤❤❰✧✳♦⑧✢✤✙✝✩Ø ✆☎✞ ✠✟☛✡ ✆ ✛ ✰✢✤✌❊☎★✂✹☎✱✝✌✛●✦✢✤✻✣✢✻ ☎ ✒➠✣❀✕☛✘✷✖✞✤✆✦✒✦✢☎★✖✞✓✠✘✄✼✿✝✠✤✆✍①❰✧✛❄✡✪✦✫✣❫✝✠☎★✖★✤✙✦✒✦✢☎★✖✞✓✠✘✄✓✠✭ ✤ ☞ ✘✷✕✗✦✢✖★☎❥✕✔✓❉✕✗✘q✟✗✕☛✲✙✰❖✓✠✟✗☞✎✟✗✤✹✡✙✣✢☎✌✣✈✳ ❶➷◆❯✤✆✘✷✘✷✕✗✾✒✟✗☎❭✖✌✡✙✘✷☎❇✰✒✡✙◆✒◆❯☎✞✦✒✘✥❊✴✰✒☎✞✦❲✡❤✦✒✤✻✣❀☎❍➘❤✛q✣✢✕✔✝✠☎★✖✱✓✠✟✗☞❪✖★✤✙✦✢❅ ✦✢☎★✖✞✓✠☎✌✣❍✓✠✤❢✓✠✰✢☎✑✘✷☎✱✝✠✂✹☎✞✝✌✛●✕☛✘❥☎✱❏✢◆❯☎✱✝✠✕☛☎✞✦✒✖★✕✗✦✒✲❢✡❢✘✷✟✗✤✌❊q✣✢✤✌❊✴✦✐✕☛✦❇✓✠✰✒☎✑✕✗✦✢❅ ✖✞✤✆✍❃✕✗✦✒✲✐✣✒✡✯✓✸✡❇✼✿✝✠✤✆✍➌✓✠✰✢☎❢✘✷☎✞✝✠✂✆☎✞✝✌✳❪⑨❀✕✗✦✒✖✞☎✧➘ ✖★✡✙✦✒✦✢✤✙✓❃✲✙✤✐✏✢◆❖❊❁✡✪✝✸✣ ✡✪✦❖☞✎✼❡✏✢✝✷✓✠✰✢☎✞✝✌✛✒✕✔✓✴✰✒✡✙✘❁✓✠✤✑♠✒✦✫✣✎✡◗✦✒☎✞❊æ◆✒✡✪✝✠☎★✦❖✓✴✕✗✦❢✓✠✰✢☎❥✣✢✤✌❊✴✦✒✘✚✓✷✝✠☎★✡✙✍❫✳ ✇✰✢✕✗✘◗✕✗✘◗✡✪✖✱✰✢✕✗☎★✂✹☎✌✣❤✾❖☞✐✘✷☎★✦✫✣❀✕✗✦✒✲❍✡✧✝✠☎★✖✞✤✆✦✒✦✢☎★✖✞✓✠✕✗✤✆✦❽✝✠☎★✺✻✏✢☎★✘✚✓❣❊✴✕✗✓✠✰❽✡ ➇❘✣✢✤✌❊✴✦✒➈❢✕✗✦✫✣✢✕✗✖✌✡✯✓✠✤✙✝❥✓✠✤✩✓✠✰✒☎✑✘✷☎✞✝✠✂✹☎✞✝✌✳✶▲❆✦❇✝✠☎✞✘✷◆❯✤✆✦✒✘✷☎✙✛●✓✠✰✢☎◗✘✷☎✞✝✠✂✹☎✱✝❥✘✷☎✞❅ ✟✗☎★✖✱✓✠✘❧✤✙✦✒☎✴✤✙✼✈✕✔✓✠✘❦✖✱✰✢✕✗✟✿✣✻✝✠☎★✦●✛✹✘✠✡✌☞✥û❪✕✗✦❃✡❉✝✠✤✙✏✒✦✒✣❀❅r✝✠✤✆✾✢✕☛✦◗✍✩✡✙✦✒✦✢☎✞✝✌✛✆✡✙✦✫✣ ✕✗✦❀✼✽✤✙✝✠✍❃✘❣➘➝✓✠✰✫✡✯✓✥û❨✕☛✘❣✘ ➘ ✴ ✘◗✦✢☎✞❊❨◆✫✡✯✝✠☎★✦❖✓✌✳❫▲❆✼✴✦✢✤✻✣✢☎❃➘Û✟☛✡✪✓✠☎✞✝◗☎✞❏✻❅ ◆❯☎✱✝✠✕☛☎✞✦✒✖★☎★✘■✣✢☎★✲✪✝✸✡✆✣✒✡✯✓✠✕✗✤✆✦❭✕☛✦❫✓✠✰✢☎◗✡✯✝✷✝✠✕✗✂✆✡✪✟✮✣✒✡✯✓✸✡❃✝✸✡✯✓✠☎✥✡✪✲✹✡✙✕✗✦✬✛✈✕✗✓❉❊✴✕✗✟☛✟ ✝✠☎✞✖★✤✆✦✢✦✒☎★✖✞✓✩✓✠✤❚✡✐✖✱✰✢✕☛✟☛✣♦✤✙✼✑û➷✘✷☎✞✟☛☎✞✖✞✓✠☎✌✣❬✕✗✦❲✡✐✝✠✤✙✏✒✦✒✣❀❅r✝✠✤✆✾✢✕☛✦♦✍✩✡✙✦❀❅ ✦✢☎✞✝❣✡✙✘✶✾❯☎✞✼❡✤✙✝✠☎✆✳❃✇✰✒✕✗✘❥◆✢✝✠✤❖✖★☎✞✘✷✘❣✤✪✼✴✣✢✤✌❊✴✦❖❊❁✡✯✝✸✣❭✝✠☎★✖✞✤✆✦✒✦✢☎★✖✞✓✠✕✗✤✆✦❭❊✴✕✗✟☛✟ ☎✞✂✹☎★✦❖✓✠✏✫✡✪✟☛✟✔☞✎✝✠☎✌✡✙✖✸✰❇✡◗✟✗☎✌✡✌✂✹☎✶✦✒✤✻✣❀☎✶✤✙✼✮✓✠✰✒☎❥✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✴✓✷✝✠☎★☎✙✳❁❶✓✴✓✠✰✒✕✗✘ ✓✠✕✗✍❃☎✆✛✆➘➫✘✚❊✴✕✔✓✠✖✱✰✢☎★✘❑✓✠✰✢☎✝✠☎★✖★✤✙✦✒✦✒☎✞✖✞✓✠✕✗✤✆✦❃✕✗✦✫✣❀✕☛✖★✡✪✓✠✤✙✝❦✓✠✤❥➈✙✏✒◆✒●➈ ✯✻✡✙✦✒✣✑✕✔✓✠✘ ✝✠☎✞✖★✤✆✦✢✦✒☎★✖✞✓✠✕✗✤✙✦◗◆✢✝✠✤❖✖✞☎★✘✷✘❦✘✚✓✸✡✪✝✷✓✠✘✵✓✠✤✄✤❖✖✞✖★✏✢✝✮✕✗✦❣✓✠✰✒☎❋✏✢◆❖❊❁✡✪✝✸✣❣✣✢✕✔✝✠☎★✖✱✓✠✕☛✤✙✦●✳ ❶q✦❱☎✞❏✢✡✙✍❃◆✢✟✗☎❭✤✪✼✑✣✢✤✌❊✴✦❖❊❁✡✪✝✸✣❬✝✠☎✞✖★✤✆✦✢✦✒☎★✖✞✓✠✕✗✤✙✦æ✕✗✘❢✲✆✕✗✂✹☎★✦❲✕✗✦③⑧✵✕✗✲✢✳ ➛❖✳✄❈❉☎✞✝✠☎✆✛❯✾❯✤✪✓✠✰❍✦✒✤✻✣❀❍ ☎ ✒❨✡✙✦✒✣✧✓✠✰✒☎✶✖★✟✗✕✗☎★✦❖✓■✦✒✤✻✣❀☎❣✡✪✝✠☎❣☎✞❏❀◆❯☎✞✝✠✕✗☎★✦✒✖★✕✗✦✢✲ ✡❍✘✷✟✗✤✌❊q✣✢✤✌❊✴✦④✕✗✦④✓✠✰✢☎❃✕✗✦✒✖★✤✙✍❃✕☛✦✢✲❇✣✒✡✯✓✸✡❍✼✿✝✠✤✆✍➞❰✧✳✐✇❄✤❍✖★✤✙✝✷✝✠☎✞✖✞✓◗✓✠✰✢☎ ◆❀✝✠✤✆✾✢✟☛☎✞✍❫✢✛ ✒æ✝✠☎★✖★✤✆✦✢✦✒☎★✖✱✓✠✘❉✣❀✤✌❊✴✦✻❊✡✪✝✸✣✩✓✠■ ✤ ✔❃✛❀✓✠✰✢☎✄✦✢☎✞❏✻✓❁✖✱✰✢✕✗✟✿✣✎✦✒✤✻✣❀☎ ✤✪✼✫❰æ✡✙✖✞✖★✤✙✝✸✣❀✕☛✦✢✲q✓✠✤❁✓✠✰✢☎❦✝✠✤✙✏✒✦✒✣❀❅r✝✠✤✆✾✢✕☛✦✄✤✙✝✸✣✢☎✱✝✌✳❦⑨❀✕✗✍❃✕✗✟☛✡✪✝✠✟✔☞❖✛✌✓✠✰✒☎❦✖★✟✗✕✗☎★✦❖✓ ✦✢✤✻✣✢☎■✝✠☎★✖✞✤✆✦✒✦✢☎★✖✞✓✠✘❁✓✠✤✥✦✢✤✻✣✢✓ ☎ ☞✥✛✢✓✠✰✢☎■✦✒☎✱❏❀✓✴✖✸✰✒✕✗✟☛✣❢✦✢✤✻✣✢☎❥✤✪✼❑❰❼✾✒✡✙✘✷☎✌✣ ✤✙✦✧✓✠✰✒☎✄✘✠✡✙✍❃☎■✝✠✤✆✏✢✦✫✣✻❅➀✝✠✤✙✾✒✕✗✦✎✍❃☎★✖✱✰✒✡✙✦✢✕☛✘✷✍❫✳ ✏✢✘✷☎✌✣✥✓✠✰✒☎❥➶■✇❋❅➀▲❘✇✴▼①✲✆☎★✦✢☎✞✝✸EVALUATION ✡✪✓✠✤✪✝✶⑤✗➎★⑥✪⑦✬✓✠✤✑✖✱✝✠☎✌✡✪✓✠☎❥✡❣⑥✆❷✙❷✪❅➀✦✒✤✻✣❀☎ s ☎✄PERFORMANCE ✓✷✝✸✡✪✦✒✘✷✕✔✓✷❅➀✘✚✓✠✏✒✾❃✲✪✝✸✡✙◆✒✰✩✡✪✘❋✤✙✏✢✝✏✢✦✫✣❀☎✞✝✠✟✔☞✢✕✗✦✢✲■✦✒☎✞✓❆❊✤✪✝✠❙◗✓✠✤✆◆❯✤✙✟☛✤✙✲✙☞❖✳❑✇✰✢☎ ✤✯✂✹☎✞✝✠✟☛✡★☞◗✦✢✤✻✣✢☎★✘❑✡✯✝✠☎q✘✷☎✞✟☛☎✞✖✞✓✠☎✌✣✥✕✗✦✑✓❆❊✤✶✡✙◆✢◆✢✝✠✤✆✡✙✖✸✰✒☎★✘★➥✵✝✸✡✪✦✫✣❀✤✆✍✥❅➀✾✫✡✪✘✷☎✌✣ ✡✙✦✒✣❍✾✫✡✙✖✸❙✻✾❯✤✆✦✢☎✞❅➀✾✫✡✙✘✷☎★✣✬✳❉▲❘✦❫✓✠✰✒☎✶✝✸✡✙✦✒✣✢✤✙✍✥❅❆✾✒✡✙✘✷☎✌✣❍✡✪◆✒◆❀✝✠✤✹✡✙✖✸✰●✛✈✤✯✂✹☎✱✝✷❅ ✟☛✡★☞✩✦✒✤✻✣✢☎✞✘✴✡✪✝✠☎■✖✸✰✒✤✙✘✷☎★✦✎✝✸✡✪✦✫✣❀✤✆✍❃✟✔☞✩✡✙✍❃✤✙✦✒✲❣✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲❣✦✒✤✻✣✢☎✞✘★✳❦▲❘✦ ✓✠✰✒☎◗✾✫✡✙✖✸❙✻✾❯✤✆✦✢☎✞❅➀✾✫✡✙✘✷☎★✣❤✡✙◆✢◆✢✝✠✤✆✡✙✖✸✰●✛✵✤✯✂✹☎✱✝✠✟✿✡★☞✐✦✒✤✻✣❀☎★✘❣✡✪✝✠☎✥✝✸✡✙✦✒✣✢✤✙✍❃✟✗☞ ✖✸✰✒✤✆✘✷☎✞✦✧✡✪✍❃✤✆✦✒✲❥✓✠✰✢☎❉✏✢✦✫✣✢☎✱✝✠✟✗☞❀✕✗✦✒✲❥✓✷✝✸✡✪✦✒✘✷✕✔✓❁✦✒✤✻✣❀☎★✘❁✡✪✦✫✣✥✓✠✰✒☎✴✝✠☎★✍✩✡✙✕✗✦❀❅ ✕✗✦✒✲❇✤✯✂✹☎✞✝✠✟☛✡★☞❽✦✢✤✻✣✢☎★✘★✛❦✕✔✼❉✡✙✦❖☞❖✛❑✡✪✝✠☎❃✝✸✡✪✦✫✣✢✤✙✍❃✟✔☞❽✖✸✰✒✤✆✘✷☎✞✦④✡✙✍❃✤✆✦✢✲❫✓✠✰✒☎ ✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲❢✘✚✓✠✏✒✾❤✦✢✤✻✣✢☎★✘★✳✩⑨❀✕✗✦✒✖★☎◗✤✪✂✆☎✞✝✠✟☛✡✌☞✐✘✷☎★✟✗☎★✖✞✓✠✕✗✤✙✦❽✕✗✘❣✾✒✡✙✘✷☎✌✣✐✤✆✦ ✝✸✡✙✦✒✣✢✤✙✍❃✦✒☎★✘✷✘★✛❉✡❽✘✷✕✗✦✒✲✙✟☛☎❭✖✸✰✒✤✆✕✗✖★☎❇✤✪✼✑✤✯✂✹☎✱✝✠✟✿✡★☞❬✦✒✤✻✣✢☎✞✘❢✕✗✘✎✦✒✤✙✓❢✘✷✏✢❂◗❅ ✖★✕✗☎★✦❖✓✮✓✠✤q✕☛✟✗✟✗✏✒✘✚✓✷✝✸✡✯✓✠☎✓✠✰✒☎❧◆❯☎✞✝✷✼✽✤✪✝✠✍✩✡✙✦✒✖✞☎❁✡✙✖★✖✞✏✢✝✸✡✪✓✠☎✞✟✗☞❖✳✵✇✰✒☎✞✝✠☎✱✼✽✤✙✝✠☎✙✛✹✼✽✤✪✝ ☎✌✡✪✖✱✰❇✓❘☞❀◆❯☎❣✤✙✼✤✯✂✹☎✱✝✠✟✿✡★☞❍✘✷☎✞✟☛☎✞✖✞✓✠✕✗✤✆✦●✛❄✘✷✕✗✍◗✏✒✟☛✡✯✓✠✕☛✤✙✦❭❊✡✙✘✄✝✠✏✢✦❇✍◗✏✒✟✔✓✠✕✗◆✒✟✗☎ 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▲✘❖❧❜✙❝✠❞❆➓◗✕✗✘✥✖★✤✆✍❃◆✢✏✢✓✠☎✌✣④✡✪✘◗✓✠✰✒☎ ✝✸✡✪✓✠✕✗✤✎✤✙✼❧✦✒☎✞✓❆❊✤✪✝✠❙✧✟✗✤✹✡✙✣❭✕✗✍❃◆❯✤✆✘✷☎★✣❫✾✻☞✧✤✯✂✹☎✞✝✠✟☛✡★☞❫✓✠✤✎✡✩✟✗✤✌❊☎✱✝❥✾❯✤✆✏✢✦✫✣ ☎★✘✚✓✠✕✗✍✩✡✪✓✠☎✄✤✙✼✵▲❘✭❬▼✧✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✴✦✒☎✱✓❘❊✤✪✝✠❙✩✟☛✤✆✡✆✣✈✳❋✇✰✢☎✄✦✢☎✞✓❘❊❋✤✙✝✠❙✩✟✗✤✹✡✆✣✎✕✗✘ ✣✢☎✱♠✫✦✒☎★✣❃✡✙✘❧✓✠✰✢☎❁✓✠✤✙✓✸✡✙✟❯✦✻✏✢✍◗✾❯☎✞✝❦✤✪✼●✓✠✕✗✍❃☎★✘❑◆✒✰❖☞❀✘✷✕✗✖✌✡✙✟✫✟✗✕✗✦✒❙✻✘❧✡✪✝✠☎❉✏✒✘✷☎✌✣✈✳ ❘ ❛✠❛✸➓✱❝✠✮ ❝ ❙■➙✽❝✠❞➀❜✙➦❯❛✸➓❧✕✗✘❑✓✠✰✒☎q✡✌✂✹☎✞✝✸✡✙✲✙☎❉✟✗☎★✦✢✲✙✓✠✰❃✕✗✦✩✰✒✤✙◆✒✘❑✤✙✼✈✓✠✰✒☎q✣✢☎✞✟☛✕✗✂✹☎✱✝✷☞ ◆✫✡✯✓✠✰❍✾❯☎✞✓❘❊❋☎★☎★✦❫✓✠✰✢☎✶✝✠☎✞◆✢✝✠☎★✘✷☎★✦❖✓✸✡✯✓✠✕☛✂✆☎❣✤✪✼❧✡✥✖★✟✗✕☛☎✞✦✻✓■✡✙✦✒✣✧✓✠✰✒☎✶✤✯✂✹☎✞✝✠✟☛✡★☞ ✦✒✤✻✣❀☎q✼❡✤✙✝✓✠✰✢☎❁✝✠☎★◆✢✝✠☎★✘✷☎✞✦✻✓✸✡✯✓✠✕✗✂✹☎q✓✠✤❁➅❘✤✆✕✗✦✎✓✠✤✶✲✙☎✞✓❁✣✢✡✪✓✸✡■✼✽✤✪✝❋✓✠✰✒☎q✖★✟✗✕✗☎★✦❖✓✌✳ ✇✰✒✕✗✘q✍❃☎✞✓✷✝✠✕✗✖★✘✴✕✗✦✢Ü✫✏✢☎★✦✒✖✞☎★✘✴✰✒✤✌❊❩✼✽✡✙✘✚✓q✓✠✰✒☎❥✖★✟✗✕✗☎★✦❖✓❉✖✌✡✙✦❫✘✚✓✸✡✯✝✷✓❉✝✠☎✞✖★☎★✕✗✂❖❅ ✕✗✦✒✲✶✣✢✡✪✓✸✡❀✳✳ ◆✶➑✌➧❖✮➓ ▼✒❞♥➔✠➓✱❝✠✩❝ ❙❥➙❡❝✸❞♥➔✸➙r➴ ↕ ❞♥➙r➑✙➦❥✝✠☎✱Ü✫☎★✖✞✓✠✘❑✰✒✤✌❊♦✾✫✡✪✟☛✡✙✦✒✖✞☎✌✣◗✓✠✰✒☎ ✘✷☎✞✝✠✂✻✕✗✖★☎❥✟✗✤✹✡✙✣❫✕☛✘q✣❀✕☛✘✚✓✷✝✠✕✗✾✢✏✢✓✠☎✌✣❢✡✙✍❃✤✆✦✢✲✥✦✒☎✱✓❘❊✤✪✝✠❙✩✦✒✤✻✣✢☎✞✘★✳ 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✓✠✰✒☎✱✝✠☎■✕✗✘❉✡✪✟✔❊❁✡★☞❀✘❉✡✯✓q✍❃✤✆✘✚✓✴✡◗✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓❁✓✷✝✠☎✞☎■✤✆✦✧✓✠✰✢☎✄✤✯✂✹☎✞✝✠✟☛✡★☞❖✳❦▲❘✦✢✕✔❅ ✓✠✕☛✡✙✟✗✟✔☞❖✛❉✡✙✟✗✟✄✓✠✰✒☎❍✤✯✂✹☎✱✝✠✟✿✡★☞❪✦✒✤✻✣❀☎★✘✧✡✯✝✠☎❇✕✿✣❀✟✗☎✐✡✪✦✫✣❬✦✢✤❽✓✷✝✠☎★☎❍✕✗✘❢✾✢✏✒✕✗✟✔✓✌✳ ♣q☎✌✺❖✏✒☎★✘✚✓✠✘❄❊❋☎✞✝✠☎✲✙☎★✦✒☎✞✝✸✡✯✓✠☎✌✣◗✡✪✦✫✣❣✣✢☎★✟✗✕✗✂✹☎✞✝✷☞✶◆✒✡✪✓✠✰✢✘❄❊☎✞✝✠☎❋✖✞✝✠☎✌✡✪✓✠☎★✣◗✡✙✖✱❅ ✖★✤✪✝✸✣✢✕✗✦✒✲✙✟✗☞■✏✒✦❖✓✠✕✗✟❖✡✓✷✝✠☎★☎❑❊✡✙✘●✾✒✏✒✕✗✟✔✓✵✖✞✤✪✂✆☎✞✝✠✕✗✦✒✲q✡✙✟✗✟❖✤✯✂✹☎✞✝✠✟☛✡★☞■✦✢✤✻✣✢☎★✘★✳✵❶❁✓ ✓✠✰✒✕✗✘❉◆❯✤✆✕✗✦❖✓✌✛✫❊☎✑✖★✤✆✍❃◆✢✏✢✓✠☎✌✣❢✓✠✰✢☎✶✍❃☎✞✓✷✝✠✕✗✖★✘■✡✪✾❯✤✪✂✆☎✆✳✄✁✄✾❀✂✻✕✗✤✆✏✢✘✷✟✔☞❖✛✫✓✠✰✒☎ ✤✯✂✹☎✞✝✠✟☛✡★☞✥✾✢✏✒✕✗✟✔✓✾✫✡✪✘✷☎✌✣✥✤✆✦✎✭❦✏✢✝✠☎✴❳✄✦✢✕✗✖✌✡✙✘✚✓❋✰✫✡✙✘❋✡■✂✹☎✞✝✷☞◗✘✷☎★✂✹☎✞✝✠☎q✘✷☎✞✝✠✂✹☎✞✝ ✾❯✤✙✓✷✓✠✟✗☎★✦✢☎★✖✸❙✑◆❀✝✠✤✆✾✒✟✗☎★✍➆✘✷✕✗✦✢✖★☎❁☎★✂✹☎✞✝✷☞❣✕✗✦❖✓✠☎✞✝✠✦✫✡✪✟✒✦✢✤✻✣✢☎✕✗✘❧✣✢✕✔✝✠☎★✖✞✓✠✟✔☞✑✖★✤✆✦❀❅ ✦✒☎✞✖✞✓✠☎✌✣✐✓✠✤✧✓✠✰✢☎✥✘✷☎✞✝✠✂✹☎✱✝✑✦✢✤✻✣✢☎✆✳❢❶q✘❣☎✱❏✢✰✢✕✗✾✒✕✔✓✠☎✌✣✐✕✗✦❚⑧✵✕✗✲❀✳❫⑥❀➊r✡✹➋✱✛❄✓✠✰✢✕✗✘ ◆✢✝✠✤✙✾✒✟✗☎★✍t✾❯☎✞✖★✤✆✍❃☎★✘✵❊❋✤✙✝✠✘✷☎q✡✙✘✵✓✠✰✢☎✤✯✂✹☎✞✝✠✟☛✡★☞❣✘✷✕☛➉✞☎❁✕☛✦✢✖✞✝✠☎✌✡✪✘✷☎★✘★✳❦▲❘✦✑✖★✤✆✦❀❅ ✓✷✝✸✡✙✘✚✓✌✛✈✓✠✰✢☎✑✘✷☎✞✝✠✂✆☎✞✝■✦✢✤✻✣✢☎❣✕☛✦❇✜❉✖✌✡✙✘✚✓❥✘✷✖★✡✙✟✗☎★✘■❊☎✞✟☛✟✵❊✴✕✔✓✠✰❇✓✠✰✒☎❣✤✯✂✹☎✞✝✠✟☛✡★☞ ✘✷✕✗➉★☎✆✳❬✇✰✒✕✗✘✥✘✚✓✠✏✒✣❀☞❚✘✷✰✢✤✯❊✴✘✥✓✠✰✒✡✪✓❃☎✞✂✹☎★✦❚✓✠✰✒✤✙✏✒✲✆✰❪✭❦✏✢✝✠☎✧❳❉✦✒✕✗✖✌✡✪✘✚✓❃✕✗✘ ☎✌✡✪✘✚☞✐✓✠✤❇✣❀☎★◆✒✟✗✤✌☞❖✛✵✕✔✓✠✘✶✘✷☎★✂✹☎✞✝✠☎❃✾❯✤✪✓✷✓✠✟✗☎★✦✒☎★✖✸❙❭✘✷☎✞✝✠✂✹☎✞✝❣◆✢✝✠✤✙✾✒✟✗☎★✍❵❊❋✤✆✏✒✟☛✣ ✾❯☎✓✠✰✒☎❋✂❀✕✔✓✸✡✪✟✢✰✻✏✢✝✸✣❀✟✗☎❋✓✠✤✄✓✠✰✒☎❋◆❯☎✞✝✷✼✽✤✪✝✠✍✩✡✙✦✒✖✞☎❁☎✞❂❃✖★✕✗☎★✦✢✖✞☞❖✳✵✜❉✖✌✡✙✘✚✓❧✣✢✤❖☎✞✘ ✦✒✤✪✓q✰✫✡✌✂✹☎✄✓✠✰✢✕☛✘❁✰✻✏❀✝✸✣✢✟✗☎✆✳ (a) Server Stress 250 vcast 200 unicast 150 100 50 100 200 300 400 500 600 Overlay Size (b) Network Waste vcast unicast 100 200 300 400 500 600 Overlay Size (c) Link Stress vcast unicast (d) Access Distance 100 200 300 400 Overlay Size 500 600 7.8 7.6 7.4 7.2 6.8 6.6 6.4 6.2 vcast unicast 100 200 300 400 Overlay Size 500 600 ỗ ➾❡è✫é❄➼✯➵❯❚✬➺❑❱✮✜❋➵❀➚✆í✐ó❯ì ❁ ➯✹❄✐ð★➵✻➼✪➽❯➵✻➼♦ð★í★➼✯➵❀ð✌ð❳❲ ❁ ➲✳❄✐ì❄➵✻í☎❂✑ó✫➼❩❨ ❂❣➯✫ð★í✞➵❬❲ ❁ ➚✽❄✑➳✽➾❡ì❭❨❪ð★í✞➼✪➵❀ð✌ð❳❲❦➯✒ì✵ị ❁ ị❅❄✑➯✫➚✹➚✆➵❀ð✌ð✥ị❄➾✽ð★í★➯✫ì❄➚✆➵ ⑨✻✕✗✦✒✖★☎■✓✠✰✢☎✶✣✢☎★✟✗✕✗✂✹☎✞✝✷☞❢◆✫✡✯✓✠✰✒✘✴✕✗✦❫✤✯✂✹☎✞✝✠✟☛✡★☞✧✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓q✘✷✖✸✰✒☎★✍❃☎★✘✴✡✯✝✠☎ ✞☎ ✦✫✣❀❅➀✘✚☞❀✘✚✓✠☎★✍t✓✠✤■☎✞✦✫✣❀❅➀✘✚☞❀✘✚✓✠☎★✍➆✤✙✦◗✓✠✤✆◆❃✤✪✼❯✓✠✰✒☎❁✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲■✦✢☎✞✓❘❊❋✤✙✝✠❙❯✛ ✓✠✰✢☎✞☞❢✍◗✏✒✘✚✓q✕✗✦❖✓✷✝✠✤✻✣✢✏✢✖★☎❣✡✆✣✒✣❀✕✔✓✠✕☛✤✙✦✫✡✪✟❄✟✗✤✹✡✙✣❇✤✙✦❫✓✠✰✒☎❥✦✢☎✞✓❘❊❋✤✙✝✠❙❢✓✷✝✸✡✯❂❃✖✆✳ ✇✰✢☎❥✝✠☎★✘✷✏✒✟✔✓✠✘q✕☛✦❇⑧✵✕✗✲❀✳✴⑥✢➊♥✾✫➋❁✘✷✰✢✤✌❊❩✓✠✰✒✡✪✓❉✜✄✖✌✡✪✘✚✓❉✕✗✦✢✖✞✝✠☎✌✡✙✘✷☎✞✘❉✓✠✰✒☎✶✦✢☎✞✓✷❅ ❊❋✤✙✝✠❙❚❊❁✡✪✘✚✓✠☎✧❊✴✕✔✓✠✰❱✡❍✼♥✡✪✖✞✓✠✤✙✝✎✤✙✼■➃✪❅❘➐❇✓✠✕✗✍❃☎★✘✥✡✙✘❃✖★✤✙✍❃◆✫✡✪✝✠☎★✣❚✓✠✤✐▲✚✭ ▼✧✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✌✳❋✇✰✒✕✗✘❁✕✗✘❁✦✒✤✙✓❁✓✠✰✒✡✪✓✴✘✷☎★✂✆☎✞✝✠☎✄✘✷✕✗✦✒✖✞☎❥✤✙✓✠✰✒☎✱✝❁✲✆✤❖✤✻✣✧✘✷✖✸✰✒☎✞✍❃☎★✘ ✘✷✏✢✖✱✰❬✡✙✘❇⑤✔➎✌❷✯⑦■◆✢✝✠✤✯✂✻✕☛✣✢☎✌✣④✖★✟✗✤✆✘✷☎❇✦✻✏✒✍✑✾❯☎✞✝✠✘★✳❲➪❦✂✹☎★✦♦✓✠✰✒✤✙✏✒✲✆✰❪✜✄✖✌✡✪✘✚✓ ✡✪✦✫✣❱✭❦✏✢✝✠☎❇❳❉✦✒✕✗✖✌✡✙✘✚✓✎✰✒✡✯✂✆☎❍✘✷✕☛✍❃✕✗✟☛✡✪✝❢✦✒☎✱✓❘❊✤✪✝✠❙♦❊✡✙✘✚✓✠☎✆✛q✜❉✖✌✡✙✘✚✓✧✣✢✕✗✘✚❅ ✓✷✝✠✕✗✾✢✏✢✓✠☎★✘✬✓✠✰✒✕✗✘❄✦✢☎✞✓❘❊❋✤✙✝✠❙✄❊✡✙✘✚✓✠☎❧✼✽✡✙✕✔✝✠✟✔☞✑✡✙✍❃✤✆✦✢✲❁✍❃✤✙✝✠☎❑◆✒✰❖☞❀✘✷✕✗✖✌✡✙✟✹✟✗✕✗✦✒❙✻✘★✳ ➤❋✤✙✦✒✘✷☎✌✺❖✏✢☎★✦❖✓✠✟✗☞❖✛●✕✔✓❣✰✫✡✙✘✶✡❢✟☛✤✌❊❋☎✞✝❣✟☛✕✗✦✢❙❭✘✚✓✷✝✠☎✞✘✷✘✶✓✠✰✒✡✙✦❤✭❑✏❀✝✠☎❃❳✄✦✒✕✗✖✌✡✪✘✚✓ ✣❀✤❖☎★✘✶➊r⑧✵✕✗✲✢✳❯⑥❀➊♥✖✯➋✷➋✱✳❑✇✰✒☎✱✝✠☎✞✼✽✤✪✝✠☎✆✛❯✜✄✖★✡✙✘✚✓✴◆✢✝✠✤✯✂✻✕☛✣✢☎★✘✴✾❯☎✞✓✷✓✠☎✱✝✴◆❯✤✙✓✠☎★✦❖✓✠✕☛✡✙✟ 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✣✢☎✞✍❃✤✆✦✒✘✚✓✷✝✸✡✯✓✠☎★✘❥✓✠✰✫✡✯✓✑✓✠✰✢☎■➅✚✤✆✕✗✦✢✕☛✦✢✲❇✤✙✼q✡❫✦✒☎✱❊➠✖★✟✗✕✗☎★✦❖✓✑✕☛✘✑✡✙✘✶✼♥✡✪✘✚✓❃✡✪✘ ✘✷☎★✦✒✣✢✕✗✦✒✲✩✡✪✦✫✣✧✝✠☎★✖★☎✞✕☛✂✻✕✗✦✒✲✎✣✢✡✪✓✸✡◗✼❡✝✠✤✙✍➷✓✠✰✢☎❥✘✷☎✞✝✠✂✹☎✞✝✌✳❉➶✄✕✗✂✹☎✞✦❫✓✠✰✒☎❥◆✢✝✠☎✱❅ ✂✻✕✗✤✆✏✒✘❥✝✠☎★✘✷✏✢✟✔✓✠✘❣✘✷✰✢✤✌❊✴✕☛✦✢✲❫✓✠✰✫✡✯✓✶✜✄✖✌✡✪✘✚✓✑✰✒✡✙✘❣✡✧✟✗✤✌❊☎✞✝✑✟✗✕✗✦✒❙❇✘✚✓✷✝✠☎★✘✷✘★✛❦✡ ✟✗✤✌❊☎✞✝❧✘✷☎✞✝✠✂✹☎✞✝❧✘✚✓✷✝✠☎★✘✷✘★✛❖✕✔✓❑✕✗✘❧✖✞✤✆✦✻✂✻✕☛✦✢✖★✕✗✦✒✲✄✓✠✰✒✡✪✓❦✓✠✰✒☎❁◆✒✡✪✓✠✰❣✼✽✤✙✝❧✘✷☎★✦✒✣✢✕✗✦✒✲ ✣✒✡✯✓✸✡✩✼✿✝✠✤✆✍❿✡❃✓✷✝✠☎★☎❣✓✠✤✎✓✠✰✢☎◗✖★✟✗✕✗☎★✦❖✓❥✕✗✦❇✜✄✖✌✡✪✘✚✓❥✕✗✘✶✡✎✟✗✤✙✓■✾❯☎✞✓✷✓✠☎✞✝■✓✠✰✒✡✙✦ ✓✠✰✒☎✄◆✫✡✪✓✠✰✧◆✢✝✠✤✯✂✻✕✿✣❀☎✌✣❃✓✠✤◗✓✠✰✒☎❥✖★✟✗✕✗☎★✦❖✓q✏✒✘✷✕✗✦✒✲✥✭❑✏❀✝✠☎■❳✄✦✢✕☛✖★✡✙✘✚✓q✤✯✂✹☎✞✝✠✟☛✡★☞❖✳ s ☎✎✘✚✓✠✏✫✣❀✕✗☎✌✣♦✰✢✤✌❊➫✦✒☎✞✓❆❊✤✪✝✠❙❚✟☛✤✆✡✆✣♦✕☛✦✢✖★✏✢✝✷✝✠☎★✣④✾❖☞❚✜❉✖✌✡✙✘✚✓✥✕☛✘✩✣❀✕✗✘✚❅ ✓✷✝✠✕✗✾✒✏❀✓✠☎✌✣❚✡✙✍❃✤✙✦✒✲❍✓✠✰✒☎✩✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲❍✦✢☎✞✓❘❊❋✤✙✝✠❙❽✾❖☞❽☎✞✘✚✓✠✕☛✍✩✡✯✓✠✕✗✦✒✲❍✓✠✰✒☎ ✦✒✤✻✣❀☎✩✘✚✓✷✝✠☎★✘✷✘✥✡✯✓◗☎✌✡✪✖✱✰❚✦✢☎✞✓❘❊❋✤✙✝✠❙✐✦✒✤✻✣✢☎✙✳❭❶➠✲✆✤❖✤✻✣❚✘✷✖✸✰✒☎★✍❃☎✩✘✷✰✒✤✙✏✒✟☛✣ ✰✫✡✌✂✹☎❦✏✢✦✒✕✔✼✽✤✪✝✠✍➄✦✒✤✻✣❀☎❧✘✚✓✷✝✠☎✞✘✷✘✵✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠✕✗✤✆✦❥✓✠✤❁✝✠☎✌✣✢✏✢✖★☎❧✾❯✤✪✓✷✓✠✟✗☎★✦✒☎★✖✸❙■✕✗✦ ✓✠✰✒☎✄✦✒☎✞✓❆❊✤✙✝✠❙❯✳❧✇✰✒☎❥✘✚✓✷✝✠☎✞✘✷✘✷☎★✘q✼❡✤✙✝✄✡✙✟✗✟✵⑥✙❷✆❷◗✦✢☎✞✓❘❊❋✤✙✝✠❙✎✦✒✤✻✣❀☎★✘❁✼✽✤✙✝✄✣✢✕✔✼✿❅ ✼✽☎✱✝✠☎★✦❖✓✮✤✯✂✹☎✞✝✠✟☛✡★☞✶✘✷✕☛➉✞☎★✘❦✡✪✝✠☎❁✣✻✝✸✡★❊✴✦✑✕✗✦✑⑧✵✕☛✲❀✳✆➐✻✳✵▲➀✓✮✕✗✘✵✦✒✤✪✓✠☎✞❊✤✪✝✷✓✠✰❖☞❥✓✠✰✫✡✪✓ ✡✑✼❡☎✞❊æ✦✒✤✻✣✢☎✞✘q✰✒✡✌✂✹☎■✰✒✕✗✲✙✰❫✦✒✤✻✣❀☎■✘✚✓✷✝✠☎★✘✷✘✷☎★✘★✳❋✇✰✒☎★✘✷☎❥✦✢✤✻✣✢☎★✘q✡✯✝✠☎✶✡✙✖✞✓✠✏❀❅ ✡✙✟✗✟✔☞✎✓✠✰✒☎■✕✗✦❖✓✠☎✞✝✷❅❆✣✢✤✙✍✩✡✙✕✗✦❢✦✢✤✻✣✢☎★✘✓✠✰✒✡✪✓✴✍❃✤✙✘✚✓✴✤✙✼✵✓✠✰✢☎❥✣✢☎★✟✗✕✗✂✹☎✞✝✷☞✎◆✒✡✪✓✠✰✒✘ ✰✫✡✌✂✹☎✥✓✠✤❍✲✙☎✞✓❣✓✠✰✢✝✠✤✆✏✢✲✆✰✬✳❫⑩✄✤✧✤✪✂✆☎✞✝✠✟☛✡✌☞❤✍◗✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓✶✓✠✤✆◆❯✤✆✟✗✤✙✲✙☞❽✖✞✤✆✏✒✟☛✣ ✡✌✂✹✤✆✕☛✣❫✓✠✰✒☎✞✘✷☎✑✰✢✤✙✓■✘✷◆❯✤✪✓✠✘★✳❥✭❦✏✢✓✷✓✠✕✗✦✒✲❃✓✠✰✢☎★✘✷☎✑✦✢✤✻✣✢☎★✘✄✡✙✘✷✕☛✣✢☎✙✛✬✓✠✰✢☎✑✦✢✤✻✣✢☎ ✘✚✓✷✝✠☎★✘✷✘❢✕☛✘✎✰✒✕✗✲✙✰✒✟✔☞❱✾✒✡✙✟☛✡✙✦✢✖★☎✌✣❲✡✙✍❃✤✙✦✒✲❤✓✠✰✢☎❇✤✙✓✠✰✒☎✱✝✧✦✢☎✞✓❘❊❋✤✙✝✠❙♦✦✒✤✻✣✢☎✞✘ ➊♥☎✆✳ ✲✢✳✗✛❋✡✙✾❯✤✙✏✢✓✩➛✧✓✠✕✗✍❃☎★✘✑✾❯☎✞✓✷✓✠☎✞✝❣✓✠✰✫✡✙✦♦✭❦✏✢✝✠☎✎❳✄✦✢✕☛✖★✡✙✘✚✓✥✕✗✦❚✓✠☎✞✝✠✍❃✘❣✤✙✼ ✘✚✓✸✡✙✦✒✣✒✡✯✝✸✣❤✣✢☎✞✂❀✕☛✡✯✓✠✕☛✤✙✦❯➋✱✳✥✇✰✒☎✞✝✠☎✞✼❡✤✙✝✠☎✆✛✵✟☛✤✆✡✆✣❤✾✒✡✙✟☛✡✙✦✢✖★✕✗✦✒✲❢✕☛✘❣✡✪✖✱✰✢✕☛☎✞✂✹☎✌✣ ✾❖☞❥✜✄✖★✡✙✘✚✓✌✳❦✇✰✢✕☛✘✮✕✗✘✮☎✞❏❀◆✢✟✿✡✪✕✗✦✫✡✙✾✢✟✗☎✘✷✕✗✦✒✖★☎✜❉✖✌✡✙✘✚✓❄✼✽✤✆✟✗✟✗✤✌❊✴✘❑✓✠✰✢☎❋♣q✤✆✏✢✦✫✣❀❅ ✝✠✤✆✾✢✕✗✦❍✍✩✡✙✦✒✦✢☎✞✝✴✓✠✤✩✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠☎✶✓✠✰✢☎✶✘✷☎✞✝✠✂✻✕☛✖✞☎✑✟✗✤✹✡✙✣❍✤✪✂✆☎✞✝■✡✪✟✗✟✵✤✯✂✹☎✞✝✠✟☛✡★☞ ✦✒✤✻✣❀☎★✘❁❊✴✰✒✕✗✖✸✰❍✡✪✝✠☎■✝✸✡✪✦✫✣✢✤✙✍❃✟✔☞❢✟✗✤❖✖✌✡✯✓✠☎✌✣✧✕✗✦✧✓✠✰✢☎■✦✒☎✞✓❆❊✤✪✝✠❙✈✳ ▲❘✦❇✓✠✰✒☎✑✘✷☎★✖★✤✙✦✫✣❇✘✷✕☛✍✑✏✒✟☛✡✪✓✠✕✗✤✙✦❤✘✷✖★☎★✦✒✡✪✝✠✕✗✤✢✛●❊☎❃✡✪✟✗✟☛✤✌❊❻✡✩✦❀✏✢✍◗✾❯☎✞✝✄✤✙✼ ✦✒✤✻✣❀☎★✘■✓✠✤✧✾❯☎✑✓✠✏✢✝✠✦✒☎★✣❭✤✪➂✮✳ Ï ✕✗✘■✓✠✰✢☎✥◆✢✝✠✤✙✾✫✡✙✾✢✕✗✟☛✕✔✓❆☞❭✓✠✰✒✡✪✓✶✡✎✦✒✤✻✣❀☎✥✕✗✘ ✤✙➂♦✣❀✏✒☎✶✓✠✤❫✡✩✼♥✡✙✕✗✟✗✏✢✝✠☎✙✳ s ☎◗✖★✤✙✍❃◆✒✏✢✓✠☎★✣❍✓✠✰✢☎◗✍❃☎✞✓✷✝✠✕✗✖★✘❉✼✽✤✙✝❥✓✠✰✢☎✑✓✷✝✠☎★☎ ✡✪✼✿✓✠☎✞✝✑✡✧✦✻✏✒✍✑✾❯☎✞✝❥✤✙✼✦✒✤✻✣✢☎✞✘✶✡✪✝✠☎❃✘✚❊✴✕✔✓✠✖✱✰✢☎✌✣✐✓✠✤✧✓✠✰✢☎✥✤✙➂④✘✚✓✸✡✯✓✠☎✆✛❦✡✪✦✫✣ ✼✽✤✪✝✥✓✠✰✒☎❃✓✷✝✠☎★☎❢✡✪✼✿✓✠☎✞✝✥✾❯☎✞✕☛✦✢✲❇✘✷☎★✟✔✼❡❅➀✤✙✝✠✲✆✡✙✦✒✕✗➉★☎★✣❬✡✙✖✞✖★✤✙✝✸✣❀✕☛✦✢✲❍✓✠✤❇✓✠✰✢☎✎✡✙✟✔❅ ✲✆✤✪✝✠✕✔✓✠✰✒✍Ú◆❀✝✠☎★✘✷☎★✦❖✓✠☎✌✣④✕☛✦❱⑨❀☎★✖✱✓✠✕☛✤✙✦❱➃✻✳ ⑥✻✳❲⑧✒✤✪✝✩✘✷✕✗✍❃◆✒✟✗✕✗✖★✕✔✓❘☞♦✡✙✦✒✣❪✣❀✏✒☎ ✓✠✤✐✓✠✰✢☎❍✣✢✕✔❂❃✖✞✏✒✟✔✓❘☞④✤✪✼❥✍❃✤✻✣✢☎★✟✗✕✗✦✒✲❭✓✠✰✒☎❢✏✒✦✫✣❀☎✞✝✠✟✔☞❀✕☛✦✢✲❤✦✢☎✞✓❘❊❋✤✙✝✠❙❽✓✷✝✸✡✪✼✿❅ ♠✫✖✙✛✒❊☎❣✡✪✘✷✘✷✏✒✍❃☎✌✣❢✓✠✰✒✡✪✓✴✓✠✰✒☎✶✡✯✝✷✝✠✕✗✂✆✡✪✟✮✣✒✡✯✓✸✡✑✝✸✡✪✓✠☎❣✡✪✓✄✡✥✦✒✤✻✣❀☎✶✕☛✘q✤✆✦✢✟✔☞ ✡✪➂✈☎✞✖✞✓✠☎✌✣❚✾❖☞✐✓✠✰✢☎❢✦✻✏✒✍✑✾❯☎✞✝✶✤✙✼❉✤✆✏❀✓✠✲✆✤✙✕☛✦✢✲❇✘✚✓✷✝✠☎✌✡✙✍❃✘◗✡✪✓◗✓✠✰✢☎✩◆✫✡✪✝✠☎✞✦✻✓ ✦✒✤✻✣❀☎✆✳❑✇✰✒☎✱✝✠☎✞✼✽✤✪✝✠☎✆✛❯✖✸✰✒✕✗✟☛✣❀✝✠☎★✦❢✤✙✼❦✡❣✦✒✤✻✣✢☎❥✰✒✡✌✂❀✕✗✦✢✲✑✓✠✰✒☎✄✍❃✤✆✘✚✓❁✤✙✏✢✓✠✲✆✤✪❅ ✕✗✦✒✲❉✘✚✓✷✝✠☎✌✡✙✍❃✘✮✘✷✰✢✤✆✏✒✟☛✣❣✾❯☎❁✡✆✣✯➅✚✏✒✘✚✓✠☎★✣❣♠✒✝✠✘✚✓❦✕✗✦✑☎✌✡✙✖✸✰◗✘✷☎★✟✔✼✿❅❆✤✪✝✠✲✹✡✪✦✒✕✗➉✌✡✪✓✠✕✗✤✙✦ ◆✒✰✒✡✙✘✷☎✆✳✑⑧✵✕✗✲✢✳●❸❀➊r✡❀✛●✖✆✛●✣✫➋q✼❡✤✆✏✒✦✒✣❇✓✠✰✒✡✪✓■✓✠✰✢☎✑✤✯✂✹☎✱✝✠✟✿✡★☞❇✾❯☎✞✼❡✤✙✝✠☎◗✝✠☎✱♠✫✦✒☎✱❅ ✍❃☎★✦❖✓❉✣✢✤❖☎★✘❉✦✒✤✪✓■✖✸✰✫✡✙✦✢✲✆☎❣✍◗✏✢✖✱✰❢✤✆✦❇✟✗✕☛✦✢❙❫✘✚✓✷✝✠☎★✘✷✘★✛✬✡✪✖★✖★☎★✘✷✘❥✣❀✕✗✘✚✓✸✡✙✦✒✖✞☎✆✛ ✡✙✦✒✣✐✦✢☎✞✓❘❊❋✤✙✝✠❙❫❊❁✡✪✘✚✓✠☎✆✳✩➪✮❏❀✖★☎★◆✢✓✠✕✗✤✙✦✫✡✙✟✗✟✔☞❖✛❄❊✴✰✢☎★✦❭✍❃✤✆✘✚✓✶✤✙✼❧✓✠✰✒☎✥✦✢✤✻✣✢☎ ✝✠☎★✍❃✤✯✂✙✡✙✟✗✘❣✡✪✝✠☎✎✣✢✏✢☎◗✓✠✤❫✼♥✡✪✕☛✟✗✏❀✝✠☎❭➊ Ï ×➫❷✻✳☛➎✌➋✱✛✮✓✠✰✒☎❃✘✷☎✞✝✠✂✆☎✞✝❣✘✚✓✷✝✠☎★✘✷✘✑✕✗✦❀❅ ✖✞✝✠☎✌✡✪✘✷☎★✘❥✘✷✕✗✲✆✦✢✕✗♠✒✖✌✡✙✦❖✓✠✟✔☞❚➊r⑧✵✕✗✲✢✳✬❸❀➊♥✾❯➋✷➋✱✳■✇✰✒✕✗✘✄✕✗✘❥✡✪✦✻✓✠✕✗✖★✕✗◆✒✡✪✓✸✡✙✾✢✟✗☎◗✘✷✕✗✦✒✖★☎ ❊✴✰✒☎✞✦❇✡✥✦✒✤✻✣✢☎❥✼✽✡✙✕✗✟✗✘★✛❄✡✪✟✗✟✵✤✙✼❑✕✔✓✠✘❉✖✸✰✒✕✗✟☛✣❀✝✠☎✞✦❇✡✪✝✠☎✶✝✠☎★✖★✤✆✦✢✦✒☎★✖✱✓✠☎✌✣✧✓✠✤✥✓✠✰✒☎ ✘✷☎✞✝✠✂✹☎✱✝✌✳✮❈✄✤✌❊☎✞✂✹☎✞✝✌✛✆✡✪✼❡✓✠☎✱✝❑✝✠☎★✡✆✣✪➅❘✏✒✘✚✓✠✕✗✦✒✲❉✓✠✰✒☎✾✢✏✢✝✸✣✢☎✞✦✒☎✌✣✻❅❆✘✷☎✱✝✠✂✹☎✞✝✵✤✯✂✹☎✱✝✷❅ ✟☛✡★☞❖✛✹✓✠✰✒☎❁✘✷☎✞✝✠✂✆☎✞✝❑✘✚✓✷✝✠☎★✘✷✘❋✕✗✘❦✝✠☎✌✣✢✏✢✖★☎✌✣✑✓✠✤✶✡✪◆✒◆✢✝✠✤✆✡✙✖✸✰✥✓✠✤✄✓✠✰✫✡✯✓❋✤✪✼✬✡■✦✒✤✪✝✷❅ ✍✩✡✙✟✗✟✔☞✩✖★✤✙✦✒✘✚✓✷✝✠✏✒✖✱✓✠☎✌✣✎✜❉✖✌✡✙✘✚✓✴✤✯✂✹☎✱✝✠✟✿✡★☞❃✓✷✝✠☎★☎✙✳❑✇✰✒✕✗✘❁✘✚✓✠✏✫✣✻☞✩✘✷✰✒✤✌❊✴✘✓✠✰✒☎ ◆❯✤✙✓✠☎✞✦✻✓✠✕☛✡✪✟❁✡✆✣✢✡✙◆✢✓✸✡✪✾✒✕✗✟✗✕✔✓❘☞❽✤✪✼✴✜✄✖✌✡✪✘✚✓◗✓✠✤❍✖✸✰✫✡✪✦✒✲✆☎✞✘✑✕✗✦❚✦✒☎✱✓❘❊✤✪✝✠❙✐✘✚✓✸✡✯❅ ✓✠✏✒✘★✳❉✁✄✏❀✝q◆✢✝✠☎★✟✗✕✗✍❃✕✗✦✫✡✪✝✷☞✧◆✢✝✠✤✪✓✠✤✙✓❘☞❀◆❯☎✶✘✚☞❀✘✚✓✠☎★✍➷✡✙✟✗✘✷✤❃✝✠☎★◆❯✤✙✝✷✓✠✘❉✘✷✕✗✍❃✕☛✟☛✡✯✝ ◆❯☎✞✝✷✼❡✤✙✝✠✍✩✡✙✦✢✖★☎❥◆✫✡✯✓✷✓✠☎✞✝✠✦✒✘❁✤✙✦✧✓✠✰✒✕✗✘q✡✆✣✢✡✙◆❀✓✸✡✙✾✒✕✗✟✗✕✔✓❘☞❢✤✙✼✮✜❉✖✌✡✙✘✚✓✌✳ ✇❄✤❫✕✗✦✻✂✹☎★✘✚✓✠✕✗✲✆✡✪✓✠☎❃❊✴✰✒☎✞✓✠✰✢☎✞✝✶✓✠✰✒☎✥✝✠☎✞♠✒✦✒☎✌✣❭✤✯✂✹☎✞✝✠✟☛✡★✑☞ ✴ ✘❣✘✷☎✞✝✠✂✻✕✗✖★☎✩✟☛✤✆✡✆✣ ✕✗✘✑✾❯☎✱✓✷✓✠☎✞✝❣✾✫✡✙✟☛✡✪✦✒✖★☎✌✣✐✤✪✂✆☎✞✝❣✦✒☎✞✓❆❊✤✙✝✠❙❭✦✒✤✻✣❀☎★✘★✛✵❊❋☎✎✖✞✤✆✍❃◆✒✏❀✓✠☎✌✣✐✦✢✤✻✣✢☎ ✘✚✓✷✝✠☎★✘✷✘◗✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏✢✓✠✕✗✤✙✦❤✼✽✤✪✝◗✓✠✰✒☎✥✝✠☎✱♠✫✦✒☎★✣❤✤✯✂✹☎✞✝✠✟☛✡★☞❚✡✙✦✒✣❤✖★✤✙✍❃◆✫✡✪✝✠☎★✣❤✕✔✓ ❊✴✕✔✓✠✰✐✓✠✰✒✡✪✓✶✤✙✼❋✓✠✰✒☎✥✤✯✂✹☎✞✝✠✟☛✡★☞❭✾❯☎✞✼✽✤✪✝✠☎✥✝✠☎✞♠✫✦✢☎★✍❃☎★✦❖✓✌✳✑➍■✏✒☎◗✓✠✤✎✓✠✰✒☎◗✝✠☎✱❅ ✍❃✤✯✂✆✡✪✟✢✤✪✼✈✦✒✤✻✣❀☎★✘★✛✹✓✠✰✒☎❁✤✯✂✹☎✱✝✠✟✿✡★☞✑✟✗✤✹✡✆✣✥✍✩✡★☞❣✾❯☎★✖★✤✙✍❃☎❁✘✷❙✹☎✞❊❋☎✌✣❃✡✙✍❃✤✙✦✒✲ ✦✒☎✱✓❘❊✤✪✝✠❙❥✦✒✤✻✣❀☎★✘★✳✵❈❉✤✯❊❋☎★✂✹☎✞✝✌✛✆✡✪✼✿✓✠☎✞✝✵✓✠✰✢☎❋✘✷☎★✟✔✼❡❅❆✡✙✣✪➅✚✏✢✘✚✓✠✍❃☎★✦❖✓✌✛✯✓✠✰✒☎❋✦✢✤✻✣✢☎ ✘✚✓✷✝✠☎★✘✷✘q✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠✕✗✤✆✦✧✕✗✘q✡◗✟✗✤✙✓q✍❃✤✪✝✠☎✄✏✒✦✢✕✔✼✽✤✙✝✠✍❫✳❑✇✰✢☎■✝✠☎★✘✷✏✒✟✔✓✠✘✼❡✤✙✝✄✡✙✦ ☎✞❏✢✡✙✍❃◆✢✟✗☎❧✘✷✖★☎✞✦✫✡✪✝✠✕✗✤✄✡✪✝✠☎❁✣✻✝✸✡✌❊✴✦❣✕✗✦❣⑧✵✕☛✲❀✳✙❸✢➊♥☎✆✛✪✼✸➋✱✳✮▲❆✟☛✟✗✏✢✘✚✓✷✝✸✡✪✓✠☎✌✣✶✕✗✦✶✓✠✰✢✕✗✘ ♠✫✲✙✏✢✝✠☎✥✕✗✘■✓✠✰✢☎✥✤✯✂✹☎✞✝✠✟☛✡★☞❭❊✴✕✔✓✠✰❽❹✙❷✆❷❢✦✒✤✻✣✢☎✞✘✶✝✠☎✞✍❃✤✪✂✆☎✌✣❫❊✴✕✗✓✠✰ Ï × ❷❀✳✗➎ ✼❡✝✠✤✙✍②➃✆❷✙❷✧✦✒✤✻✣❀☎★✘❥✕✗✦✒✕✔✓✠✕☛✡✙✟✗✟✔☞❖✳✩✇✰✒✕✗✘❥✘✚✓✠✏✫✣✻☞❇✘✷✰✒✤✌❊✴✘❥✓✠✰✫✡✯✓❥✜✄✖✌✡✪✘✚✓✶✰✫✡✪✘ ✡❥◆❯✤✙✓✠☎★✦❖✓✠✕☛✡✙✟❯✕✗✦✩❙✹☎★☎✞◆✒✕✗✦✒✲❥✓✠✰✒☎✴✤✯✂✹☎✞✝✠✟☛✡★☞❃✘✷☎✞✝✠✂✻✕✗✖★☎q✟✗✤✹✡✆✣❃❊☎✞✟☛✟❯✾✒✡✙✟☛✡✙✦✢✖★☎✌✣ ❊✴✕✔✓✠✰✒✤✙✏✢✓❁✾❯☎★✕✗✦✢✲◗✘✷✕✗✲✆✦✢✕✗♠✒✖✌✡✙✦❖✓✠✟✔☞✎✡✪➂✈☎✞✖✞✓✠☎✌✣✩✾✻☞◗✓✠✰✒☎✄✦✢☎★✲✹✡✯✓✠✕✗✂✹☎✄✖✸✰✫✡✪✦✒✲✆☎✞✘ ✕✗✦❫✦✒☎✱✓❘❊✤✪✝✠❙❃✓✷✝✸✡✪❂❃✖✆✳ CONCLUSION s ☎❉✰✫✡✌✂✹☎■◆❀✝✠✤✆◆❯✤✙✘✷☎✌✣✧✡❣✘✷✕☛✍❃◆✢✟✗☎✄☞❖☎✞✓❁☎✱❂❃✖★✕✗☎★✦❖✓✴✤✯✂✹☎✞✝✠✟☛✡★☞❢✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓ ✘✷✖✸✰✒☎★✍❃☎✆✛✫✖✌✡✙✟✗✟✗☎✌✣❍✜✄✖✌✡✪✘✚✓✌✛✬✡✙✘✄✡✩✍❃☎★✡✙✦✒✘✴✼✽✤✪✝❥◆✒✏❀✓✷✓✠✕✗✦✒✲✩✭✮✡✪✓✠✖✸✰✒✕✗✦✢✲✎✕✗✦❖✓✠✤ 200 Overlay Nodes 10 12 529 573 441 485 353 397 265 309 25 20 15 10 200 1.17 3.27 300 1.5 7.7 541 586 451 496 361 406 316 271 Underlying Node ID Underlying Node ID 100 0.82 5.85 181 91 136 589 505 547 463 421 337 379 295 169 211 253 46 0 Underlying Node ID Num of Overlay Nodes Vcast (Std Dev) Pure Unicast (Std Dev) 221 589 505 547 421 463 337 379 253 295 211 85 127 85 560 517 431 474 345 388 259 302 10 127 15 10 216 600 Overlay Nodes 30 43 15 130 Underlying Node ID Node Stress 20 Node Stress 20 173 500 Overlay Nodes 25 44 169 400 Overlay Nodes 25 87 Underlying Node ID Underlying Node ID 43 589 505 547 421 463 337 379 253 295 169 211 43 85 127 226 10 89 177 133 45 Node Stress 14 Node Stress 300 Overlay Nodes 12 Node Stress Node Stress 100 Overlay Nodes 400 2.02 11.99 500 2.38 12.49 600 2.73 10.12 ỗ ốộúũớớộớúỡớủúộ q ✡❫✖✞✏✢✝✷✝✠☎★✦❖✓✠✟✔☞❤✕✗✦❀✼✽☎✌✡✪✘✷✕☛✾✢✟✗☎✧▲✚✭➄▼✧✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✌✳❭➪❦✂✹☎★✦✐✓✠✰✒✤✆✏✢✲✆✰❚✣❀✕✔➂✈☎✞✝✠☎★✦❖✓ ✘✷✖✸✰✒☎✞✍❃☎★✘❥✤✆✦❤✡✙◆✒◆✢✟✗✕☛✖★✡✪✓✠✕✗✤✆✦❀❅❆✟✗☎★✂✆☎★✟❧✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓■✰✫✡✌✂✹☎✥✾❯☎★☎✞✦✐◆❀✝✠✤✆◆❯✤✆✘✷☎★✣ ✼❡✤✙✝✴✂✙✡✪✝✠✕✗✤✆✏✢✘❁✡✙◆✢◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✙✦✒✘★✛❀✜✄✖✌✡✪✘✚✓❁✰✫✡✪✘❁✣✢✕✗✘✚✓✠✕✗✦✒✲✙✏✒✕✗✘✷✰✒✕✗✦✢✲✥✡✙✦✒✣✩✣✢☎★✘✷✕✔✝✷❅ ✡✪✾✒✟✗☎■✼✽☎★✡✪✓✠✏✢✝✠☎✞✘★➥ ❴ ✇❄✤✙◆❯✤✆✟✗✤✆✲✪☞❀❅➀✟✗☎★✘✷✘ ➥✮✜✄✖★✡✙✘✚✓❁✣❀✤❖☎★✘❋✦✢✤✙✓❧✦✒☎★☎★✣◗✓✠✤❣◆❀✝✠✤✆◆✒✡✙✲✹✡✯✓✠☎❉✘✚✓✸✡✯✓✠☎ ✏✒◆✈✣✢✡✪✓✠☎★✘✸➡✯◆✢✝✠✤✙✾❯☎★✘✄✡✪✖✞✝✠✤✆✘✷✘q✓✠✰✒☎❥✦✢☎✞✓❘❊❋✤✙✝✠❙❯✛✒✓✠✰✻✏✒✘✴✡✌✂✹✤✙✕☛✣✢✕✗✦✒✲✥✓✠✰✢☎ ✖★✤✙✍❃◆✒✟✗☎✞❏❀✕✔✓❘☞❢✡✪✓✴☎✌✡✪✖✱✰✧✤✪✂✆☎✞✝✠✟☛✡✌☞❢✦✒✤✻✣❀☎✄✼✽✤✪✝■✣❀✤✆✕✗✦✒✲◗✘✷✤✢✳ ❴ ➟●✤✆✡✆✣✧✾✒✡✙✟☛✡✙✦✢✖★✕✗✦✒✲ ➥❁➪❑✂✹☎✞✦❇✓✠✰✢✤✆✏✢✲✆✰❍✕✗✍❃◆❯✤✙✝✷✓✸✡✪✦✻✓✌✛✢✓✠✰✒✕✗✘✄✕✗✘✷✘✷✏✢☎✑✕✗✘ ✦✒✤✪✓✧✍❃☎✞✦✻✓✠✕✗✤✙✦✒☎✌✣❱✕✗✦❲☎✌✡✯✝✠✟☛✕✗☎✞✝✧❊✤✙✝✠❙❬✤✆✦❲✤✯✂✹☎✞✝✠✟☛✡★☞❲✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✌✳ ✁✄✦✒☎❑✤✙✼✢✓✠✰✒☎❑✲✆✤✆✡✙✟✗✘❦✕☛✦✑✣✢☎✞✘✷✕☛✲✙✦✒✕✗✦✒✲q✜✄✖★✡✙✘✚✓✮✕✗✘✵✓✠✤q✲✆✕✗✂✹☎❋☎✞✂✹☎✞✝✷☞❥✦✢☎✞✓✷❅ ❊✤✪✝✠❙❇✦✒✤✻✣✢☎◗✡✙✦❭☎✌✺❖✏✫✡✪✟✮✖✱✰✒✡✙✦✒✖✞☎◗✓✠✤❢✘✷☎✱✝✠✂❀✕✗✖★☎◗✖★✟✗✕☛☎✞✦✻✓❥✝✠☎★✺✻✏✢☎★✘✚✓✠✘★✛ ✰✒☎✞✦✒✖★☎■✲✙✏✫✡✯✝✸✡✙✦❖✓✠☎★☎★✕✗✦✒✲❃✘✷☎✱✝✠✂❀✕✗✖★☎❥✟✗✤✆✡✆✣❫✾✫✡✪✟☛✡✙✦✒✖✞✕☛✦✢✲✢✳ ❴ ➟●✕✗✲✙✰✻✓❆❊☎★✕✗✲✙✰✻✓q✘✷☎★✟✔✼✿❅❆✖✞✤✆✦✢♠✒✲✆✏❀✝✸✡✙✾✒✟✗☎ ➥✬✜✄✖✌✡✪✘✚✓✵✡✪✟✗✟☛✤✌❊✴✘✮✡✙✣✪➅❘✏✒✘✚✓✠✍❃☎★✦❖✓✠✘ ✤✙✼❧✤✆✦❀❅➀✲✆✤✆✕✗✦✢✲✧✣❀☎★✟✗✕☛✂✆☎✞✝✷☞❍◆✫✡✯✓✠✰✒✘q✓✠✤✎✝✠☎✞Ü✒☎★✖✞✓❉✓✠✰✒☎✑✣❀☞❀✦✫✡✪✍❃✕☛✘✷✍❼✤✪✼ ✏✒✦✒✣✢☎✞✝✠✟✔☞❀✕✗✦✒✲■✦✢☎✞✓❘❊❋✤✙✝✠❙✶✓✷✝✸✡✪❂❃✖✙✳❑✁❉✓✠✰✒☎✞✝✮✓✠☎✞✖✱✰✢✦✒✕☛✺❖✏✒☎★✘❑✡✙✟✗✘✷✤❥✰✒✡✯✂✆☎ ✓✠✰✒✕✗✘❫✼❡☎✌✡✪✓✠✏❀✝✠☎✆✛❣✰✒✤✌❊☎★✂✆☎✞✝❇✜✄✖✌✡✪✘✚✓❭✣✢✤❖☎★✘❍✦✢✤✙✓❍✝✠☎✌✺❖✏✢✕✗✝✠☎❤✰✒☎✌✡✌✂❖☞ ➊♥☎✆✳ ✲✢✳✗✛❄◆❯☎✞✝✠✕✗✤✻✣✢✕✗✖✯➋✄✕✗✦❖✓✠☎✞✝✷❅➀✦✒✤✻✣✢☎✑✖★✤✆✍❃✍✑✏✒✦✢✕☛✖★✡✪✓✠✕✗✤✆✦❍✓✠✤✎✍❃☎✌✡✙✘✷✏❀✝✠☎ ✓✠✰✒☎✄✖★✤✆✦✢✲✆☎★✘✚✓✠✕✗✤✆✦❍✤✪✝✴✓✠✰✒☎✶✡✙✟✗✕✗✂✹☎★✦✢☎★✘✷✘✴✤✙✼❑✡◗◆✒✡✪✓✠✰✬✳ ⑨✻✕✗✦✒✖★☎✑✜✄✖✌✡✪✘✚✓❥✕✗✘❥✾✒✏✒✕✗✟✔✓❥✤✙✦❤✡✪✦✐✤✯✂✹☎✞✝✠✟☛✡★☞❖✛✈✕✔✓✶✍◗✏✢✘✚✓✄✕✗✦❖✓✷✝✠✤✻✣✢✏✢✖★☎✥✡✙✣❀❅ ✣❀✕✔✓✠✕☛✤✙✦✫✡✪✟❁✤✪✂✆☎✞✝✠✰✒☎✌✡✙✣④✡✙✘◗✖✞✤✆✍❃◆✫✡✯✝✠☎✌✣❽✓✠✤❇▲✚✭✉▼✧✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓✌✳❚❈✄✤✌❊☎✞✂✹☎✞✝✌✛ ✤✙✏✢✝❁✘✷✕✗✍✑✏✒✟☛✡✪✓✠✕✗✤✆✦✩✘✚✓✠✏✒✣❀☞◗✼❡✤✆✏✢✦✫✣✥✓✠✰✫✡✯✓✜✄✖★✡✙✘✚✓❁✕✗✦✒✖✞✏✢✝✠✘✡✶✟✗✤✌❊❲◆❯☎★✦✫✡✪✟✔✓❘☞❖✳ s ✰✒☎★✦❃✖★✤✙✍❃◆✫✡✯✝✠☎✌✣✑✓✠✤✶✭❦✏✢✝✠☎✴❳✄✦✢✕☛✖★✡✙✘✚✓✌✛✻✡■✖★☎✞✦✻✓✷✝✸✡✪✟✗✕☛➉✞☎✌✣❃✤✙✝✠✲✹✡✪✦✒✕✗➉✌✡✯✓✠✕☛✤✙✦ ✤✪✼❧✓✠✰✢☎✶✤✪✂✆☎✞✝✠✟☛✡✌☞❖✛✫✜✄✖✌✡✪✘✚✓✄◆❀✝✠✤✪✂✻✕☛✣✢☎✞✘❉✓✠✰✒☎✶✘✠✡✪✍❃☎✑✡✪✍❃✤✆✏✢✦✻✓❉✤✙✼❑✦✢☎✞✓❘❊❋✤✙✝✠❙ ✟✗✤✆✡✆✣❢✾✢✏✢✓✴✡❣✘✷✕✗✲✆✦✒✕✔♠✒✖✌✡✙✦❖✓✝✠☎✌✣❀✏✒✖✞✓✠✕✗✤✙✦✧✤✆✦✎✘✷☎✞✝✠✂✹☎✱✝❁✾❯✤✙✓✷✓✠✟✗☎★✦✢☎★✖✱❙❯✛❀◆✒✰❖☞❀✘✷✕✔❅ ✖★✡✙✟❄✟✗✕✗✦✒❙✎✡✪✦✫✣❢✦✢✤✻✣✢☎■✘✚✓✷✝✠☎✞✘✷✘★✳✇✰✢☎❥✣✢☎★✟☛✡★☞✎✼✽✤✙✝❉✡◗✖✞✟☛✕✗☎★✦❖✓❁✓✠✤❃✡✪✖★✖★☎★✘✷✘❉✡✙✦ ☎✱❏✢✕✗✘✚✓✠✕✗✦✒✲◗✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓❉✕✗✘q✡✙✟✗✘✷✤❃✟✗☎★✘✷✘★✳ 6.⑤✗➎✱⑦✶➪❁REFERENCES ✳✫➩❋✤✙✍❃✍✩✡✙✕☛✡✙✰✬✛✒➹✥✳✒➶✄✏✢✤✢✛✈▼✐✳✢❈✄✤✪✼✽✍✩✡✪✦✒✦●✛✢✡✪✦✫✣❫⑨❯✳✫✭✮✡✪✏✒✟♥✳ ➍■☎★✘✷✕✗✲✙✦❍✡✙✦✒✣✧✕✗✍❃◆✒✟✗☎★✍❃☎★✦❖✓✸✡✪✓✠✕✗✤✙✦❢✤✪✼❦✡◗✖✌✡✪✖✱✰✢✕☛✦✢✲✥✘✚☞❀✘✚✓✠☎★✍ ✼✽✤✪✝ ✘✚✓✷✝✠☎✌✡✪✍❃✕☛✦✢✲✥✍❃☎✌✣❀✕✿✡❣✤✯✂✹☎✞✝❁✓✠✰✒☎❥✕✗✦❖✓✠☎✞✝✠✦✢☎✞✓✌✳❀▲❘✍ ✦ ❵➔✷➑✌❛✸➓✠➓✷➧✙➙✽➦❜❛✙❝◗➑❞❝ ❀❞ ❡✒❈ ➓ ▼✢✝➙ ❢✙❀❞ ❡ ➨❤❣✐❣✳❣❦❥ ➓✠❜✙→✔❉÷ ❧✵➙ ↔ ✎ ➓ ❧❯➓✠☎❛ ❡❖➦❯➑✆→✗◗➑ ❛✙➣❢❜✙➦✫➧ ❘ ö✹ö❯→ ➙r❛✠❜✙❞♥➙r➑✪➦✒✕ ❝ ▼✢➣ ↔ ö❀➑✙❝✠➙ ↕✻↔ ✛✈▼❫✡★☞✧❹✙❷✙❷✆❷✻✳ ⑤ ❹✌⑦✑▼✐✳✒➹✥✳✒➩❧✝✸✡✆✣❀✘✷✰✫✡★❊❥✛❯➩q✳ s ✡✙✦✒✲❀✛❯⑨❯✳❯⑨✻☎★✦●✛✢➟❦✳❯➶■✡✪✤✢✛✹♠❀✳✫➹❥✏✢✝✠✤✙✘✷☎✆✛ ✭✮✳✫⑨❀✰✢☎★✦✒✤✌☞❖✛❀✡✪✦✫✣✧➍◗✳✢✇❄✤✌❊✴✘✷✟✗☎✞☞❖✳✫✭✵☎✞✝✠✕✗✤✻✣✢✕✗✖✶✾✢✝✠✤✹✡✙✣✢✖✌✡✪✘✚✓❉✡✙✦✫✣ ◆✫✡✪✓✠✖✸✰✒✕✗✦✢✲◗✘✷☎✞✝✠✂✻✕✗✖★☎★✘✴❅❑✕☛✍❃◆✢✟✗☎★✍❃☎★✦❖✓✸✡✪✓✠✕✗✤✆✦✬✛❀✍❃☎✌✡✙✘✷✏❀✝✠☎★✍❃☎★✦❖✓✴✡✙✦✒✣ ✡✙✦✫✡✪✟✔☞✢✘✷✕✗✘q✕✗✦❫✡✙✦✧✕☛✦❖✓✠☎✞✝✠✦✢☎✞✓✴✘✚✓✷✝✠☎✌✡✪✍❃✕☛✦✢✲✥✂✻✕☛✣✢☎★✤◗✓✠☎✞✘✚✓✠✾❯☎✌✣✬✳❀▲❘✦ ❵❁➔✚➑✌♦❛ ♥❑❤➑ ❝ ❘ q ➢ ♣ù➢❑➑✙r➦ ❝✌➓✱➔✠➓✱➦✫❛✱➓✑➑✙s ➦ ♣ ↕ → ❞♥➙ ↔ ➓✷➧✙➙r❜✪✛✫➤✡✪✦✫✡✙✣✒✡❀✛ ⑨❀☎★◆❀✓✠☎★✍◗✾❯☎✞✝✴❹✙❷✆❷✻➎✆✳ ⑤ ➃✯⑦✑⑨✈✳ s ✳✒➤✡✪✝✷✓✠☎✞✝✄✡✙✦✒✣❢➍◗✳✢➍◗✳✢➪✴✳✫➟●✤✙✦✒✲✢✳✢▲❘✍❃◆❀✝✠✤✯✂❀✕✗✦✢✲ ✾✫✡✙✦✒✣❀❊✴✕☛✣❀✓✠✰❢☎✞❂❃✖★✕✗☎★✦✢✖✞☞❢✤✙✼✮✂✻✕☛✣✢☎★✤✪❅➀✤✆✦✢❅❆✣❀☎★✍✩✡✙✦✒✣✎✘✷☎✞✝✠✂✆☎✞✝✠✘★✳ ➢❑➑ ↔ ö ↕ ❞❆➓✱✕ ➔ ◆✶➓✱❞ ❖❋➑✪◗➔ ▲✪❝❣❜✙➦✫➧ ➨ ▼✽❙t◆✚▼✢➣✙❝✠❞❆➓ ↔ ❝✸✛❯➃❀➎✹➊✚➎✌➋✱➥ ➜✆♦➜ ✉✒➎✆➎✙➎✆✛ ▼❫✡✪✝✠✖✸✰❤➎✌➜✙➜✆➜❀✳ ⑤ ➏✪✇ ⑦ ✈◗✳✒➤❋✰✫✡★❊❁✡✯✓✠✰✒☎✆✛❯⑨✈✳✫▼✧✖✯➤✡✙✦✢✦✒☎✆✛✫✡✙✦✒✣✧➪❁✳✫➩❧✝✠☎✱❊☎✞✝✌✳✫❶❉✦ ✡✪✝✠✖✸✰✒✕✔✓✠☎★✖✞✓✠✏❀✝✠☎■✼✽✤✙✝q✕✗✦❖✓✠☎✞✝✠✦✒☎✱✓❉✖✞✤✆✦❖✓✠☎★✦❖✓q✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠✕☛✤✙✦❫✡✪✘✄✡✪✦ ✕☛✦❀✼❡✝✸✡✪✘✚✓✷✝✠✏✒✖✞✓✠✏❀✝✠☎❥✘✷☎✞✝✠✂✻✕☛✖✞☎✆✳✫❳❉✦✒◆✒✏✢✾✒✟✗✕✗✘✷✰✒☎✌✣❃❊✤✪✝✠❙❯✛✫⑧✒☎✞✾✢✝✠✏✫✡✯✝✷☞ ❹✙❷✆❷✙❷❀✳ ⑤ ➛✌✇ ⑦ ✈◗✳ ❅➀❈✑✳✒➤❋✰✻✏●✛✫⑨✈✳✒➶✑✳✒♣❉✡✙✤❀✛✈⑨❯✳✫⑨✻☎★✘✷✰✫✡✪✦●✛✒✡✙✦✒✣❢❈✑✁✳ ①❯✰✫✡✙✦✢✲✢✳ ➪❑✦✒✡✙✾✒✟✗✕✗✦✒✲◗✖★✤✆✦❀✼✽☎✞✝✠☎★✦✢✖★✕✗✦✒✲✩✡✪◆✒◆✒✟✗✕✗✖✌✡✯✓✠✕☛✤✙✦✒✘q✤✆✦✧✓✠✰✢☎■✕✗✦❖✓✠☎✞✝✠✦✒☎✞✓ ✏✒✘✷✕✗✦✒✲❃✡✪✦❫✤✯✂✹☎✞✝✠✟☛✡★☞✎✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓q✡✪✝✠✖✸✰✒✕✔✓✠☎★✖✞✓✠✏❀✝✠☎✆✳✫▲❆✦ ❘ q➢ ♣ ▼ ❩➨ ② ✬ ➢ ③✐♣✶♣❇✛✒⑨✢✡✙✦❢➍■✕✗☎★✲✆✤❀✛✈➤❶✶✛✫❶q✏✒✲✆✏✢✘✚✓❉❹✙❷✙❷❀➎✆✳ ⑤ ⑥✯⑦✑⑨✈✳✢➍■☎★☎✞✝✠✕✗✦✒✲❀✳✒❈❉✤✆✘✚✓q☎✞❏✻✓✠☎★✦✢✘✷✕☛✤✙✦❢✼❡✤✙✝❉✕☛◆❢✍◗✏✢✟✗✓✠✕✗✖✌✡✪✘✚✓✠✕✗✦✒✲✢✳ ❥✮④ ➢❦❤÷ ⑤❳⑤⑥⑤❩⑦✹✛✫❶❉✏✒✲✙✏✒✘✚✓❥➎★➜✆❸✆➜✻✳ ⑤ ➐✌⑦✑➤❉✳❯➶❉✝✠✕✔❊✤✻✣❀➉✆✛✬▼✐✁✳ ①✈✕✗✦✢❙✈✛✒▼✐✳✫➟●✕✗☎★◆❯☎✞✝✷✓✌✛✫➶✑✳❯✁✄✦✬✛✢✡✙✦✫✣ ♣❣✳✒⑨✻✓✠☎✞✕☛✦✢✍❃☎✞✓✠➉✆✳✒▼✧✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓❉✼❡✤✙✝q✘✠✡✌✂❀✕✗✦✢✲✆✘q✕☛✦❢✖✌✡✙✖✸✰✒☎✱❅❆✾✒✡✙✘✷☎✌✣ ✂❀✕☛✣❀☎★✤❃✣✢✕✗✘✚✓✷✝✠✕✗✾✒✏❀✓✠✕✗✤✆✦●✳✢▲❘s ✦ ❵❁➔✚➑✌♦❛ ♥❑❞➑ ❝ ❘ q➢ ♣✎⑧✢▼✽❵ ➨❤❣ ♣ ↕ → ❞♥➙ ↔ ➓✠➧✪➙r❜ ➢❑➑ ↔◗↕ ❞♥➙✽❜➦ ❛❢❜✙➦✫■ ➧ ◆✶➓✱❞ ❖❧➑✙◗➔ ▲✪➙❡✽➦ ❛✙✛✈⑨❀✡✙✍ ✦ ♠✙✤✆✘✷☎✆✛✒❳❥⑨✢❶✶✛✒❹✙❷✆❷✙❷❀✳ ⑤ ❸✯⑦✶➹✥✳✫❶✶✳✢❈❉✏✫✡✻✤✛ ✈✑✳✫➤✡✪✕♥✛❯✡✙✦✒✣❍⑨✈✳✒⑨✻✰✒☎★✏✬✳✒✭✮✡✯✓✠✖✱✰✢✕✗✦✒✲✢➥❧❶ ✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓❁✓✠☎★✖✱✰✢✦✒✕☛✺❖✏✒☎✄✼❡✤✙✝✴✓✷✝✠✏✒☎✄✂❀✕☛✣❀☎★✤✙❅➀✤✆✦❀❅❆✣✢☎★✍✩✡✪✦✫✣❃✘✷☎✞✝✠✂✻✕✗✖★☎★✘★✳ ▲❘✍ ✦ ❵➔✷➑✌♦❛ ♥❦❤➑ ❝ ❘ q➢ ♣⑨♣✙⑩✁❏❇❧ ➨ ♣ ❣ ❙ ➨ ❘ ✛❀◆✫✡✪✲✆☎★✘❥➎✌➜✻❉➎ ✉✻❹✙❷✆❷✻✛ ➩❧✝✠✕✗✘✚✓✠✤✆✟♥✛✫❳❣✳ ➹✥✳✗✛✫⑨❀☎★◆❀✓✠☎★✍◗✾❯☎✱✝■➎✌➜✙➜✆❸❀✳ ⑤ ➜✯⑦✑⑨✈✢✳ ♠✹✡✙✕✗✦●✛✢♣✶✳❯▼❫✡✪✰✫✡✌➅✷✡✙✦✬✛✫➍◗✳ s ☎✱✓✠✰✒☎✞✝✸✡✪✟☛✟♥✛✒✡✙✦✒✣❍➶✑✳✫➩❧✤✙✝✷✝✠✕✗☎★✟✗✟✗✤✢✳ ⑨❀✖✌✡✪✟✿✡✪✾✒✟✗☎✶✘✷☎★✟✔✼❡❅➀✤✙✝✠✲✆✡✙✦✢✕☛➉✞✕☛✦✢✲✩✤✪✂✆☎✞✝✠✟☛✡✌☞❀✘★✳✒✇❄☎★✖✸✰✒✦✢✕☛✖★✡✙✟✈✝✠☎★◆❯✤✙✝✷✓✌✛ s ✡✙✘✷✰✢✕✗✦✒✲✙✓✠✤✙✦❫❳✄✦✢✕✗✂✹☎✞✝✠✘✷✕✔✓❘☞❖✛✢❹✪❷✆❷✆❷✻✳ ⑤✔➎✌❷✯❈ ⑦ ♠✢✁✳ ♠✆✡✙✦✒✦✢✤✙✓✷✓✠✕♥✛✫➍✑✳✢➹✥✳✫➶✄✕✔➂✈✤✙✝✸✣✈✛❯✡✙✦✒✣❢➹✥✳✒➟❑✤✳ ♠✆✤✙✰✒✦✒✘✷✤✙✦●✳ ✁✄✂✹☎✞✝✠✖✌✡✪✘✚✓✌➥❦♣❉☎★✟✗✕☛✡✙✾✢✟✗☎❣✍✑✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓✠✕✗✦✢✲◗❊✴✕✔✓✠✰❍✡✙✦❢✤✪✂✆☎✞✝✠✟☛✡✌☞ ✦✒☎✞✓❆❊✤✙✝✠❙❯✳✢▲❘❑ ✦ ⑩❃▼ ❣ ◆ ➨❤❶ ▼✒➣ ↔ ö❀➑✪❝✸➙ ↕❀↔ ➑✙❊ ➦ ③❄ö✢➓✱➔✷❜✙❞♥➙✽❜➦ ❛✭▼✒➣✪❝✠❞❆➓ ↔ ❙✑➓✱❝✠✝➙ ❛✙➦✐❜✙➦❯➧ ➨ ↔ ö✫→☛➓ ↔ ➓✱➦✒❞➀❜✪❞♥➙r➑✙➦✒✛✫⑨✢✡✪✦❫➍■✕✗☎★✲✙✤✢✛✈➤❶✶✛✒✁✄✖✞✓✠✤✆✾❯☎✞✝ ❹✙❷✆❷✙❷❀✳ ⑤✔➎✆➎✱❈ ⑦ ♠✢✳✫➟✬✕✗☎★✾❯☎★✰✒☎✱✝✷✝✄✡✪✦✫✣❍▼✐✳✢⑩■✡✪✰✫✡✪✘★✳✫❶q◆✒◆✒✟✗✕✗✖✌✡✯✓✠✕☛✤✙✦✢❅➀✟☛✡★☞❖☎✞✝ ✍◗✏✒✟✔✓✠✕✗✖✌✡✪✘✚✓✠✕☛✦✢✲◗❊✴✕✔✓✠✰❍✣✢☎✞✟✿✡✪✏✒✦✒✡✌☞✩✓✷✝✠✕☛✡✙✦✢✲✆✏✢✟✿✡✯✓✠✕✗✤✆✦✒✘★✳✒▲❘✦ ② →✗➑✹➴✠❜✆→ 80 70 60 50 50 100 150 200 250 Number of Nodes Removed (b) 50 100 150 200 250 Number of Nodes Removed (d) 586 508 547 430 469 391 313 352 235 274 157 15 10 586 p=0.1 p=0.9 Re-created Refined (p=0.1) 508 20 547 469 391 Mean=0.67, Standard Deviation=2.05 25 430 10 30 313 20 352 30 (e) After Refinement 235 40 Underlying Node ID 274 50 250 157 Server Stress 60 200 (c) Access Distance p=0.1 p=0.9 Re-created Refined (p=0.1) 70 150 196 (a) 80 100 Number of Nodes Removed Number of Nodes Removed 196 50 250 79 200 118 150 10 79 100 118 50 40 30 20 p=0.1 p=0.9 Re-created Refined (p=0.1) 40 0.5 p=0.1 p=0.9 Re-created Refined (p=0.1) Mean=0.69, Standard Deviation=5.12 40 1.5 Node Stress 2.5 Node Stress Network Waste Link Stress Before Refinement 3.5 Underlying Node ID (f) ỗ ốộ ✸✾❹q➵✻❩➼ ✥➀ó✫❺➼ ✣✐➯✒ì✵➚✆❼ ➵ ❻✑✽➵ ✥➀ó✫➼✯➵❫➯✫ì❄ị❬✎ ê ✥❆í★➵✻➼✩ỵ❃➵❀➚✆ó❯❃ì ❽✵è❯é❄➼✯➯✒í✌➾✿ó❯ì✐❾s❿✹ỵ✩➵❜➀✠➚✙➼✪➵✻➯✢í★➵❀ị❭➁❚➼✪➵✻ú✵➼✯➵❀ð★➵❀ì✬í★ð✑í☛✺❄➵✧ó✢➽❯➵✻➼✪➳❡➯✽✸❊❂❃➾❡í☛✺ ír✺❄➵③ð★➯✹✣✐➵❬ì●é❭✣❇➲❦➵✻➼❽ó✁✥✩➼✯➵✤✣✐➯✫➾✽ì❄➾✽ì❄è➆ì❄ó✬ị❄➵❀ð❳❲✓❂❫✺❄➾✽➚❺✺❻➾✽ð❽➚✆ó✫ì✵ð★í★➼✪é✵➚✆í★➵❀ị ì●ó✫➼❺✣✐➯✫➳✽➳➂✸❻➯✒➚✹➚✆ó✫➼✪ị✵➾✽ì●ètí★ó➄đ❢➚✆➯✒ð★í❤ó❀➽❯➵❀➼✪➳❡➯✽✸t➲✵é✵➾✽➳✽ị✵➾❡ì❄è ú❦ó❯➳❡➾✽❳➚ ✸ ➨ ➦✒❞❆➓✱➔✸➦✈➓✱➃❞ ▼✒➣ ↔ ư❀➑✙❝✠➙ ↕✻❍ ↔ ➄ ❤➨ ❣✳❣✐❣➅② →✗➑✹➴✸➓✠❛✠➑ ↔ ✛✈❹✪❷✆❷❀➎✙✳ ⑤✔➎✌❹✯⑦✶➍◗✳✒✭✵☎★✦✫✣✢✡✙❙✙✡✪✝✠✕✗✘q✡✙✦✒✣❫⑨✈✳✫⑨❀✰✢✕♥✳✒❶❉➟✵▼✧▲✸➥✫❶q✦❫✡✙◆✢◆✒✟✗✕✗✖✌✡✪✓✠✕✗✤✙✦❫✟✗☎★✂✹☎★✟ ✍◗✏✢✟✔✓✠✕☛✖★✡✙✘✚✓✴✕✗✦✢✼✿✝✸✡✙✘✚✓✷✝✠✏✒✖✱✓✠✏✢✝✠☎✆✳✒▲❘✗ ✦ ⑩✑▼ ❣ ◆ ❤➨ ❶ ▼✒➣ ↔ ö❀➑✙❝✠➙ ↕✻↔ ➑✙➦ ❞ ❧✈➓✷☎❛ ❡✻➦❯➑✆→✗◗➑ ❛✙➙r➓✱❝❣❜✙➦❯❫ ➧ ▼✒➣✪❝✠❞❆➓ ↔ ❝✠✛✬⑨✢✡✪✦✢✼✿✝✸✡✙✦✒✖✞✕☛✘✷✖✞✤✢✛✈➤❶✶✛ ➨ ➦✒❞❆➓✱➔✸➦✈➓✱✕ ▼❫✡✪✝✠✖✸✰❇❹✪⑥✪❅❘❹✙❸✩❹✪❷✆❷❀➎✙✳ ⑤✔➎★➃✪⑦✑⑨✈✳✢♣❉✡✙✍❃☎★✘✷✰✬✛✢▲✸✳❀♣❉✰✢☎★☎✆✛✒✡✙✦✫✣✎➹✥✳❯➶✄✏✢✤✢✳✫▼✧✏✒✟✔✓✠✕✗✖✌✡✙✘✚✓q❊✴✕✔✓✠✰✧✖✌✡✪✖✱✰✢☎ ➊♥✍❃✖✌✡✪✖✱✰✢☎✯➋✱➥❑❶❉✦✧✡✆✣✒✡✪◆✢✓✠✕✗✂✹☎■➉✞☎✞✝✠✤✙❅❆✣✢☎✞✟✿✡★☞❢✂✻✕✿✣❀☎★✤✙❅➀✤✙✦✢❅❆✣✢☎★✍✩✡✪✦✫✣ ✘✷☎✞✝✠✂✻✕✗✖★☎✆✳✒▲❘✍ ✦ ❵➔✷➑✌♦❛ ♥❦❤➑ ❝ ➨❤❣✳❣✐❣❲➨ ◆ ④ ③✄✬➢ ③✐♣❇✛✒⑨✢✡✪✦✧➍■✕✗☎★✲✙✤✢✛ ❳❥⑨❀❶❣✛✒❹✙❷✙❷❀➎✙✳ ⑤✔➎✞➏✙⑦✑⑨✈✳✫⑨❀☎✞✦●✛✢➟❑✳✫➶■✡✙✤❀✹✛ ♠✢✳✢♣❉☎✱❏❀✼❡✤✙✝✸✣✈✛✫✡✪✦✫✣❢➍✑✳✫✇❄✤✌❊✴✘✷✟✗☎✞☞❖✳❯✁✄◆✢✓✠✕✗✍✩✡✙✟ ◆✫✡✯✓✠✖✱✰✢✕✗✦✒✲✥✘✷✖✸✰✒☎★✍❃☎✞✘✼✽✤✙✝q☎✞❂✥✖★✕✗☎★✦❖✓❉✍✑✏✒✟✔✓✠✕✗✍❃☎✌✣✢✕☛✡✶✘✚✓✷✝✠☎✌✡✙✍❃✕✗✦✢✲✢✳ ▲❘s ✦ ❵❁➔✚➑✌♦❛ ♥❑❞➑ ❝ ➨❤❣✳❣✳❣ ◆■③➃▼✢▼●❙ ❘ ❴✬✛✢✕ ⑩ ♠✢✛✢❳❥⑨❀❶❣✤✛ ♠✆✏✒✦✢☎✥➎✌➜✙➜✆➜❀✳ ⑤✔➎✌➛✯⑦✶➍◗✳✒❶❣✳✢✇●✝✸✡✪✦●✛✢➹✥✳✫❶✶✳✢❈❉✏✫✡✻✛✫✡✪✦✫✣✧✇✄✳✫✇✄✳✒➍✄✤✢✁✳ ①✈✕✗✲✆➉★✡✙✲✢➥❋❶❉✦ ☎✞❂❃✖✞✕☛☎✞✦✻✓q◆❯☎★☎✱✝✷❅➀✓✠✤✪❅➀◆❯☎★☎✞✝✴✘✷✖✸✰✒☎★✍❃☎✄✼❡✤✙✝❉✍❃☎✌✣✢✕☛✡❣✘✚✓✷✝✠☎✌✡✙✍❃✕✗✦✒✲❀✳✒▲❆✦ ❧❯➑✎❜✱ö✹ö✢➓✷❜✙➔✑❜✙❞ ➨❤❣✐❣✳❣❲➨ ◆ ④ ③■✬ ➢ ③✐♣❍✛✫⑨❀✡✙✦✧⑧✢✝✸✡✙✦✢✖★✕✗✘✷✖★✤✢✛❯➤❶❣✛ ▼❫✡✪✝✠✖✸✰✢❅❆❶q◆✢✝✠✕✗✟✵❹✪❷✆❷✙➃❀✳ ⑤✔➎★⑥✪⑦❣➪❁✳ s ✁✳ ①❯☎★✲✆✏❀✝✸✡❀✛✫➹✥✳✒➤✡✪✟☛✂✆☎✞✝✷✓✌✛❯✡✪✦✫✣❫⑨❯✳✫➩❧✰✫✡✪✓✷✓✸✡✪✖✱✰✒✡✪✝♥➅❘☎★☎✆✳✫❈❉✤✌❊ ✓✠✤✥✍❃✤✻✣❀☎★✟✬✡✙✦❫✕✗✦❖✓✠☎✞✝✠✦✒☎✱✓❘❊✤✪✝✠❙❯✳✒▲❆✍ ✦ ❵➔✷➑✌❛✸➓✠➓✠➧✪➙✽✽➦ ❛✙❝❣❤➑ ❝ ❤➨ ❣✳❣✐❣ ➨ ☛➦ ❝✞➑✌❛✸➑ ↔ ✛✫⑨✢✡✙✦✧⑧✢✝✸✡✙✦✢✖★✕✗✘✷✖★✤✢✛❯➤❶❣✛✬➎✌➜✙➜✆⑥❀✳ ⑤✔➎✌➐✯⑦✑⑨✈✁✳ ➆✑✢✳ ①✈✰✻✏✒✡✙✦✒✲❀✛✫➩q✤✳ ✈✑✹✳ ①❯✰✫✡✪✤✢✛✒✡✙✦✫✣❢❶❣✳✢➍◗✤✳ ♠✆✤✆✘✷☎✞◆✒✰●✳✫➩✡★☞❖☎★✏❀❏✬➥ ❶❉✦✧✡✪✝✠✖✸✰✒✕✔✓✠☎★✖✞✓✠✏❀✝✠☎■✼✽✤✪✝❉✘✷✖★✡✙✟☛✡✙✾✢✟☛☎✑✡✙✦✒✣✎✼✽✡✙✏✒✟✔✓✷❅r✓✠✤✆✟✗☎✞✝✸✡✪✦❖✓ ❊✴✕☛✣✢☎✞❅❆✡✯✝✠☎✌✡❃✣✒✡✯✓✸✡✥✣✢✕✗✘✷✘✷☎★✍❃✕✗✦✫✡✯✓✠✕✗✤✆✦●✳✢▲❘✛ ✦ ⑤⑥⑤✪❀❞ ❡ ❘ q➢ ♣✭⑧ ➨❤❣✳❣✐❣ ◆❍③✩▼✢▼✽❙ ❘ ❴●✛✢⑩✄☎✞✙ ❊ ✈❧✤✙✝✠❙❯✤✛ ♠✆✏✒✦✢☎❣❹✙❷✙❷❀➎✆✳