2. 305"Vt́pi"mj噂 p (Match)
4.3.1 Gi違i thu壱t BruteForce
""v逢荏pi"ej pj"e栄a gi違i thu壱t Brute-Hqteg"8吋 v·o"v医t c違 m磯u tu亥n t詠 ph鰻 bi院n
nk‒p"8嘘k"v逢嬰pi"vt‒p"f英 li羽u chu厩i th運i giap"8逢嬰e"z¤{"f詠ng d詠c"vt‒p"vkpj"vj亥n c栄a gi違i thu壱v"v·o"o磯u ph鰻 bi院n Apriori [1, 30]. Gi違i thu壱t Brute-Force th詠c hi羽p"swƒ"vt·pj" mjck"rjƒ"n員p t瑛ng m泳c t瑛 f逢噂k"n‒p"x "d逸v"8亥u t瑛 t壱p L1 (t壱r"eƒe"o磯w"e挨"d違p"e pi" ej pj"n "eƒe"oqvkhu"x噂i chi隠w"f k"mjƒe"pjcw"e„"8逢嬰c t瑛 swƒ"vt·pj"v·o"oqvkh"vt‒p"eƒe"
chu厩i th運k"ikcp"mjw{pj"j逢噂pi+0"N#"fq"vc"ej丑n t壱p L1 n "v壱r"eƒe"oqvkhu"n "x·"d違p"vj¤p" eƒe"oqvkhu"p {"8«"e„"u嘘 l亥n xu医t hi羽n l噂p"j挨p"jq員c b茨pi"pi逢叡ng h厩 tr嬰 t嘘i thi吋u do
pi逢運k"f́pi"8鵜pj"pij c0"Ucw"mjk" 8«"e„"v壱r"eƒe"rj亥n t穎 ph鰻 bi院n L1 vj·"ik違i thu壱t Brute-Force s胤 tri吋n khai s逸p x院p l衣k"eƒe"vj吋 hi羽n c栄a L1 theo th泳 t詠 th運k"ikcp"8亥u
x q"d茨pi"rj逢挨pi"rjƒr"SwkemUqtv0"雲d逢噂c k院 gi違i thu壱t ti院p"j pj"m院t h嬰r"eƒe"vj詠c th吋p {"8吋 t衣q"vj pj"v壱p 泳pi"xk‒p"E2x "mk吋m tra t壱p 泳pi"xk‒p"p {"8吋 ch丑p"eƒe"rj亥n t穎e„"uwrrqtv"vj臼a min-uwr"x "8逢c"x q"N2.Swƒ"vt·pj"p {"8逢嬰c th詠c hi羽n cho t噂i khi
mj»pi"vj吋 t衣q"8逢嬰c 泳pi"xk‒p"Ek cho Lk m噂i t瑛 Lk-1 (v噂i k 半 2). M員e"f́"#"v逢荏ng c栄a gi違i thu壱t Brute-Hqteg" v逢挨pi" 8嘘k" 8挨p" ik違n nj逢pi" swƒ" vt·pj" m院t h嬰r" eƒe" vj吋 hi羽n trong Lk-1 8吋 t衣q"vj pj"eƒe"泳pi"xk‒p"vtqpi"Nk d宇 f pi"f磯p"8院n kh違p<pi"d́pi"p鰻 t鰻
h嬰r"*8員c bi羽v"n "mjk"vc"zgo"zfiv"v噂i m嘘i quan h羽 d詠c"vt‒p"v pj"ej医t th運i kho違ng gi英a nh英ng th吋 hi羽p"p {+0"U嘘 n逢嬰ng t鰻 h嬰r"e„"vj吋 e„"p院w"swƒ l噂n s胤 d磯n t噂i swƒ"vt·pj"
ki吋m tra support count c栄a t瑛ng k院t h嬰p s胤 r医t t嘘p"mfio"x隠 m員t th運i gian (c泳 n ph亥n t穎 k院t h嬰r" 8逢嬰c t衣q" tc" vj·" rj違i ki吋m tra t嘘k" 8c" p2 l亥p" 8吋 l医{" 8逢嬰e" vj»pi" vkp" x隠
support count cho t瑛ng ph亥n t穎+0"A吋 v<pi"v嘘e"ejq"swƒ"vt·pj"v pj"uwrport count cho
eƒe"rj亥n t穎 k院t h嬰r"e pi"pj逢"mk吋o"vtc"8瓜 ph鰻 bi院n c栄a nh英pi"vj pj"rj亥n m磯u con (subpattern), lu壱p"x<p"u胤 s穎 d映ng m瓜t b違pi"d<o"f衣ng Dictionary trong C#. Ph亥n sau s胤vt·pj"d {"eƒe"d逢噂c c映 th吋 c栄a gi違i thu壱t.
