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Approximating maximum independent sets in uniform hypergraphs

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

We consider the problems of approximating the independence number and the chromatic number of k-uniform hypergraphs on n vertices. For fixed k≥2, we describe for both problems polynomial time approximation algorithms with approximation ratios O(n/(log(k-1) n)2). This extends results of Boppana and Halldórsson [5] who showed for the case of graphs that an approximation ratio of O(n/(log n)2) can be achieved in polynomial time. On the other hand, assuming NP ⊋ ZPP, there are no polynomial time algorithms for the independence number and the chromatic number of k-uniform hypergraphs with approximation ratio of n 1-ɛ for any fixed ε > 0.

This research was supported by the Deutsche Forschungsgemeinschaft as part of the Collaborative Research Center “Computational Intelligence” (SFB 531).

Part of this work was done during this author's visit at Humboldt-Universität zu Berlin.

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Authors and Affiliations

  1. LS Informatik 2, Universität Dortmund, D-44221, Dortmund, Germany

    Thomas Hofmeister & Hanno Lefmann

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  1. Thomas Hofmeister
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  2. Hanno Lefmann
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Hofmeister, T., Lefmann, H. (1998). Approximating maximum independent sets in uniform hypergraphs. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055806

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  • DOI: https://doi.org/10.1007/BFb0055806

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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