Digraph measures: Kelly decompositions, games, and orderings

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 07-09-January-2007, Issue , 2007, Pages 637-644

  Hunter, Paul ^a   Kreutzer, Stephan ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DIRECTED GRAPHS; FACTORIZATION; POLYNOMIAL APPROXIMATION; TREES (MATHEMATICS);

COMPLEXITY ANALYSIS; COMPLEXITY MEASURES; COPS AND ROBBERS; K-TREES; MATRIX FACTORIZATIONS; POLYNOMIAL-TIME ALGORITHMS;

GRAPH THEORY;

EID: 84969211349     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. I. Adler. Directed tree-width examples. To appear in Journal of Combinatorial Theory, Series B.
2. B. S. Baker. Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM, 41(1):153-180, 1994.
3. J. Barát. Directed path-width and monotonicity in digraph searching. To appear in Graphs and Combinatorics.
4. D. Berwanger, A. Dawar, P. Hunter, and S. Kreutzer. DAGwidth and parity games. In Proceedings of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), pages 524-536, 2006.
5. H. Bodlaender. Treewidth: Algorithmic techniques and results. In Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 19-36, 1997.
6. H. Bodlaender, F. Fomin, A. Koster, D. Kratsch, and D. Thilikos. On exact algorithms for treewidth. In Proceedings of the 14th Annual European Symposium on Algorithms (ESA), 2006.
7. H. Bodlaender, J. Gilbert, H. Hafsteinsson, and T. Kloks. Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. Journal of Algorithms, 18(2):238-255, 1995.
8. B. Courcelle. Graph rewriting: An algebraic and logic approach. In J. van Leeuwan, editor, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pages 193-242. 1990.
9. B. Courcelle and S. Olariu. Upper bounds to the clique width of graphs. Discrete Applied Mathematics, 1.3:77-114, 2000.
10. E. Demaine, M. Hajiaghayi, and K. Kawarabayashi. Algorithmic graph minor theory: Decomposition, approximation, and coloring. In Proceedings of the 46th IEEE Symposium on Foundations of Computer Science (FOCS), pages 637-646, 2005.
11. N. Dendris, L. Kirousis, and D. Thilikos. Fugitive-search games on graphs and related parameters. Theoretical Computer Science, 172(1-2):233-254, 1997.
12. R. Diestel. Graph Theory. Springer, 3rd edition, 2005.
13. F. Dorn, E. Penninkx, H. Bodlaender, and F. Fomin. Efficient exact algorithms on planar graphs: Exploiting sphere cut branch decompositions. In Proceedings of the 13th Annual European Symposium on Algorithms (ESA), pages 95-106, 2005.
14. D. Eppstein. Subgraph isomorphism in planar graphs and related problems. Journal of Graph Algorithms and Applications, 3(3):1-27, 1999.
15. F. V. Fomin, P. Heggernes, and J. A. Telle. Graph searching, elimination trees, and a generalization of bandwidth. Algorithmica, 41(2):73-87, 2004.
16. J. Gilbert and J. Liu. Elimination structures for unsymmetric sparse LU factors. SIAM Journal of Matrix Analysis and Applications, 14:334-352, 1993.
17. Erich Grädel, Wolfgang Thomas, and Thomas Wilke, editors. Automata Logics, and Infinite Games, volume 2500 of LNCS. Springer, 2002.
18. T. Johnson, N. Robertson, P. Seymour, and R. Thomas. Directed tree-width. Journal of Combinatorial Theory, Series B, 82(1):138-154, 2001.
19. J. W. H. Liu. The role of elimination trees in sparse factorization. SIAM Journal of Matrix Analysis and Applications, 11(1):134-172, 1990.
20. J. Obdržálek. DAG-width: connectivity measure for directed graphs. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 814-821, 2006.
21. S.-I. Oum. Rank-width and vertex-minors. Journal of Combinatorial Theory, Series B, 95:79-100, 2005.
22. S.-I. Oum and P. Seymour. Approximating clique-width and branch-width. Journal of Combinatorial Theory, Series B, 2006. to appear.
23. B. Reed. Introducing directed tree width. In 6th Twente Workshop on Graphs and Combinatorial Optimization, volume 3 of Electronic Notes in Discrete Mathematics. Elsevier, 1999.
24. D. J. Rose. Triangulated graphs and the elimination process. Journal of Mathematical Analysis and Applications, 32:597-609, 1970.
25. 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), pages 745-756, 2005.