D逢噂c 1<"Z¤{"f詠ng L2 t瑛 L1
Zfiv"4"th詠c th吋 o"x "p"e栄a L1 Hai th詠c th吋 p {"ej雨 e„"vj吋 8逢嬰c k院t h嬰p n院u
pj逢"vj運k"8k吋m b逸v"8亥u c栄a th詠c th吋 m nh臼j挨p"jq員c b茨ng th運k"8k吋m b逸v"8亥u c栄a th詠c th吋: m.StartPosition 判p0UvctvRqukvkqp0"Swƒ"vt·pj"m院t h嬰r"8吋 t衣o ra m瓜t 泳pi"xk‒p"E2 8逢嬰e"o»"v違pj逢"ucw<
‚N院u 2 th詠c th吋 o"x "p"8院n t瑛 épi"o瓜v"8嘘k"v逢嬰pi"*épi"o瓜t c鰻 phi院w+"vj·"
chu厩i s詠 ki羽n m ch雨 e„"vj吋 k院t h嬰p v噂i n khi chu厩i s詠 ki羽n n x違y ra sau khi chu厩i s詠
J·pj"4.6 Minh h丑a quan h羽 precedes
Mjk"8„"m院t h嬰p t衣q"8逢嬰c s胤e„"f衣ng: m-m.ID<p:delta>n-n.ID
V噂k"ÐrÑ"n "m "jk羽w"8衣i di羽p"ejq"rjfir"vqƒp"ÐrtgegfguÑ"vtqpi"9"rjfir"vqƒp"8衣i s嘘
quan h羽 Allen. Ch雨 s嘘fgnvc"*fgnvc"@"2+"8員e"vt逢pi"ejq"kho違pi"eƒej"x隠 th運i gian gi英a 2 chu厩i s詠 ki羽p"o"x "p0"M "jk羽w"o0KF"x "p0KF"8員e"vt逢pi"ejq"8鵜pj"fcpj"rj¤p"dk羽t c栄a t瑛pi"8嘘k"v逢嬰pi"*8吋 ta bi院v"o"x "p"8院n t瑛 8嘘k"v逢嬰pi"p q+0"Vtqpi"vt逢運ng h嬰r"vt‒p"vj·" o0KF"?"p0KF"*épi"8嘘k"v逢嬰ng).
X "f映<"vc"e„"4"vj詠c th吋 L1: EEB-CED"]2̲""*2"n "vj運k"8k吋m b逸v"8亥u c栄c"ơ"x "
ABB-CED"]9̲"*9"n "vj運k"8k吋m b逸v"8亥u c栄c"p+"vj·"ucw"mjk"m院t h嬰p ta s胤 e„"o瓜t th詠c th吋 thu瓜c C2 pj逢"ucw<""GGD"ÎACB<p:4>ABB ÎACB b逸v"8亥u t衣i th運k"8k吋m 0.
‚N院u 2 th詠c th吋 o"x "p"8院n t瑛 2 chu厩i d英 li羽u th運k"ikcp"mjƒe"nhau (ch鰯ng h衣n t瑛 2 lo衣i c鰻 phi院w" mjƒe" pjcw<" o0ID 塙 n.KF+" vj·" piq k" o嘘i quan h羽 8k" vt逢噂c
*rtgegfgư"pj逢"8«"ik噂i thi羽w"vj·"vc"e„"vj‒o"8"f衣ng quan h羽 e„"vj吋 e„"ik英c"o"x "p" vjgq"8衣i s嘘 quan h羽 Allen: meets, overlaps, Finished by, contains, starts."x "equal.
J·pj"4.8 Minh h丑a quan h羽ÐcontainsÑ
J·pj"4.9 Minh h丑a quan h羽ÐqxgtncruÑ
J·pj"4.11 Minh h丑a quan h羽ÐHkpkujgf"d{Ñ
J·pj"4.12 Minh h丑a quan h羽ÐgswcnÑ
Gi違i thu壱t s胤 ti院p"j pj"mk吋m tra t瑛ng m嘘i quan h羽e„"vj吋 e„"mjk"v衣o k院t h嬰p t瑛 eƒe"vj詠c th吋. K院t h嬰p t衣q"vj pj"u胤 e„"vj‒o"8"f衣ng sau (ngo衣i tr瑛 rtgegfgu"8«"8隠
c壱p)
- meets (m): m-m.ID<m:0>n-n.ID - overlaps (o): m-m.ID<o:d>n-n.ID - Finished by (F): m-m.ID<F:d>n-n.ID - contains (D): m-m.ID<D:d>n-n.ID - starts (s): m-m.ID<s:d>n-n.ID - equal (e): m-m.ID<e:d>n-n.ID
Ucw"mjk"8«"e„"8逢嬰c th詠c th吋 thu瓜c t壱p 泳pi"xk‒p"E2, gi違i thu壱t s胤 ti院p"j pj"
ki吋m tra xem support c栄a 泳pi"xk‒p"p {"e„"vj臼c"o«p"okp-uwr"fq"pi逢運k"f́pi"8逢c"tc" jc{"mj»pi0"P院u th臼c"o«p"vj·"8逢c"泳pi"xk‒p"vtqpi"C2 x q"N2.
