Approximating Coloring and Maximum Independent Sets in 3-Uniform Hypergraphs

Journal of Algorithms

Volumn 41, Issue 1, 2001, Pages 99-113

  Krivelevich, Michael ^a   Nathaniel, Ram ^a   Sudakov, Benny ^b,c  

^a TEL AVIV UNIVERSITY   (Israel)

^b PRINCETON UNIVERSITY   (United States)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011523905     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.2001.1173     Document Type: Article

References (22)

1. N. Alon and N. Kahale, Approximating the independence number via the θ-function, Math. Program. 80 (1998), 253-264.
2. N. Alon, P. Kelsen, S. Mahajan, and H. Ramesh, Coloring 2-colorable hypergraphs with a sublinear number of colors, Nordic J. Comput. 3 (1996), 425-439.
3. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetii-Spaccamela, and M. Protasi, "Complexity and Approximation," Springer-Verlag, Berlin, 1999. [See also http://www.nada.kth.se/∼viggo/problemlist/compendium.html]
4. R. Bar-Yehuda and S. Even, A local ratio theorem for approximating the weighted vertex cover problem, in "Analysis and Design of Algorithms for Combinatorial Problems" (G. Ausiello and M. Lucertini, Eds.), Annals of Discrete Math., Vol. 25, pp. 27-46, Elsevier, Amsterdam, 1985.
5. 3/14)-coloring algorithm for 3-colorable graphs, Inform. Process. Lett. 61 (1997), 49-53.
6. R. Boppana and M. M. Halldórsson, Approximating maximum independent sets by excluding subgraphs, BIT 32 (1992), 180-196.
7. H. Chen and A. Frieze, Coloring bipartite hypergraphs, in "Proc. 5th Intern. IPCO Conf.," Lecture Notes in Computer Science, Vol. 1084, pp. 345-358, Springer-Verlag, Berlin/New York, 1996.
8. 1-o(1), in "Proc. 27th Intern. Colloquium on Automata, Languages and Programming (ICALP 2000)," Lecture Notes in Computer Science, Vol. 1853, pp. 2-12, Springer-Verlag, Berlin/New York, 2000.
9. U. Feige and J. Kilian, Zero knowledge and the chromatic number, in "Proc. 11th Annual IEEE Conf. on Computational Complexity," 1996; J. Comput. System Sci. 57 (1998), 187-199, doi: 10.1006/jcss.1998.1587.
10. U. Feige and J. Kilian, Zero knowledge and the chromatic number, in "Proc. 11th Annual IEEE Conf. on Computational Complexity," 1996; J. Comput. System Sci. 57 (1998), 187-199, doi: 10.1006/jcss.1998.1587.
11. M. Grötschel, L. Lovász, and A. Schrijver, The ellipsoid method and its consequences in combinatorial optimization, Combinatorica 1 (1981), 169-197.
12. V. Guruswami, J. Håstad, and M. Sudan, Hardness of approximate hypergraph coloring, in "Proc. 41st IEEE FOCS," pp. 149-158, IEEE Press, New York, 2000.
13. M. M. Halldórsson, A still better performance guarantee for approximate graph coloring, Inform. Process. Lett. 45 (1993), 19-23.
14. E. Halperin, Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs, in "Proc. 11th Symposium on Discrete Algorithms (SODA '2000)," pp. 329-337.
15. 1-ε, in "Proc. 37th IEEE FOCS," pp. 627-636, IEEE Press, New York, 1996; Acta Math. 182 (1999), 105-142.
16. 1-ε, in "Proc. 37th IEEE FOCS," pp. 627-636, IEEE Press, New York, 1996; Acta Math. 182 (1999), 105-142.
17. T. Hofmeister and H. Lefmann, Approximating maximum independence sets in uniform hypergraphs, in "Proc. 23rd Symp. on Math. Found. Comp. Sci.," Lecture Notes in Computer Science, Vol. 1450, pp. 562-570, Springer-Verlag, Berlin/New York.
18. D. Karger, R. Motwani, and M. Sudan, Approximate graph coloring by semidefinite programming, J. Assoc. Comput. Mach. 45 (1998), 246-265.
19. S. Khanna, N. Linial, and M. Safra, On the hardness of approximating the chromatic number, in "Proc. 2nd Israeli Symposium on Theor. Comp. Sci.," pp. 250-260, IEEE Press, New York, 1992.
20. M. Krivelevich, Approximate set covering in uniform hypergraphs, J. Algorithms 25 (1997), 118-143, doi: 10.1006/jagm.1997.0872.
21. M. Krivelevich and B. Sudakov, Approximate coloring of uniform hypergraphs, in "Proc. 6th European Symposium on Algorithms (ESA '98)," Lecture Notes in Computer Science, Vol. 1461, 477-489, Springer-Verlag, Berlin/New York, 1998.
22. S. Mahajan and H. Ramesh, Derandomizing approximation algorithms based on semidefinite programming, SIAM J. Comput. 28 (1999), 1641-1663.