Advances in Greedy Algorithms Advances in Greedy Algorithms Edited by Witold Bednorz I-Tech IV Published by In-Teh In-Teh is Croatian branch of I-Tech Education and Publishing KG, Vienna, Austria. Abstracting and non-profit use of the material is permitted with credit to the source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. Publisher assumes no responsibility liability for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained inside. After this work has been published by the In-Teh, authors have the right to republish it, in whole or part, in any publication of which they are an author or editor, and the make other personal use of the work. © 2008 In-teh www.in-teh.org Additional copies can be obtained from: publication@ars-journal.com First published November 2008 Printed in Croatia A catalogue record for this book is available from the University Library Rijeka under no. 120115050 Advances in Greedy Algorithms, Edited by Witold Bednorz p. cm. ISBN 978-953-7619-27-5 1. Advances in Greedy Algorithms, Witold Bednorz Preface The greedy algorithm is one of the simplest approaches to solve the optizmization problem in which we want to determine the global optimum of a given function by a sequence of steps where at each stage we can make a choice among a class of possible decisions. In the greedy method the choice of the optimal decision is made on the information at hand without worrying about the effect these decisions may have in the future. Greedy algorithms are easy to invent, easy to implement and most of the time quite efficient. However there are many problems that cannot be solved correctly by the greedy approach. The common example of the greedy concept is the problem of ‘Making Change’ in which we want to make a change of a given amount using the minimum number of US coins. We can use five different values: dollars (100 cents), quarters (25 cents), dimes (10 cents), nickels (5 cents) and pennies (1 cent). The greedy algorithm is to take the largest possible amount of coins of a given value starting from the highest one (100 cents). It is easy to see that the greedy strategy is optimal in this setting, indeed for proving this it suffices to use the induction principle which works well because in each step either the procedure has ended or there is at least one coin we can use of the actual value. It means that the problem has a certain optimal substructure, which makes the greedy algorithm effective. However a slight modification of ‘Making Change’, e.g. where one value is missing, may turn the greedy strategy to be the worst choice. Therefore there are obvious limits for using the greedy method: whenever there is no optimal substructure of the problem we cannot hope that the greedy algorithm will work. On the other hand there is a lot of problems where the greedy strategy works unexpectedly well and the purpose of this book is to communicate various results in this area. The key point is the simplicity of the approach which makes the greedy algorithm a natural first choice to analyze the given problem. In this book there are discussed several algorithmic questions in: biology, combinatorics, networking, scheduling or even pure mathematics, where the greedy algorithm can be used to produce the optimal or nearly optimal answer. The book was written in 2008 by the numerous authors who contributed the publication by presenting their researches in a form of a self-contained chapters. The idea was to coordinate the international project where specialists all over the world can share their knowledge on the greedy algorithms theory. Each chapter comprises a separate study on some optimization problem giving both an introductory look into the theory the problem comes from and some new developments invented by author(s). Usually some elementary knowledge is assumed, yet all the required facts are quoted mostly in examples, remarks or theorems. The publication may be useful for all graduates and undergraduates interested in the algorithmic theory with the focus on the greedy approach and applications of this VI method to various concrete examples. Most of scientists involved in the project are young at the full strength of their career, hence the presented content is fresh and acquaints with the new directions where the theory of greedy algorithms