D逢噂e"4<"Z¤{"f詠ng t壱p L3 t瑛 t壱p L2
Gi違 s穎vc"e„"4"vj詠c th吋 thu瓜c t壱p L2 n "o"x "p."eƒe"vj詠c th吋p {"e„"8鵜nh d衣ng
pj逢"ucw<
Th詠c th吋 m: m1-m1.ID<operator type1 : delta time1>n1-n1. ID Th詠c th吋 n: m2-m2.ID<operator type2 : delta time2>n2-n2.ID
Hai th詠c th吋o"x "p ch雨 e„"vj吋8逢嬰c k院t h嬰r"mjk""ej¿pi"z違{"tc"épi"vj運k"8k吋m
x "rj亥p"8亥u c栄a 2 th詠c th吋 p {"vt́pi"mj噂r"pjcw."pij c"n <"m1-m1. ID 岩 m2-m2. ID, 2 ph亥n t穎 8w»k"e„"vj吋 k院t h嬰r"8逢嬰c v噂i nhau (n1-n1. ID 橋 n2-n2. ID). Th詠c th吋 k院t h嬰p m噂i s胤e„"8鵜nh d衣ng:
m1-m1.ID<operator type1 : delta time1>n1-n1.ID< operator type3 : delta time3>n2-n2.ID
雲 8¤{"vj»pi"vkp"x隠 operator type3 x "fgnvc"vkog3 e„"8逢嬰c t瑛 vi羽c k院t h嬰p 2 ph亥n t穎8w»k0"Swƒ"vt·pj"m院t h嬰p 2 ph亥n t穎8w»k"8逢嬰c th詠c hi羽n gi嘘pi"pj逢"m院t h嬰p 2 th詠c th吋 thu瓜c L1 *vj»pi"swc"9"rjfir"vqƒp"8衣i s嘘 quan h羽 th運i gian Allen). Operator type3 ej pj"n "o瓜v"vtqpi"9"rjfir"vqƒp"8衣i s嘘 quan h羽 th運i gian Allen th吋 hi羽n m嘘i quan h羽 v隠 th運i gian gi英a 2 ph亥n t穎 8w»k0" Fgnvc" vkog3 cho ta bi院v" vj»pi" vkp" vj運i kho違pi"ej pj"zƒe"e栄a m嘘i quan h羽p {0"Ucw"8„"vc"vk院p"j pj"mk吋o"vtc"zgo"8嘘k"v逢嬰ng C3 v瑛a t衣q"e„"uwrrqtv"vj臼a min-sup jc{"mj»pi"x "8逢c"x q"v壱p L3 n院u th臼ạ
D逢噂e"5<"Z¤{"f詠ng Lk t瑛 Lk-1
M瓜v"eƒej"v鰻pi"swƒv."vc"jq p"vq p"e„"vj吋 t衣o m瓜t 泳pi"xk‒p"荏 m泳c k t瑛 2 th詠c th吋 trong Lk-1.G丑k"o"x "p"n "jck"vj詠c th吋 trong Lk-1 , 2 th詠c th吋p {"u胤e„"f衣ng:
- m = m1-m1.ID <operator type1 : delta time1> m2-m2.ID <operator type2 : delta time2>È0>"qrgtcvqt"v{rgk-2 : delta timek-2> mk-1-mk-1.ID
- n = n1-n1.ID <qrgtcvqt" v{rgÓ1 <" fgnvc" vkogÓ1> n2-n2.ID <qrgtcvqt" v{rgÓ2 :
V噂i m1."È."ok-1, n1."È."pk-1 n "eƒe"vj詠c th吋 trong L10"Eƒe"m "jk羽u operator type1." È." qrgtcvqt" v{rgk-2." qrgtcvqt" v{rgÓ1." È." qrgtcvqt" v{rgÓk-2 n " o瓜t trong b違y
rjfir"vqƒp"swcp"j羽 8衣i s嘘 th運k"ikcp"Cnngp"*r."ọ"q."H."F."ụ"g+0"E”p"fgnvc"vkog1."È."
delta timek-2." fgnvc" vkogÓ1." È." fgnvc" vkogÓk-2 n " pj英pi" vj»pi" vkp" ej pj" zƒe" x隠 th運i kho違ng 泳ng v噂k"eƒe"o嘘i quan h羽 gi英c"eƒe"vj pj"rj亥n trong hai th詠c th吋荏 m泳c k Î
1.
