Exact Algorithms for List-Coloring of Intersecting Hypergraphs

Author Khaled Elbassioni

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Khaled Elbassioni

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Khaled Elbassioni. Exact Algorithms for List-Coloring of Intersecting Hypergraphs. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


We show that list-coloring for any intersecting hypergraph of m edges on n vertices, and lists drawn from a set of size at most k, can be checked in quasi-polynomial time (mn)^{o(k^2*log(mn))}.
  • Hypergraph coloring
  • monotone Boolean duality
  • list coloring
  • exact algorithms
  • quasi-polynomial time


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  1. N. Alon, P. Kelsen, S. Mahajan, and R. Hariharan. Approximate hypergraph coloring. Nord. J. Comput., 3(4):425-439, 1996. Google Scholar
  2. N. Alon and J.H. Spencer. The Probabilistic Method. Wiley Series in Discrete Mathematics and Optimization. Wiley, 2004. Google Scholar
  3. G. Bacsó, C. Bujtás, Z. Tuza, and V. Voloshin. New challenges in the theory of hypergraph coloring. In S. Arumugam and R. Balakrishnan, editors, ICDM 2008. International conference on discrete mathematics. Mysore, 2008., pages 67-78, Mysore, 2008. Univ. of Mysore. Google Scholar
  4. J. Beck and S. Lodha. Efficient proper 2-coloring of almost disjoint hypergraphs. In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, January 6-8, 2002, San Francisco, CA, USA., pages 598-605, 2002. Google Scholar
  5. V. V. S. P. Bhattiprolu, V. Guruswami, and E. Lee. Approximate hypergraph coloring under low-discrepancy and related promises. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2015, August 24-26, 2015, Princeton, NJ, USA, pages 152-174, 2015. URL: http://dx.doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.152.
  6. J. C. Bioch and T. Ibaraki. Complexity of identification and dualization of positive boolean functions. Information and Computation, 123(1):50-63, 1995. Google Scholar
  7. E. Boros and K. Makino. A fast and simple parallel algorithm for the monotone duality problem. In Automata, Languages and Programming, 36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part I, pages 183-194, 2009. Google Scholar
  8. A. Chattopadhyay and B. A. Reed. Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 10th International Workshop, APPROX 2007, and 11th International Workshop, RANDOM 2007, Princeton, NJ, USA, August 20-22, 2007. Proceedings, chapter Properly 2-Colouring Linear Hypergraphs, pages 395-408. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007. Google Scholar
  9. H. Chen and A. Frieze. Integer Programming and Combinatorial Optimization: 5th International IPCO Conference Vancouver, British Columbia, Canada, June 3-5, 1996 Proceedings, chapter Coloring bipartite hypergraphs, pages 345-358. Springer Berlin Heidelberg, Berlin, Heidelberg, 1996. Google Scholar
  10. D. de Werra. Restricted coloring models for timetabling. Discrete Mathematics, 165–166:161-170, 1997. Graphs and Combinatorics. Google Scholar
  11. I. Dinur and V. Guruswami. PCPs via Low-Degree Long Code and Hardness for Constrained Hypergraph Coloring. In 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, 26-29 October, 2013, Berkeley, CA, USA, pages 340-349, 2013. Google Scholar
  12. I. Dinur, O. Regev, and C. D. Smyth. The hardness of 3-uniform hypergraph coloring. Combinatorica, 25(5):519-535, 2005. Google Scholar
  13. C. Domingo. Polynominal time algorithms for some self-duality problems. In CIAC'97: Proceedings of the 3rd Italian Conference on Algorithms and Complexity, Rome, Italy, pages 171-180, 1997. Google Scholar
  14. M. Dror, G. Finke, S. Gravier, and W. Kubiak. On the complexity of a restricted list-coloring problem. Discrete Mathematics, 195(1–3):103-109, 1999. Google Scholar
  15. T. Eiter and G. Gottlob. Identifying the minimal transversals of a hypergraph and related problems. SIAM Journal on Computing, 24(6):1278-1304, 1995. Google Scholar
  16. T. Eiter, G. Gottlob, and K. Makino. New results on monotone dualization and generating hypergraph transversals. In STOC'02: Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, pages 14-22, 2002. Google Scholar