evolves to. On the behalf of authors I would like to acknowledge all who made the publication possible, in particular to Vedran Kordic who coordinated this huge project. Many thanks also for those who helped in the manuscripts preparation making useful suggestions and finding errors. November 2008 Editor Witold Bednorz Warsaw, Poland, Contents Preface V 1. A Greedy Algorithm with Forward-Looking Strategy 001 Mao Chen 2. A Greedy Scheme for Designing Delay Monitoring Systems of IP Networks 017 Yigal Bejerano and Rajeev Rastogi 3. A Multilevel Greedy Algorithm for the Satisfiability Problem 039 Noureddine Bouhmala and Xing Cai 4. A Multi-start Local Search Approach to the Multiple Container Loading Problem 055 Shigeyuki Takahara 5. A Partition-Based Suffix Tree Construction and Its Applications 69 Hongwei Huo and Vojislav Stojkovic 6. Bayesian Framework for State Estimation and Robot Behaviour Selection in Dynamic Environments 85 Georgios Lidoris, Dirk Wollherr and Martin Buss 7. Efficient Multi-User Parallel Greedy Bit-Loading Algorithm with Fairness Control For DMT Systems 103 Cajetan M. Akujuobi and Jie Shen 8. Energy Efficient Greedy Approach for Sensor Networks 131 Razia Haider and Dr. Muhammad Younus Javed 9. Enhancing Greedy Policy Techniques for Complex Cost-Sensitive Problems 151 Camelia Vidrighin Bratu and Rodica Potolea VIII 10. Greedy Algorithm: Exploring Potential of Link Adaptation Technique in Wideband Wireless Communication Systems 169 Mingyu Zhou, Lihua Li, Yi Wang and Ping Zhang 11. Greedy Algorithms for Mapping onto a Coarse-grained Reconfigurable Fabric 193 Colin J. Ihrig, Mustafa Baz, Justin Stander, Raymond R. Hoare, Bryan A. Norman, Oleg Prokopyev, Brady Hunsaker and Alex K. Jones 12. Greedy Algorithms for Spectrum Management in OFDM Cognitive Systems - Applications to Video Streaming and Wireless Sensor Networks 223 Joumana Farah and François Marx 13. Greedy Algorithms in Survivable Optical Networks 245 Xiaofei Cheng 14. Greedy Algorithms to Determine Stable Paths and Trees in Mobile Ad hoc Networks 253 Natarajan Meghanathan 15. Greedy Anti-Void Forwarding Strategies for Wireless Sensor Networks 273 Wen-Jiunn Liu and Kai-Ten Feng 16. Greedy Like Algorithms for the Traveling Salesman and Multidimensional Assignment Problems 291 Gregory Gutin and Daniel Karapetyan 17. Greedy Methods in Plume Detection, Localization and Tracking 305 Huimin Chen 18. Greedy Type Bases in Banach Spaces 325 Witold Bednorz 19. Hardware-oriented Ant Colony Optimization Considering Intensification and Diversification 359 Masaya Yoshikawa 20. Heuristic Algorithms for Solving Bounded Diameter Minimum Spanning Tree Problem and Its Application to Genetic Algorithm Development 369 Nguyen Duc Nghia and Huynh Thi Thanh Binh 21. Opportunistic Scheduling for Next Generation Wireless Local Area Networks 387 Ertuğrul Necdet Çiftçioğlu and Özgür Gürbüz IX 22. Parallel Greedy Approximation on Large-Scale Combinatorial Auctions 411 Naoki Fukuta and Takayuki Ito 23. Parallel Search Strategies for TSPs using a Greedy Genetic Algorithm 431 Yingzi Wei and Kanfeng Gu 24. Provably-Efficient Online Adaptive Scheduling of Parallel Jobs Based on Simple Greedy Rules 439 Yuxiong He and Wen-Jing Hsu 25. Quasi-Concave Functions and Greedy Algorithms 461 Yulia Kempner, Vadim E. Levit and Ilya Muchnik 26. Semantic Matchmaking Algorithms 481 Umesh Bellur and Harin Vadodaria 27. Solving Inter-AS Bandwidth Guaranteed Provisioning Problems with Greedy Heuristics 503 Kin-Hon Ho, Ning Wang and George Pavlou 28. Solving the High School Scheduling Problem Modelled with Constraints Satisfaction using Hybrid Heuristic Algorithms 529 Ivan Chorbev, Suzana Loskovska, Ivica Dimitrovski and Dragan Mihajlov 29. Toward Improving b-Coloring based Clustering using a Greedy re-Coloring Algorithm 553 Tetsuya Yoshida, Haytham Elghazel, Véronique Deslandres, Mohand-Said Hacid and Alain Dussauchoy 30. WDM Optical Networks Planning using Greedy Algorithms 569 Nina Skorin-Kapov [...]