K院t h嬰p gi英c"o"x "p"ej雨e„"vj吋8逢嬰c ch医p nh壱p"mjk"x "ej雨mjk"o"x "p"e„"épi"
th運k"8k吋m b逸v"8亥w"x "e„"v医t c違eƒe"vj pj"rj亥n t衣q"vj pj"ik嘘ng nhau (tr瑛vj pj"rj亥n cu嘘k"épi"ok-1-mk-1.ID != nk-1-nk-1.ID. K院t qu違 c栄c"rjfir"m院t h嬰p s胤 ra 泳pi"xk‒p"Ek e„"f衣ng:
m1-m1.ID<operator type1 : delta time1> m2-m2.ID<operator type2 : delta time2>È0>"qrgtcvqt"v{rgk-2 : delta timek-2> mk-1-mk-1.ID <operator typek-1 : delta timek-1> nk-1-nk-1.ID
V逢挨pi"v詠 v噂k"eƒe"d逢噂e"vt‒p."ej雨 nh英ng k院t h嬰p Ck e„"uwrrqtv"eqwpv"n噂p"j挨p"
ho員c b茨ng min-sup vj·"o噂k"8逢嬰e"8逢c"x q"Nk.
X " f映<" Zfiv" 4" vj詠c th吋 thu瓜c L2: m = AA-NY<p:2>AAA-P[" x " p" ?" CC- NY<p:10>FF-NỴ M瓜t k院t h嬰p h嬰p l羽 C3 c„" vj吋 e„" n <" CC-NY<p:2>AAA- NY<p:5>FF-NỴ
O«"ik違 c栄a gi違i thu壱v"Dtwvg"Hqteg"8逢嬰e"8隠 xu医v"e„"p瓜k"fwpi"pj逢"j·pj"60350" Vc"n逢w"#"t茨pi"t pi"dw瓜c theo Apriori s胤 8逢嬰c ki吋m tra t衣k"f”pi"vj泳 34"e pi"pj逢"
vi羽c ki吋o" vtc" v pj" j嬰p l羽 c栄a th詠c th吋 k院t h嬰r" 8逢嬰c th詠c hi羽n b荏k" j o"
CombineInstances t衣k"f”pi"320"Pic{"ucw"mjk"8逢嬰c ch泳pi"okpj"n "o瓜t k院t h嬰p h嬰p l羽, ta s胤 n逢w"vj詠c th吋 k院t h嬰r"x q"o瓜t b違pi"d<o0"Ucw"8„"泳ng v噂i m厩i l亥n m瓜t th詠c th吋 k院t h嬰p m噂k"8逢嬰c t衣q"tc"8«"zw医t hi羽p"vt逢噂e"8„"vtqpi"d違pi"d<ọ"vc"v<pi"ej雨 s嘘 8院m trong b違pi"d<o"n‒p"30"Vj»pi"swc"xk羽c s穎 d映ng b違pi"d<ọ"ik違i thu壱v"ik¿r"vk院t ki羽m th運k"ikcp"v·o"mk院m cho nh英ng th詠c th吋 k院t h嬰r"8«"zw医t hi羽p"vt逢噂e"8„"x·"vj運i
ikcp"v·o"mk院o"vt‒p"d違pi"d<o"n "Q*3+"8嘘i v噂k"vt逢運ng h嬰r"vtwpi"d·pj0"Vj»pi"swc"xk羽c
n逢w"vt英 m瓜v"ikƒ"vt鵜 bi院p"8院o"d‒p"e衣nh t瑛ng ph亥n t穎 trong b違pi"d<ọ"vc"e pi"f宇f pi"
ki吋m tra xem ph亥n t穎 p q"n "o瓜t m磯u th詠c s詠 *pij c"n "e„"uwrrqtv"eqwpv"半 min- sup+0"Piq k"tc."v医t c違eƒe"o磯u ph鰻 bi院n 荏 m泳c k Î 3"e pi"8逢嬰e"n逢w"vtqpi"o瓜t b違ng
d<o"mjƒe"8吋 h厩 tr嬰 ejq"swƒ"vt·pj"z¤{"f詠ng t壱p m磯u ph鰻 bi院n 荏 m泳c k (c映 th吋 n "
ki吋o"vtc"8瓜 ph鰻 bi院n c栄c"eƒe"uwdrcvvgtp+0
F́"d違n ch医v"n "o瓜t gi違i thu壱v"vjgq"j逢噂pi"xfiv"e衣p"pj逢pi"8隠 v k"x磯p"e„"pj英ng c違i ti院n nh医v"8鵜nh cho Brute-Hqteg"vj»pi"swc"xk羽c s穎 d映ng b違pi"d<o"8吋 v<pi"v嘘e"x "
h厩 tr嬰 cho qwƒ"vt·pj"mjck"rjƒ"8逢嬰c t嘘v"j挨p0
Input:
-listPattern: an input list of primitive patterns
-min_sup: a minimum support count which is a user-specified threshold -TSLen: length of each time series
-Dictionary<string, byte> SubDictionary: a hash table used to check if a subsequence is frequent
Output: List<Pattern> returnList: an output list of all frequent patterns
Algorithm:
