Other Title s i n Thi s Serie s

26 Davi d S . Johnso n an d Michae l A . Trick , Editors , Cliques , Coloring , an d Satisfiability: Secon d DIMAC S Implementatio n Challeng e

25 Gilber t Baumslag , Davi d Epstein , Rober t Gilman , Hamis h Short , an d

Charles Sims , Editors , Geometri c an d Computationa l Perspective s o n Infinit e Group s

24 Loui s J . Billera , Curti s Greene , Rodic a Simion , an d Richar d P . Stanley , Editors, Forma l Powe r Serie s an d Algebrai c Combinatorics/Serie s formelle s e t combinatoire algebriqu e

23 Pano s M . Pardalos , Davi d I . Shalloway , an d Guolian g Xue , Editors , Global Minimizatio n o f Nonconvc x Energ y Functions : Molecula r Conformatio n an d

Protein Foldin g

22 Pano s M . Pardalos , Maurici o G . C . Resende , an d K . G . Ramakrishnan ,

Editors, Paralle l Processin g o f Discret e Optimizatio n Problem s

21 D . Pran k Hsu , Arnol d L . Rosenberg , an d Dominiqu e Sotteau , Editors ,

Interconnection Network s an d Mappin g an d Schedulin g Paralle l Computation s

20 Wil l ia m Cook , Laszl o Lovasz , an d Pau l Seymour , Editors , Combinatoria l

Optimization

19 Ingema r J . Cox , Pierr e Hansen , an d Bel a Julesz , Editors , Partitionin g Dat a

Sets

18 Gu y E . Blel loch , K . Man i Chandy , an d Sures h Jagannathan , Editors ,

Specification o f Paralle l Algorithm s

17 Eri c Sve n Ristad , Editor , Languag e Computation s

16 Pano s M . Pardalo s an d Henr y Wolkowicz , Editors , Quadrati c Assignmen t an d

Related Problem s

15 Nathanie l D e a n an d Gregor y E . Shannon , Editors , Computationa l Suppor t fo r

Discrete Mathematic s

14 Rober t Calderbank , G . Davi d Forney , Jr. , an d Nade r Moayeri , Editors ,

Coding an d Quantization : DIMACS/IEE E Worksho p

13 Jin-Y i Cai , Editor , Advance s i n Computationa l Complexit y Theor y

12 Davi d S . Johnso n an d Catherin e C . McGeoch , Editors , Networ k Flow s an d

Matching: Firs t DIMAC S Implementatio n Challeng e

11 Larr y Finkelstei n an d Wil l ia m M . Kantor , Editors , Group s an d Computatio n

10 Joe l Friedman , Editor , Expandin g Graph s

9 Wil l ia m T . Trotter , Editor , Plana r Graph s

8 S imo n Gindikin , Editor , Mathematica l Method s o f Analysis o f Biopolyme r Sequence s

7 Lyl e A . M c G e o c h an d Danie l D . Sleator , Editors , On-Lin e Algorithm s

6 Jaco b E . G o o d m a n , Richar d Pollack , an d Will ia m Steiger , Editors , Discret e

and Computationa l Geometry : Paper s fro m th e DIMAC S Specia l Yea r

5 Fran k Hwang , Fre d Roberts , an d Clyd e Monma , Editors , Reliabilit y o f

Computer an d Communicatio n Network s

4 Pete r Gri tzman n an d Bern d Sturmfels , Editors , Applie d Geometr y an d Discret e

Mathematics, Th e Victo r Kle e Festschrif t

3 E . M . Clark e an d R . P . Kurshan , Editors , Computer-Aide d Verificatio n '9 0

2 Joa n Feigenbau m an d Michae l Merritt , Editors , Distribute d Computin g an d

Cryptography

1 Wil l ia m Coo k an d Pau l D . Seymour , Editors , Polyhedra l Combinatoric s

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Cliques, Coloring , and Satisfiabilit y

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DIMACS Series i n Discrete Mathematic s

and Theoretica l Compute r Scienc e

Volume 2 6

Cliques, Coloring , and Satisfiabilit y

Second DIMAC S Implementation Challeng e

October 11-13 , 199 3

David S . Johnso n Michael A . Tric k

Editors

NSF Science an d Technolog y Cente r in Discret e Mathematic s an d Theoretica l Compute r Scienc e A consortium o f Rutger s University , Princeto n University ,

AT&T Bell Labs , Bellcor e

American Mathematical Societ y

https://doi.org/10.1090/dimacs/026

This DIMAC S volum e resultin g fro m th e secon d DIMAC S Implementatio n Challeng e contains referee d paper s presente d a t th e Challeng e worksho p hel d a t DIMAC S o n October 11-13 , 1993 .

