A simulated annealing algorithm for determining the thickness of a graph

Information Sciences

Volumn 172, Issue 1-2, 2005, Pages 155-172

  Poranen, Timo ^a  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Optimization; Simulated annealing; Thickness; Tripartite graph

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; GRAPH THEORY; HEURISTIC METHODS; OPTIMIZATION; THICKNESS MEASUREMENT;

SUBGRAPHS; THICKNESS; TRIPARTITE GRAPH; VERTEX;

SIMULATED ANNEALING;

EID: 18144399635     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2004.02.029     Document Type: Article

References (33)

1. E. Aarts, and J.K. Lenstra Local search in combinatorial optimization 1997 John Wiley and Sons New York
2. V.B. Alekseev, and V.S. Gonchakov Thickness for arbitrary complete graphs Math. Sbornik. 143 1976 212 230
3. C.R. Aragon, D.S. Johnson, L.A. McGeoch, and C. Schevon Optimization by simulate dannealing: An experimental evaluation; part II, graph coloring and number partitioning Operat. Res. 3 39 1991 378 406
4. L.W. Beineke, and F. Harary The thickness of the complete graph Can. J. Math. 17 1965 850 859
5. L.W. Beineke, F. Harary, and J.W. Moon On the thickness of the complete bipartite graphs Proc. Camb. Philos. Soc. 60 1964 1 5
6. F. Berhart, and P.C. Kainen The book thickness of a graph J. Comp. Theory Ser. B. 27 1979 330 331
7. K.S. Booth, and G.S. Lueker Testing for the consecutive ones property, interval graphs and graph planarity testing using PQ-tree algorithms J. Comp. Syst. Sci. 13 1976 335 379
8. J. Cai, X. Han, and R.E. Tarjan An O(m log n)-time algorithm for maximal planar subgraph problem SIAM J. Comput. 22 1993 1142 1162
9. R. Cimikowski On heuristics for determining the thickness of a graph Inform. Sci. 85 1995 87 98
10. C. Cooper On the thickness of sparse random graphs Comb. Probab. Comput. 1 1992 303 309
11. J.P. Dean, A.M. Hutchinson, and E.R. Scheinerman On the thickness and arboricity of a graph J. Comb. Theory Ser. B. 52 1991 147 151
12. G. Di Battista, P. Eades, R. Tamassia, and I.G. Tollis Graph drawing 1999 Prentice-Hall Englewood Cliffs, NJ
13. M.B. Dillencourt, D. Eppstein, and D.S. Hirschberg Geometric thickness of complete graphs JGAA 4 3 2000 5 17
14. R.K. Guy Outerthickness and outercoarseness of graphs Comb. London Math. Soc. Lect. Notes 13 1974 57 60
15. J.H. Halton On the thickness of graphs of given degree Inform. Sci. 54 1991 219 238
16. J. Hopcroft, and R.E. Tarjan Efficient planarity testing J. ACM 21 1974 549 568
17. D.S. Johnson, A theoretician's guide to the experimental analysis of algorithms. In: M.H. Goldwasser, D.S. Johnson, C.C. McGeoch (Eds.), Data Structures, Near Neighbor Searches, and Methodology: Fifth and Sixth DIMACS Implementation Challenges, 2002, pp. 215-250
18. D.S. Johnson, C.R. Aragon, L.A. McGeoch, and C. Schevon Optimization by simulated annealing: An experimental evaluation; part I, graph partitioning Oper. Res. 6 37 1989 865 892
19. M. Jiinger, and P. Mutzel Maximum planar subgraphs and nice embeddings: practical layout tools Algorithmica 16 1996 33 59
20. 2) maximal planarization algorithm based on PQ-trees. Technical report, Utrecht University, 1992, Technical Report RUU-CS-92-03
21. S. Kawano, and K. Yamazaki Worst case analysis of a greedy algorithm for the graph thickness Inform. Process. Lett. 85 2003 333 337
22. M. Kleinert Die Dicke des n-dimensionale Wiirfel-Graphen J. Comb. Theory 3 1967 10 15
23. LEDA version 4.3 (commercial). Available from < http://www. algorithmic-solutions.com >
24. A. Liebers Planarizing graphs - a survey and annotated bibliography JGAA 5 1 2001 1 74
25. A. Mansfield Determining the thickness of graphs is NP-hard Math. Proc. Camb. Philos. Soc. 93 1983 9 23
26. E. Mäkinen, T. Poranen, and P. Vuorenmaa A genetic algorithm for determining the thickness of a graph Inform. Sci. 138 2001 155 164
27. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller Equation of state calculation by fast computing machines J. Chem. Phys. 21 1953 1087 1091
28. T. Mutzel, P. Odenthal, and M. Scharbrodt The thickness of graphs: a survey Graph. Comb. 14 1998 59 73
29. C.R. Reeves Modern Heuristic Techniques for Combinatorial Problems 1995 McGraw-Hill New York
30. O. Sykora, L.A. Szekely, and X. Vrto A note on Halton's conjecture Inform. Sci. 164 2004 61 64
31. P.J.M. van Laarhoven, and E. Aarts Simulated Annealing: Theory and Applications 1987 Kluwer Dordrecht
32. I. Vrtó, Crossing numbers of graphs: a bibliography. Available from < ftp://ifi.savba.sk/pub/imrich/crobib.ps.gz > 2002
33. W. Wessel Über die Abhängigkeit der Dicke eines Graphen von seinen Knotenpunktvalenzen Geom. Komb. 2 2 1984 235 238