1. if (listPattern.count == 0) return; 2. //Obtain all instances from listPattern 3. listInstances = listPattern.GetInstances();
4. //Sort these instances by their starting points in time 5. QuickSort(listInstances)
6. //Create a hash table to help calculating the support count of each pattern
7. dictionary = [];
8. for i = 0 to listInstances.Count - 1
9. for j = i + 1 to listInstances.Count - 1
10. instance = CombineInstances (listInstances[i], listInstances[j] );
11. if(instance is not null)
12. if(instancẹk <= 1 || CheckSubSequence(instance, SubDictionary)
13. if (!dictionarỵcontains(instances))
14. //Create a pattern corresponding to the instance which has been combined
15. Pattern p = new Pattern(instance);
16. dictionarỵađ(p);
17. else
18. //Find an existing pattern in the hash table to ađ the instance which has been combined into the list of instances of the pattern
20. p.listInstances.Ađ(instance);
21. //Create a list of patterns who support counts satisfy min_sup 22. List<Pattern> L = [];
23. //Initialize SubDictionary to help checking if a subsequence is frequent in the next invocation
24. SubDictionary = [];
25. foreach (var item in dictionary)
26. if(CheckFrequentPattern(item, min_sup, TSLen)) 27. L.ađ(item);
28. returnList.ađ(item); 29. if(L.k >= 2)
30. SubDictionarỵađ(item)
31. RunBruteForce(L, minsup, TSLen, SubDictionary, returnList);
J·pj"4.13 O«"ik違 gi違i thu壱t Brute Force 4.3.2 Gi違i thu壱t d詠c"vt‒p"e医w"vt¿e"e¤{
Gi違i thu壱t Brute-Hqteg" 8逢嬰e" 8隠 c壱p 荏 vt‒p" 8«" e„" pj英ng c違i ti院n nh医v" 8鵜nh nh茨m h厩 tr嬰 v<pi"v嘘e"ejq"swƒ"vt·pj"mjck"rjƒ"o磯w0"Vw{"pjk‒p"ik違i thu壱t v磯n ph違i ti院n
j pj"mk吋o"vtc"x "mj荏i t衣o m瓜t s嘘n逢嬰ng k院t h嬰p r医t l噂p0"Vt逢噂c v医p"8隠 p {."nw壱p"x<p" 8«"8隠 xu医v"vj‒o"o瓜t gi違i thu壱v"mjck"rjƒ"vj泳 hai e pi d詠c"vt‒p"eƒej"vk院p c壱n l員p t瑛ng m泳c t瑛f逢噂k"n‒p0"Ik違i thu壱v"p {"u胤e„"mj違p<pi"pj壱n bi院v"8逢嬰c ph亥n l噂p"eƒe"m院t h嬰p h嬰p l羽 ngay t瑛 8亥w"x "nq衣i b臼 nh英pi"rjfir"m院t h嬰r"o "vc"dk院t ch逸e"n "u胤 mj»pi"vj吋
t衣q"tc"8逢嬰c k院t h嬰p h嬰p l羽. Gi違i thu壱v"mj»pi"ej雨 d詠c"vt‒p"d違pi"d<o"o "e”p"z¤{"
d詠ng d詠c"vt‒p"o瓜t c医w"vt¿e"f英 li羽u d衣pi"e¤{"rj́"j嬰r"ejq"swƒ"vt·pj"mjck"rjƒ"o磯u xu
j逢噂ng tu亥n t詠 nk‒p"8嘘k"v逢嬰ng d詠c"vt‒p"vkpj"vj亥n c栄a gi違i thu壱t FP-Itqyvj"8«"v瑛ng
8逢嬰e"8隠 c壱p 荏 [1, 37]