... widely studied in recent decades, as it has numerous applications in the cutting and packing industry, e.g wood, glass and cloth industries, newspapers paging, VLSI floor planning and so on, with different applications incorporating different constraints and objectives We consider the following rectangular packing problem: given a rectangular empty container with fixed width and infinite height and... the greedy solution of ordering problems ORSA Journal on Computing, 1989, 1: 181-189 [2] W.Q Huang, Y Li, S Gerard, et al A “learning from human” heuristic for solving unequal circle packing problem Proceedings of the First International Workshop on Heuristics, Beijing, China, 2002, 39-45 [3] Z Huang, W.Q Huang A heuristic algorithm for job shop scheduling Computer Engineering & Appliances (in Chinese),... and industrial activity in the area of developing novel tools and infrastructures for measuring network parameters Existing network monitoring tools can be divided into two categories Node-oriented tools collect monitoring information from network devices (routers, switches and hosts) using SNMP/RMON probes [1] or the Cisco NetFlow tool [2] These are useful for collecting statistical and billing information,... monitoring information It does not deal with the aspects of analyzing and distributing this information, which are application-dependent If one of the end points of e is in S, let say u ∈ S, then A is only required to include the probe (u, v) 2 22 Advances in Greedy Algorithms 5 Link monitoring We show in this section that for link monitoring both the station selection and probe assignment problems are... approximate arbitrary path latencies In [15], Breitbart et al propose a monitoring scheme where a single network operations center (NOC) performs all the required measurements In order to monitor links not in its routing tree, the NOC uses the IP source routing option to explicitly route probe packets along these links The technique of using source routing for determining the probe routes has been used... on the problem of determining the minimum cost set of multicast trees that cover links of interest in a network, which is similar to the station selection problem tackled in this chapter The two-phase scheme of station placement and probe assignment have been proposed in [10] In this work, Bejerano and Rastogi show a combined approach for minimizing the cost of both the monitoring stations as well as... of a minimal set of monitoring stations that can generate these probes Moreover, by using techniques from a max-plus algebra theory, they show that the optimal set of probes can be determined in polynomial time In [22], Suh et al 20 Advances in Greedy Algorithms propose a scheme for cost-effective placement of monitoring stations for passive monitoring of IP flows and controlling their sampling rate... similar to ping 1 A Greedy Scheme for Designing Delay Monitoring Systems of IP Networks 21 monitoring station Thus, the monitoring station s can estimate the round-trip delay of the link by measuring the difference in the round-trip times of the two probe messages From the above description, it follows that a monitoring station can only measure the delays of links in its RT Consequently, a monitoring system... monitoring station set requirement and minimizes the total cost of all the monitoring stations given be the sum Σs∈S ws After selecting the monitoring stations S, the optimal probe assignment A is one that satisfies the covering probe assignment constraint and minimizes the total probing cost defined by the sum Σ(s,v)∈ cs,v Note that choosing csv = 1 essentially results in an assignment A with the minimum... monitoring systems A link monitoring (LM) system that guarantees that very link is monitored by a monitoring station Such system is useful for delay monitoring, bottleneck links detection and fault isolation, as demonstrated in [10] A path monitoring (PM) system that ensures the coverage of every routing path between any pair of nodes by a single station, which provides accurate delay monitoring For link . no. 12 011 5050 Advances in Greedy Algorithms, Edited by Witold Bednorz p. cm. ISBN 978-953-7 619 -27-5 1. Advances in Greedy Algorithms, Witold Bednorz Preface The greedy. Networks Planning using Greedy Algorithms 569 Nina Skorin-Kapov 1 A Greedy Algorithm with Forward-Looking Strategy Mao Chen Engineering Research Center for Educational Information Technology,. solution composed of n sets of quadruples 11 11 12 12 {, , , } x yxy ,…, 11 2 2 {, , , } nnn n x yx y , where ( 11 , ii x y ) denotes the bottom-left corner coordinates of rectangle i, and ( 22 , ii x y