Treedepth Parameterized by Vertex Cover Number

Authors Yasuaki Kobayashi, Hisao Tamaki

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Yasuaki Kobayashi
Hisao Tamaki

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Yasuaki Kobayashi and Hisao Tamaki. Treedepth Parameterized by Vertex Cover Number. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 18:1-18:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


To solve hard graph problems from the parameterized perspective, structural parameters have commonly been used. In particular, vertex cover number is frequently used in this context. In this paper, we study the problem of computing the treedepth of a given graph G. We show that there are an O(tau(G)^3) vertex kernel and an O(4^{tau(G)}*tau(G)*n) time fixed-parameter algorithm for this problem, where tau(G) is the size of a minimum vertex cover of G and n is the number of vertices of G.
  • Fixed-parameter algorithm
  • Polynomial kernelization
  • Structural parameterization
  • Treedepth
  • Vertex cover


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  1. B. Aspvall and P. Heggernes. Finding minimum height elimination trees for interval graphs in polynomial time. BIT Numerical Mathematics, 34(4):484-509, 1994. Google Scholar
  2. A. Björklund, T. Husfeldt, P. Kaski, and M. Koivisto. Fourier meets möbius: Fast subset convolution. In Proceedings of the Thirty-ninth Annual ACM Symposium on Theory of Computing, STOC'07, pages 67-74. ACM, 2007. Google Scholar
  3. H. L. Bodlaender. A tourist guide through treewidth. Acta Cybern., 11(1-2):1-21, 1993. Google Scholar
  4. H. L. Bodlaender, J. S. Deogun, K. Jansen, T. Kloks, D. Kratsch, H. Müller, and Z. Tuza. Rankings of graphs. SIAM J. Discrete Math., 11(1):168-181, 1998. Google Scholar
  5. H. L. Bodlaender, R. G. Downey, M. R. Fellows, and D. Hermelin. On problems without polynomial kernels. J. Comput. Syst. Sci., 75(8):423-434, 2009. Google Scholar
  6. H. L. Bodlaender, B. M. P. Jansen, and S. Kratsch. Kernel bounds for structural parameterizations of pathwidth. In Algorithm Theory - SWAT 2012 - 13th Scandinavian Symposium and Workshops, Helsinki, Finland, July 4-6, 2012. Proceedings, pages 352-363, 2012. Google Scholar
  7. H. L. Bodlaender, B. M. P. Jansen, and S. Kratsch. Preprocessing for treewidth: A combinatorial analysis through kernelization. SIAM J. Discrete Math., 27(4):2108-2142, 2013. Google Scholar
  8. M. Chapelle, M. Liedloff, I. Todinca, and Y. Villanger. Treewidth and pathwidth parameterized by the vertex cover number. In Algorithms and Data Structures - 13th International Symposium, WADS 2013, London, ON, Canada, August 12-14, 2013. Proceedings, pages 232-243, 2013. Google Scholar
  9. M. Cygan, D. Lokshtanov, M. Pilipczuk, M. Pilipczuk, and S. Saurabh. On cutwidth parameterized by vertex cover. Algorithmica, 68(4):940-953, 2014. Google Scholar
  10. J. S. Deogun, T. Kloks, D. Kratsch, and H. Müller. On the vertex ranking problem for trapezoid, circular-arc and other graphs. Discrete Applied Mathematics, 98(1-2):39-63, 1999. Google Scholar
  11. D. Dereniowski and A. Nadolski. Vertex rankings of chordal graphs and weighted trees. Inf. Process. Lett., 98(3):96-100, 2006. Google Scholar
  12. Andrew Drucker. New limits to classical and quantum instance compression. SIAM J. Comput., 44(5):1443-1479, 2015. Google Scholar
  13. Z. Dvořák, D. Král, and R. Thomas. Testing first-order properties for subclasses of sparse graphs. J. ACM, 60(5):36, 2013. Google Scholar
  14. L. C. Eggan. Transition graphs and the star-height of regular events. Michigan Math. J., 10(4):385-397, 12 1963. Google Scholar
  15. M. R. Fellows, D. Hermelin, F. A. Rosamond, and H. Shachnai. Tractable parameterizations for the minimum linear arrangement problem. In Algorithms - ESA 2013 - 21st Annual European Symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings, pages 457-468, 2013. Google Scholar
  16. M. R. Fellows, D. Lokshtanov, N. Misra, F. A. Rosamond, and S. Saurabh. Graph layout problems parameterized by vertex cover. In Algorithms and Computation, 19th International Symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings, pages 294-305, 2008. Google Scholar
  17. F. V. Fomin, A. C. Giannopoulou, and M. Pilipczuk. Computing tree-depth faster than 2^n. Algorithmica, 73(1):202-216, 2015. Google Scholar
  18. F. V. Fomin, B. M. P. Jansen, and M. Pilipczuk. Preprocessing subgraph and minor problems: When does a small vertex cover help? J. Comput. Syst. Sci., 80(2):468-495, 2014. Google Scholar
  19. F. V. Fomin and Y. Villanger. Finding induced subgraphs via minimal triangulations. In 27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010, March 4-6, 2010, Nancy, France, pages 383-394, 2010. Google Scholar
  20. F. V. Fomin and Y. Villanger. Treewidth computation and extremal combinatorics. Combinatorica, 32(3):289-308, 2012. Google Scholar
  21. G. Gutin, M. Jones, and M. Wahlström. Structural parameterizations of the mixed chinese postman problem. In Algorithms - ESA 2015 - 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, pages 668-679, 2015. Google Scholar
  22. B. M. P. Jansen. On sparsification for computing treewidth. Algorithmica, 71(3):605-635, 2015. Google Scholar
  23. K. Kitsunai, Y. Kobayashi, K. Komuro, H. Tamaki, and Toshihiro Tano. Computing directed pathwidth in o(1.89^n) time. Algorithmica, 75(1):138-157, 2016. Google Scholar
  24. C. E. Leiserson. Area-efficient graph layouts. In Foundations of Computer Science, 1980., 21st Annual Symposium on, pages 270-281, Oct 1980. Google Scholar
  25. J. W. H. Liu. The role of elimination trees in sparse factorization. SIAM J. Matrix Anal. Appl., 11(1):134-172, January 1990. Google Scholar
  26. B. Monien. The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete. SIAM J. Algebraic Discrete Methods, 7(4):505-512, October 1986. Google Scholar
  27. J. Nešetřil and P. O. de Mendez. Tree-depth, subgraph coloring and homomorphism bounds. Eur. J. Comb., 27(6):1022-1041, 2006. Google Scholar
  28. J. Nešetřil and P. O. de Mendez. Sparsity - Graphs, Structures, and Algorithms, volume 28. Springer, 2012. Google Scholar
  29. A. Pothen. The complexity of optimal elimination trees. Technical Report CS-88-13, Pennsylvania State University, 1988. Google Scholar
  30. F. Reidl, P. Rossmanith, F. Sanchez Villaamil, and S. Sikdar. A faster parameterized algorithm for treedepth. In Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part I, pages 931-942, 2014. Google Scholar
  31. A. Sen, H. Deng, and S. Guha. On a graph partition problem with application to vlsi layout. Inf. Process. Lett., 43(2):87-94, August 1992. Google Scholar