Digraph measures: Kelly decompositions, games, and orderings

Theoretical Computer Science

Volumn 399, Issue 3, 2008, Pages 206-219

  Hunter, Paul ^a   Kreutzer, Stephan ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Cop and robber games; Directed graphs; Graph decompositions

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DOMAIN DECOMPOSITION METHODS; POLYNOMIALS; PROBLEM SOLVING;

COP AND ROBBER GAMES; DIRECTED GRAPHS; GRAPH DECOMPOSITIONS; NATURAL CONNECTIVITY MEASURES;

GRAPH THEORY;

EID: 43149108119     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.02.038     Document Type: Article

References (29)

1. Adler I. Directed tree-width examples. Journal of Combinatorial Theory, Series B 97 5 (2007) 718-725
2. Baker B.S. Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM 41 1 (1994) 153-180
3. Barát J. Directed path-width and monotonicity in digraph searching. Graphs and Combinatorics 22 2 (2006) 161-172
4. D. Berwanger, A. Dawar, P. Hunter, S. Kreutzer, DAG-width and parity games, in: Proceedings of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), 2006, pp. 524-536
5. H. Bodlaender, Treewidth: Algorithmic techniques and results, in: Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science (MFCS), 1997, pp. 19-36
6. H. Bodlaender, F. Fomin, A. Koster, D. Kratsch, D. Thilikos, On exact algorithms for treewidth, in: Proceedings of the 14th Annual European Symposium on Algorithms (ESA), 2006
7. Bodlaender H., Gilbert J., Hafsteinsson H., and Kloks T. Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. Journal of Algorithms 18 2 (1995) 238-255
8. B. Courcelle, Graph rewriting: An algebraic and logic approach, in: J. van Leeuwan (Ed.), Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics (B), 1990, pp. 193-242
9. Courcelle B., and Olariu S. Upper bounds to the clique width of graphs. Discrete Applied Mathematics 1-3 (2000) 77-114
10. E. Demaine, M. Hajiaghayi, K. Kawarabayashi, Algorithmic graph minor theory: Decomposition, approximation, and coloring, in: Proceedings of the 46th IEEE Symposium on Foundations of Computer Science (FOCS), 2005, pp. 637-646
11. Dendris N., Kirousis L., and Thilikos D. Fugitive-search games on graphs and related parameters. Theoretical Computer Science 172 1-2 (1997) 233-254
12. Diestel R. Graph Theory. 3rd edition (2005), Springer
13. F. Dorn, E. Penninkx, H. Bodlaender, F. Fomin, Efficient exact algorithms on planar graphs: Exploiting sphere cut branch decompositions, in: Proceedings of the 13th Annual European Symposium on Algorithms (ESA), 2005, pp. 95-106
14. Eppstein D. Subgraph isomorphism in planar graphs and related problems. Journal of Graph Algorithms and Applications 3 3 (1999) 1-27
15. Fomin F.V., Heggernes P., and Telle J.A. Graph searching, elimination trees, and a generalization of bandwidth. Algorithmica 41 2 (2004) 73-87
16. Gilbert J., and Liu J. Elimination structures for unsymmetric sparse LU factors. SIAM Journal of Matrix Analysis and Applications 14 (1993) 334-352
17. In: Grädel E., Thomas W., and Wilke T. (Eds). Automata Logics, and Infinite Games. LNCS vol. 2500 (2002), Springer
18. P. Hunter, S. Kreutzer, Digraph Measures: Kelly Decompositions, Games, and Orderings, in: Proc. of the Eighteenth ACM-SIAM Symp. on Discrete Algorithms (SODA), 2007, pp. 637-644
19. T. Johnson, N. Robertson, P. Seymour, R. Thomas, Addendum to "directed tree-width", unpublished manuscript, 2001
20. Johnson T., Robertson N., Seymour P., and Thomas R. Directed tree-width. Journal of Combinatorial Theory, Series B 82 1 (2001) 138-154
21. S. Kreutzer, S. Ordyniak, Digraph Decompositions and Monotonicity in Digraph Searching, unpublished manuscript, 2007
22. Liu J.W.H. The role of elimination trees in sparse factorization. SIAM Journal of Matrix Analysis and Applications 11 1 (1990) 134-172
23. J. Obdrz ̌álek, DAG-width: Connectivity measure for directed graphs, in: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2006, pp. 814-821
24. Oum S.-I. Rank-width and vertex-minors. Journal of Combinatorial Theory, Series B 95 (2005) 79-100
25. Oum S.-I., and Seymour P. Approximating clique-width and branch-width. Journal of Combinatorial Theory, Series B 96 4 (2006) 514-528
26. Reed B. Introducing directed tree width. 6th Twente Workshop on Graphs and Combinatorial Optimization. Electronic Notes in Discrete Mathematics vol.~3 (1999), Elsevier
27. Rose D., and Tarjan R. Algorithmic aspects of vertex elimination on directed graphs. SIAM Journal of Applied Mathematics 34 1 (1978) 176-197
28. Rose D.J. Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications 32 (1970) 597-609
29. M. Safari, D-width: A more natural measure for directed tree width, in: Proceedings of the 30th International Symposium on Mathematical Foundations of Computer Science (MFCS), 2005, pp. 745-756