Treewidth reduction for constrained separation and bipartization problems

Leibniz International Proceedings in Informatics, LIPIcs

Volumn 5, Issue , 2010, Pages 561-572

  Marx, Dániel ^a   O'Sullivan, Barry ^b   Razgon, Igor ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Fixed parameter algorithms; Graph separation problems; Treewidth

Indexed keywords

BIPARTIZATION; FIXED-PARAMETER ALGORITHMS; FIXED-PARAMETER TRACTABILITY; INDEPENDENT SET; PARAMETERIZED COMPLEXITY; SEPARATION PROBLEMS; TREE-WIDTH;

COMPUTER SCIENCE;

SEPARATION;

EID: 84880311521     PISSN: 18688969     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.4230/LIPIcs.STACS.2010.2458     Document Type: Conference Paper

References (28)

1. N. Bansal, A. Blum, and S. Chawla. Correlation clustering. Machine Learning, 56(1-3):89-113, 2004.
2. H. L. Bodlaender. Treewidth: Characterizations, applications, and computations. In WG, pages 1-14, 2006.
3. H. L. Bodlaender, M. R. Fellows, P. Heggernes, F. Mancini, C. Papadopoulos, and F. A. Rosamond. Clustering with partial information. In MFCS, pages 144-155, 2008.
4. L. S. Chandran and T. Kavitha. The treewidth and pathwidth of hypercubes. Discrete Math., 306(3):359-365, 2006.
5. J. Chen, Y. Liu, and S. Lu. An improved parameterized algorithm for the minimum node multiway cut problem. In WADS, pages 495-506, 2007.
6. J. Chen, Y. Liu, S. Lu, B. O'Sullivan, and I. Razgon. A fixed-parameter algorithm for the directed feedback vertex set problem. J. ACM, 55(5), 2008.
7. E. Demaine, G. Z. Gutin, D. Marx, and U. Stege. Seminar 07281 Open problems. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs, 2007.
8. E. D. Demaine, D. Emanuel, A. Fiat, and N. Immorlica. Correlation clustering in general weighted graphs. Theor. Comput. Sci., 361(2-3):172-187, 2006.
9. J. Díaz, M. Serna, and D. M. Thilikos. (H,C,K)-coloring: fast, easy, and hard cases. In MFCS 2001, pages 304-315, 2001.
10. R. G. Downey and M. R. Fellows. Parameterized Complexity. Monographs in Computer Science. Springer, New York, 1999.
11. U. Feige and M. Mahdian. Finding small balanced separators. In STOC 2006, pages 375-384. ACM, 2006.
12. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer, 2006.
13. G. Gottlob and S. T. Lee. A logical approach to multicut problems. Inform. Process. Lett., 103(4):136-141, 2007.
14. M. Grohe. Logic, graphs, and algorithms. In J. Flum, E. Grädel, and T. Wilke, editors, Logic and Automata-History and Perspectives. Amsterdam University Press, 2007.
15. S. Guillemot. FPT algorithms for path-transversals and cycle-transversals problems in graphs. In IWPEC, pages 129-140, 2008.
16. J. Guo, F. Hüffner, E. Kenar, R. Niedermeier, and J. Uhlmann. Complexity and exact algorithms for vertex multicut in interval and bounded treewidth graphs. European Journal of Operational Research, 186(2):542-553, 2008.
17. I. Kanj. Open problem session of Dagstuhl seminar 08431, 2008.
18. D. Lokshtanov, S. Saurabh, and S. Sikdar. Simpler parameterized algorithm for OCT. In IWOCA 2009, pages 380-384, 2009.
19. D. Marx. Parameterized graph separation problems. Theoretical Computer Science, 351(3):394-406, 2006.
20. D. Marx and I. Razgon. Constant ratio fixed-parameter approximation of the edge multicut problem. In ESA 2009, pages 647-658, 2009.
21. R. Niedermeier. Invitation to fixed-parameter algorithms, volume 31 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, 2006.
22. J.-C. Picard and M. Queyranne. On the structure of all minimum cuts in a network and applications. Math. Programming Stud., (13):8-16, 1980. Combinatorial optimization, II (Proc. Conf., Univ. East Anglia, Norwich, 1979).
23. I. Razgon and B. O'Sullivan. Almost 2-SAT is fixed-parameter tractable. In ICALP (1), pages 551-562, 2008.
24. B. Reed. Tree width and tangles: A new connectivity measure and some applications. In R. Bailey, editor, Surveys in Combinatorics, volume 241 of LMS Lecture Note Series, pages 87-162. Cambridge University Press, 1997.
25. B. Reed, K. Smith, and A. Vetta. Finding odd cycle transversals. Operations Research Letters, 32(4):299-301, 2004.
26. N. Robertson and P. Seymour. Graph minors. X. Obstructions to tree-decomposition. J. Comb. Theory, Ser. B, 52(2):153-190, 1991.
27. M. Samer and S. Szeider. Complexity and applications of edge-induced vertex-cuts. CoRR, abs/cs/0607109, 2006.
28. M. Xiao. Algorithms for multiterminal cuts. In CSR, pages 314-325, 2008.