Lu壱p"x<p"i丑i gi違i thu壱v"p { n "ik違i thu壱t d詠c"vt‒p"e医w"vt¿e"e¤{"*vtgg"dcugf" cniqtkvjơ" x " e¤{" 8逢嬰c s穎 d映pi" 8逢嬰c g丑k" n " VR-tree (Temporal Pattern Tree). Nh英ng ph亥n n瓜k"fwpi"8逢嬰e"vt·pj"d {"rj c"ucw"u胤 8逢c"tc"eƒe"8鵜pj"pij c"e映 th吋 cho
e¤{"e pi"pj逢"eƒe"j o"x "vj栄 t映e"ik¿r"vc"vjcq"vƒe"vt‒p"e医w"vt¿e"e¤{"p {0
E¤{"i欝o"p"p¿v."o厩k"p¿v"8衣i di羽n cho m瓜v"vj pj"rj亥n c栄a m磯u tu亥n t詠 ph鰻
bi院p"nk‒p"8嘘k"v逢嬰pi0"A嘘i v噂k"eƒe"o磯u tu亥n t詠 ph鰻 bi院n 荏 m泳c 1 (泳ng v噂i L1+"vj·"o厩i
p¿v"ej pj"n "o瓜v"oqvkh"e„"8逢嬰c t瑛ikck"8q衣p"v·o"mk院o"oqvkhu0"Swƒ"vt·pj"k院t h嬰r"eƒe" p¿v"荏 m泳c k Î 3"8吋 t衣q"vj pj"eƒe"p¿v"荏 m泳e"m"e pi"v逢挨pi"v詠 v噂k"swƒ"vt·pj"v衣o t壱p
泳pi"xk‒p"Ek t瑛 t壱p m磯u tu亥n t詠 ph鰻 bi院n Lk-1. Nh英pi"p¿v"p q"8逢嬰c t衣q"vj pj"e„"8瓜
h厩 tr嬰 l噂p"j挨p"jq員c b茨ng min-sup s胤8逢嬰e"8逢c"x q"e¤{0"Xk羽e"vt ej"zw医v"tc"eƒe"o磯u tu亥n t詠 ph鰻 bi院p"e„"8逢嬰c b茨pi"eƒej"fw{羽v"8羽swk"vt‒p"e¤{"x瑛a t衣ọ
J·pj"4.14 Minh h丑a m瓜t node trong c医w"vt¿e"e¤{
M瓜v"p¿v"vtqpi"e¤{"dcq"i欝o"eƒe"vj pj"rj亥n:
oParentNode ch泳a tham kh違o t噂i node cha c栄a node hi羽n t衣i
oOperatorType ch泳c"vj»pi"rjfir"vqƒp"8衣i s嘘 quan h羽 th運i gian Allen (g欝m 7
8鵜nh d衣pi">r@.">o@.">g@.">u@.">H@.">F@.">q@+"x "ejq"dk院t d衣ng quan h羽 gi英c"p¿v" 8cpi"zfiv"x噂k"p¿v"ejc"e栄c"p„
oDeltaTime: ch泳c"vj»pi"vkp"vj運i kho違ng c映 th吋ejq"rjfir"vqƒp"8衣i s嘘 quan h羽
th運i gian v瑛c"p‒w0
oPatternLength: chi隠w"f k"o磯w"v pj"v噂k"p¿v"jk羽n t衣ị
oInfo: n瓜i dung c栄a m磯w"o "p¿v"p {"vj吋 hi羽n
oKF<"8鵜nh danh c栄c"8嘘k"v逢嬰ng (c鰻 phi院w+"o "p¿v"p {"dk吋u di宇n
ok: m泳c c栄c"p¿v"*ej鰯ng h衣n 泳ng v噂k"p¿v"泳ng v噂i L2 vj·"m"?"4+
oList of Instances: t医t c違 eƒe"vj詠c th吋 泳ng 荏 t瑛ng v鵜 vt "zw医t hi羽n c栄a m磯u
泳ng v噂k"p¿v"8cpi"zfiv0
oList of ChildNodes: b違pi"d<o"ej泳a tham kh違o t噂k"eƒe"p¿v"eqp"e栄c"p¿v"jk羽n t衣k"x "eƒe"p¿v"eqp"p {"荏 t亥ng th泳 m"-"30"Vj»pi"vkp"ejq"mj„c"e栄a m瓜t ph亥n t穎 8逢嬰c
z¤{"f詠ng trong b違ng b<o"dcq"i欝m: [OperatorType t噂k"p¿v"eqp"-"DeltaTime + Info c栄c"p¿v"eqp"-"ID c栄c"8嘘k"v逢嬰ng o "p¿v"eqp"rj映 thu瓜c].
b.Z¤{"f詠ng TP-tree
永ng v噂i c医w"vt¿e"pqfg"8«"8逢嬰e"8鵜pj"pij c"pj逢"vt‒p."vc"u胤 z¤{"f詠ng TP-tree
vjgq"rj逢挨pi"rjƒr"l員p t瑛ng m泳c t瑛 m泳c 0 t噂i m泳c k. Eƒej"vj泳e"z¤{"f詠pi"p {"v逢挨pi"
t詠 v噂k"swƒ"vt·pj"v·o"eƒe"o磯u tu亥n t詠 ph鰻 bi院n 荏 m泳c k Î 1 r欝k"ucw"8„"f́pi"m院t qu違 p {"8吋v·o"v壱p m磯u tu亥n t詠 ph鰻 bi院n 荏 m泳c k. Ta nh壱n th医y m瓜t qui t逸c 荏 8¤{"n "o瓜t m磯u 荏 m泳c k ch雨 e„"vj吋 8逢嬰c t衣o t瑛 t医t c違 nh英pi"p¿v"荏 m泳c k-1 e„"épi"p¿v"ejc0" V pj"ej医v"p {"ik¿r"ejq"ik違i thu壱v"vtƒpj"8逢嬰c vi羽c ki吋m tra t衣o nh英ng t鰻 h嬰r"mj»pi"
c亥n thi院v"x "fq"8„"v<pi"v嘘e"8逢嬰e"swƒ"vt·pj"mjck"rjƒ.
