Advances in Greedy Algorithms

Edited by

Witold Bednorz

I-Tech

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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

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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

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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 Franois 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

Erturul Necdet iftiolu and zgr Grbz

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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, Vronique Deslandres, Mohand-Said Hacid and Alain Dussauchoy

30. WDM Optical Networks Planning using Greedy Algorithms 569

Nina Skorin-Kapov

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Quasi-Concave Functions and Greedy Algorithms

Yulia Kempner1, Vadim E. Levit2 and Ilya Muchnik3 1 Holon Institute of Technology,

2 Ariel University Center of Samaria, 3 Rutgers - the State University of New Jersey,

1,2Israel 3USA

1. Introduction Many combinatorial optimization problems can be formulated as: for a given set system over E (i.e., for a pair (E, ) where 2E is a family of feasible subsets of finite set E), and for a given function F : R, find an element of for which the value of