1991 Mathematics Subject Classification. Primar y 68R10 , 90C27 .

Library o f Congres s Cataloging-in-Publicatio n Dat a

Cliques, coloring , an d satisfiabilit y : secon d DIMAC S implementatio n challeng e : DIMAC S work -shop, Octobe r 11-13 , 199 3 / Davi d S . Johnson , Michae l A . Trick , editors .

p. cm . — (DIMAC S serie s i n discret e mathematic s an d theoretica l compute r science , ISS N 1052-1798; v . 26 )

"NSF Scienc e an d Technolog y Cente r i n Discret e Mathematic s an d Theoretica l Compute r Science, a consortiu m o f Rutger s University , Princeto n University , AT& T Bel l Labs , Bellcore. "

Includes bibliographica l references . ISBN 0-8218-6609- 5 (alk . paper ) 1. Compute r algorithms . 2 . Compute r science—Mathematics . I . Johnson , Davi d S. ,

1945- . II . Trick , Michae l A . III . Series . QA76.9.A43C56 199 6 511'.5—dc20 96-518 4

CIP

Copying an d reprinting . Materia l i n this book may be reproduced b y any means for educationa l and scientifi c purpose s withou t fe e o r permissio n wit h th e exceptio n o f reproductio n b y service s that collec t fee s fo r deliver y of documents an d provide d tha t th e customar y acknowledgmen t o f th e source i s given . Thi s consen t doe s no t exten d t o othe r kind s o f copyin g fo r genera l distribution , for advertisin g o r promotiona l purposes , o r fo r resale . Request s fo r permissio n fo r commercia l use o f materia l shoul d b e addresse d t o th e Assistan t t o th e Publisher , America n Mathematica l Society, P . O . Bo x 6248 , Providence , Rhod e Islan d 02940-6248 . Request s ca n als o b e mad e b y e-mail t o reprint-permiss ionQams . org .

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© Copyrigh t 199 6 b y th e America n Mathematica l Society . Al l right s reserved . The America n Mathematica l Societ y retain s al l right s

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Contents

Foreword x i

Introduction t o th e Secon d DIMAC S Challenge : Cliques , coloring , an d satisfiability

DAVID S . JOHNSO N AN D MICHAE L A . TRIC K 1

Clique

Polyhedral method s fo r th e maximu m cliqu e proble m EGON BALAS , SABASTIA N CERIA , GERAR D CORNUEJOLS , AN D

GABOR PATAK I 1 1

Finding larg e clique s i n arbitrar y graph s b y bipartit e matchin g EGON BALA S AN D WILLIA M NIEHAU S 2 9

An exac t quadrati c 0- 1 algorith m fo r th e stabl e se t proble m JEAN-MARIE BOURJOLLY , PAU L GILL , GILBER T LAPORTE , AN D

HELENE MERCUR E 5 3

Camouflaging independen t set s i n quasi-rando m graph s MARK BROCKINGTO N AN D JOSEP H C . CULBERSO N 7 5

Constructing clique s using restricte d backtrackin g MARK K . GOLDBER G AN D REI D D . RIVENBURG H 8 9

A continuou s base d hueristi c fo r th e maximu m cliqu e proble m L. E . GIBBONS , D . W . HEARN , AN D P . M . PARDALO S 10 3

Applying th e IN N mode l t o the Maximu m Cliqu e proble m TAL GROSSMA N 12 5

Experiments wit h polynomial-tim e CLIQU E approximatio n algorithm s o n very larg e graph s

STEVEN HOME R AN D MARCU S PEINAD O 14 7

Approximately solvin g Maximum Cliqu e usin g neura l networ k an d relate d heuristics