Chi ti院t t瑛pi"d逢噂c c栄a thu壱t gi違k"8逢嬰e"o»"v違pj逢"ucw<
D逢噂c 1 - Kh荏i t衣o TP-tree:
T衣q"p¿v"i嘘c root mang ikƒ"vt鵜 pwnn0"Vc"iƒp"pj«p"ejq"p¿v"tqqv"p {"n "2"x·"p¿v" p {"v逢挨pi"泳ng v噂i m泳c 0 c栄a m磯ụ
D逢噂c 2 Î X穎n#"N1:
T瑛 t壱p L1 Îej pj"n "o"oqvkhu"e„"8逢嬰c t瑛 eƒe"ejw厩i th運k"ikcp"mjw{pj"j逢噂ng
mjƒe"pjcw"x噂i support count l噂p"j挨p"jq員c b茨ng min-sup, ta t衣q"o"pqfgu"x "8逢c"x q" vtqpi"e¤{"泳ng v噂i m泳c 1. Kho違pi"eƒej"v瑛 eƒe"pqfg"荏 m泳e"3"p {"v噂k"p¿v"i嘘c b茨ng 0
x "Cnngp"QrgtcvqtV{rg"e栄a t瑛pi"pqfg"j逢噂ng t噂k"pqfg"tqqv"8隠w"8逢嬰e"ugv"ikƒ"vt鵜 r厩ng.
J·pj"違nh c栄c"e¤{"ucw"4"d逢噂e"3"x "4"8逢嬰c th吋 hi羽p"pj逢"j·pj 4.15 d‒p"f逢噂i (gi違 s穎 L1
e„"5 m磯u)
J·pj"4.15 O»"v違 c医w"vt¿e"e¤{"ucw"d逢噂e"3"x "4 D逢噂c 3 - Z¤{"f詠ng L2 t瑛 L1
Ta t衣o ra t医t c違 nh英ng k院t h嬰r"e„"vj吋 e„"ik英c"eƒe"p¿v"荏 m泳e"3"x·"v医t c違 eƒe" p¿v"荏 m泳e"3"8隠w"e„"ejwpi"p¿v"ejc"*ej pj"n "p¿v"g嘘e+0"D逢噂e"p {"e pi"v逢挨pi"v詠 pj逢" d逢噂c 1 trong gi違i thu壱t Brute-Force v噂k" 9" rjfir" vqƒp" 8衣i s嘘 th運i gian Allen. Tuy
pjk‒p"vtqpi"vt逢運ng h嬰p s穎 d映ng c医w"vt¿e"e¤{."o瓜t k院t h嬰r"e„"8逢嬰c trong gi違i thu壱t d詠c"vt‒p"e医w"vt¿e"e¤{"u胤nk‒p"swcp"v噂i m瓜v"p¿v"vtqpi"VR-tree, nh運 8„"ik¿r"vc"f宇f pi"
ki吋m tra xem k院t h嬰r"8„"e„"rj鰻 bi院p"jc{"mj»pi0"永ng v噂i m厩i k院t h嬰p h嬰p l羽, ta s胤
t衣o m瓜v"p¿v"v逢挨pi"泳pi"8吋 n逢w"vj»pi"vkp"x隠 k院t h嬰r"8„0"Eƒe"p¿v"p {"8逢嬰e"8員t trong m瓜t b違pi"d<o"x噂k"m ej"vj逢噂c nh臼 j挨p"j鰯n so v噂i b違pi"d<o"8逢嬰e"f́pi"vtqpg gi違i thu壱t Brute-Force (do m厩i b違pi"d<o"p {"ej雨 8逢嬰c t衣q"ejq"swƒ"vt·pj"m院t h嬰p t瑛ng c員r"p¿v"vtqpi"N1 o "vj»k+0"P院w"pj逢"o瓜t k院t h嬰p m噂i t衣q"v逢挨pi"泳ng v噂i m瓜v"p¿v"8«"
xu医t hi羽p"vj· vc"mj»pi"e亥n ph違i t衣o ra m瓜t k院t h嬰p th壱t s詠o "ej雨 c亥n c壱p nh壱t v鵜 vt "
xu医t hi羽n c栄a th詠c th吋 k院t h嬰r"8„"vtqpi"vt逢運ng List of Instances c栄c"p¿v"v逢挨pi"泳ng. Sau khi t医t c違 k院t h嬰r"8«"8逢嬰e"8逢c"x q"eƒe"pqfg."vc"u胤 duy羽t qua b違pi"d<o"ej泳c"eƒe" pqfg"p {"8吋 zgo"8瓜 h厩 tr嬰 c栄c"eƒe"o磯u 泳ng v噂i t瑛pi"pqfg"e„"vj臼c"o«p"min-sup
jc{"mj»pi0"A嘘i v噂i m厩k"vt逢運ng h嬰p th臼c"o«p"okp-uwr."vc"8逢c"pqfg"v逢挨pi"泳pi"x q" e¤{"d茨pi"eƒej"v衣q"nk‒p"m院t gi英c"pqfg"8„"v噂k"p¿v"ejc"荏 m泳c L1.