  17. T. Eiter, G. Gottlob, and K. Makino. New results on monotone dualization and generating hypergraph transversals. SIAM Journal on Computing, 32(2):514-537, 2003. Google Scholar
  18. T. Eiter, K. Makino, and G. Gottlob. Computational aspects of monotone dualization: A brief survey. KBS Research Report INFSYS RR-1843-06-01, Vienna University of Technology, 2006. Google Scholar
  19. K. Elbassioni. On the complexity of monotone dualization and generating minimal hypergraph transversals. Discrete Applied Mathematics, 156(11):2109-2123, 2008. Google Scholar
  20. P. Erdős, A. L. Rubin, and H. Taylor. Choosability in graphs. In Proceedings of the West Coast Conference on Combinatorics, Graph Theory and Computing, Arcata, CA, Congr. Numer. XXVI, pages 125-157, 1979. Google Scholar
  21. M. L. Fredman and L. Khachiyan. On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms, 21:618-628, 1996. Google Scholar
  22. D. R. Gaur and R. Krishnamurti. Average case self-duality of monotone boolean functions. In Canadian AI'04: Proceedings of the 17th Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence,, pages 322-338, 2004. Google Scholar
  23. G. Gottlob. Hypergraph transversals. In FoIKS'04: Proceedings of the 3rd International Symposium on Foundations of Information and Knowledge Systems, pages 1-5, 2004. Google Scholar
  24. G. Gottlob and E. Malizia. Achieving new upper bounds for the hypergraph duality problem through logic. In Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS'14, Vienna, Austria, July 14-18, 2014, pages 43:1-43:10, 2014. Google Scholar
  25. S. Gravier, D. Kobler, and W. Kubiak. Complexity of list coloring problems with a fixed total number of colors. Discrete Applied Mathematics, 117(1–3):65-79, 2002. Google Scholar
  26. V. Guruswami, P. Harsha, J. Håstad, S. Srinivasan, and G. Varma. Super-polylogarithmic hypergraph coloring hardness via low-degree long codes. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 614-623, 2014. Google Scholar
  27. K. Jansen and P. Scheffler. Generalized coloring for tree-like graphs. Discrete Applied Mathematics, 75(2):135-155, 1997. Google Scholar
  28. D. J. Kavvadias and E. C. Stavropoulos. Monotone boolean dualization is in co-NP[log²n]. Information Processing Letters, 85(1):1-6, 2003. Google Scholar
  29. S. Khot and R. Saket. Hardness of coloring 2-colorable 12-uniform hypergraphs with 2^(log n)^Ω(1) colors. In 55th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2014, Philadelphia, PA, USA, October 18-21, 2014, pages 206-215, 2014. Google Scholar
  30. M. Krivelevich, R. Nathaniel, and B. Sudakov. Approximating coloring and maximum independent sets in 3-uniform hypergraphs. In Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'01, pages 327-328, Philadelphia, PA, USA, 2001. Society for Industrial and Applied Mathematics. Google Scholar
  31. L. Lovász. Combinatorial optimization: some problems and trends. DIMACS Technical Report 92-53, Rutgers University, 2000. Google Scholar
  32. C. H. Papadimitriou. NP-Completeness: A Retrospective. In ICALP'97: Proceedings of the 24th International Colloquium on Automata, Languages and Programming, pages 2-6, London, UK, 1997. Springer-Verlag. Google Scholar
  33. M. Pei. List colouring hypergraphs and extremal results for acyclic graphs. PhD thesis, University of Waterloo, Canada, 2008. Google Scholar
  34. Y. Person and M. Schacht. An expected polynomial time algorithm for coloring 2-colorable 3-graphs. Electronic Notes in Discrete Mathematics, 34:465-469, 2009. European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009). Google Scholar
  35. P. D. Seymor. An expected polynomial time algorithm for coloring 2-colorable 3-graphs. The Quarterly Journal of Mathematics, 25(1):303-311, 1974. Google Scholar
  36. K. Takata. On the sequential method for listing minimal hitting sets. In DM &DM 2002: Proceedings of Workshop on Discrete Mathematics and Data Mining, 2nd SIAM International Conference on Data Mining, pages 109-120, 2002. Google Scholar
  37. V. G. Vizing. Vertex colorings with given colors. Metody Diskret. Analiz., 29:3-10, 1976. Google Scholar
  38. V. I. Voloshin. Coloring Mixed Hypergraphs: Theory, Algorithms, and Applications. Fields Institute monographs. American Mathematical Society, 2002. Google Scholar