ARUN JAGOTA , LAUR A SANCHIS , AN D RAVIKANT H GANESA N 16 9

viii CONTENT S

Edge projectio n an d th e maximu m cardinalit y stabl e se t proble m CARLO MANNIN O AN D ANTONI O SASSAN O 20 5

Tabu searc h algorithm s fo r th e maximu m cliqu e proble m

PATRICK SORIAN O AN D MICHE L GENDREA U 22 1

Coloring

Exploring th e /c-colorabl e landscap e wit h Iterate d Greed y JOSEPH C . CULBERSO N AN D FEN G LU O 24 5

Coloring b y tabu branc h an d boun d FRED GLOVER , MAR K PARKER , AN D JENNIFE R RYA N 28 5

Experiments wit h paralle l grap h colorin g heuristic s an d application s o f graph colorin g

GARY LEWANDOWSK I AN D ANN E CONDO N 30 9

Distributed coloratio n neighborhoo d searc h CRAIG MORGENSTER N 33 5

An improve d algorith m fo r exac t grap h colorin g

E. C . SEWEL L 35 9

Satisfiability

Random generatio n o f tes t instance s wit h controlle d attribute s YUICHI ASAHIRO , KAZU O IWAMA , AN D EIJ I MIYAN O 37 7

A linear programmin g an d roundin g approac h t o ma x 2-sa t J. CHERIYAN , W . H . CUNNINGHAM , L . TuNgEL , AN D Y . WAN G 39 5

SAT versu s UNSA T O. DUBOIS , P . ANDRE , Y . BOUFKHAD , AN D J . CARLIE R 41 5

Large plateaus and plateau search in Boolean Satisfiability problems : Whe n to giv e u p searchin g an d star t agai n

STEVEN HAMPSO N AN D DENNI S KIBLE R 43 7

Tabu searc h an d a quadrati c relaxatio n fo r th e Satisfiabilit y proble m BRIGITTE JAUMARD , MIHNE A STAN , AN D JACQUE S DESROSIER S 45 7

Efficiency an d stabilit y o f hypergraph SA T algorithm s DANIELE PRETOLAN I 47 9

A GRAS P fo r satisfiabilit y MAURICIO G . C . RESEND E AN D THOMA S A . F E O 49 9

Local searc h strategie s fo r satisfiabilit y testin g BART SELMAN , HENR Y KAUTZ , AN D BRA M COHE N 52 1

CONTENTS IX

Simulated annealin g fo r har d satisfiabilit y problem s WILLIAM M . SPEAR S 53 3

Satisfiability testin g wit h mor e reasonin g an d les s guessin g ALLEN VA N GELDE R AN D YUM I K . TSUJ I 55 9

Comparative studie s o f constrain t satisfactio n an d Davis-Putna m algo -rithms fo r maximu m satisfiabilit y problem s

RICHARD J . WALLAC E AN D EUGEN E C . FREUDE R 58 7

Combination

Object-oriented implementatio n of heuristic search methods for Graph Coloring , Maximum Clique , an d Satisfiabilit y

CHARLES FLEUREN T AN D JACQUE S A . FERLAN D 61 9

Appendix: Secon d DIMAC S Challeng e tes t problem s MICHAEL A . TRIC K 65 3

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Foreword

This AMS-DIMAC S volum e resultin g fro m ou r secon d DIMAC S Implementa -tion Challeng e contain s referee d paper s tha t resulte d fro m th e yea r o f researc h o n clique finding , grap h coloring , an d satisfiability . Ther e hav e bee n tw o challenge s since this , an d a fift h i s no w unde r way . Th e cente r hope s tha t thes e program s encourage experimenta l researc h o n algorithm s an d hel p t o buil d researc h commu -nities o f sufficien t siz e to suppor t continuin g activ e progress .

We would lik e to thank Davi d S . Johnson an d Michae l A. Trick for thei r effort s to pla n an d organiz e th e challeng e a s wel l a s th e worksho p tha t culminate d th e year.

Fred Roberts , Directo r Andrew Yao , Co-Directo r

Stephen Mahaney , Associat e Directo r

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