J·pj"f衣ng c栄a TP-vtgg"ucw"d逢噂e"5"8逢嬰c th吋 hi羽p"swc"j·pj"6038"vtqpi"8„"eƒe" pqfg"}6.7.8.9.:ʼ"n "pj英ng node m噂k"8逢嬰e"8逢c"x q"e¤{"v衣i m泳c 2. M厩k"p¿v"泳ng v噂i m瓜t m磯u ph鰻 bi院p"x "pj逢"x壱{"vc"e„"7"o磯u ph鰻 bi院n 荏 m泳c 2.
J·pj"4.16 Minh h丑a c医w"vt¿e"e¤{"ucw"d逢噂c 3
Ta l医{"vj»pi"vkp"x隠 eƒe"o磯u ph鰻 bi院n 荏 m泳c 2 b茨pi"eƒej"fw{羽v"pi逢嬰c t瑛eƒe" p¿v"荏 m泳e"4"n‒p"v噂k"p¿v"o泳e"30"X "f映: duy羽t t瑛p¿v"6"n‒p"p¿v"3"vc"u胤 e„"o瓜t m磯u ph鰻
泳ng v噂k"eƒe"p¿v"3"x "6.""qrgtcvqt"v{rg"x "fgnvc"n "vj»pi"vkp"x隠 m嘘i quan h羽8逢嬰e"z¤{"
d詠ng d詠a tr‒p"rjfir"vqƒp"8衣i s嘘 th運k"ikcp"Cnngp"x "8逢嬰e"n逢w"vtqpi"pqfg"60"A瓜 h厩 tr嬰
c栄a m磯w"vt‒p"v逢挨pi"泳ng v噂i s嘘 th詠c th吋 n茨o"vtqpi"fcpj"uƒej"vj詠c th吋荏 node 4.
D逢噂c 4 ÎZ¤{"f詠ng L3 t瑛 L2
Vtqpi"vt逢運ng h嬰p n院u ta s穎 d映ng gi違i thu壱t Brute-Force, ta ph違i ki吋m tra kh違 p<pi"m院t h嬰p t衣o ra ph亥n t穎泳pi"xk‒p"E3 t瑛 t医t c違eƒe"vj詠c th吋 trong t壱p L20"A嘘i v噂i gi違i thu壱t d詠c"vt‒p"e医w"vt¿e"e¤{."vc"fw{羽t qua TP-tree t噂i t亥ng th泳 2 (泳ng v噂i L2+"x "
ch雨 ti院p"j pj"mj荏i t衣o k院t h嬰p gi英c"eƒe"pqfg"e„"ejwpi"pqfg"ejc"o "vj»k0"Pij c"n "vc"
ch雨 c亥p"zgo"zfiv"eƒe"pqfg"e„"ejwpi"rtghkz"rcvj"ejq"v噂i m泳c n茨m vt逢噂c 1 m泳c c栄a
eƒe"pqfg"8cpi"zfiv0"Vc"zfiv"e¤{"e„"8逢嬰e"ucw"d逢噂c 3 荏 j·pj"60380"P院w"pj逢"u穎 d映ng gi違i thu壱t Brute-Force, ta ph違i ki吋m tra kh違 p<pi"v衣o k院t h嬰p t瑛 t医t c違 nh英ng m磯u
泳ng v噂i t壱p L2 o "e映 th吋n "}2."3."6ʼ."}2."3."7ʼ."}2."3."8ʼ."}2."5."9ʼ."x "}2."5.":ʼ0"A嘘i v噂i gi違i thu壱t d詠c"vt‒p"e医w"vt¿e"e¤{."vc"ej雨 c亥n ki吋m tra kh違p<pi"v衣o k院t h嬰p c栄c"eƒe"
m磯u trong L2 e„"ejwpi"rtghkz"rcvj<"}}2."3."6ʼ."}2."3."7ʼ."}2."3."8ʼʼ"x "}}2."5."9ʼ."}2."
3, 8}}. 雲 8¤{"t "t pi"jq p"vq p"mj»pi"vj吋 t衣q"8逢嬰c k院t h嬰p t瑛 nh英ng m磯u 泳ng v噂i