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On the Complexity of Approximating k-Dimensional Matching

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Book cover Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (RANDOM 2003, APPROX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2764))

Abstract

We study the complexity of bounded variants of graph problems, mainly the problem of k-Dimensional Matching (k-DM), namely, the problem of finding a maximal matching in a k-partite k-uniform balanced hyper-graph. We prove that k-DM cannot be efficiently approximated to within a factor of \( O(\frac{k}{ \ln k}) \) unless P = NP. This improves the previous factor of \(\frac{k}{2^{O(\sqrt{\ln k}})} \) by Trevisan [Tre01]. For low k values we prove NP-hardness factors of \(\frac{54}{53} -- \varepsilon,\frac{30}{29} -- \varepsilon\) and \(\frac{23}{22} -- \varepsilon\) for 4-DM, 5-DM and 6-DM respectively. These results extend to the problem of k-Set-Packing and the problem of Maximum Independent-Set in (k+1)-claw-free graphs.

Research supported in part by the Fund for Basic Research Administered by the Israel Academy of Sciences, and a Bikura grant.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Princeton University, Princeton, NJ, 08544, USA

    Elad Hazan

  2. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Shmuel Safra & Oded Schwartz

  3. School of Mathematics, Tel Aviv University, Tel Aviv, 69978, Israel

    Shmuel Safra

Authors
  1. Elad Hazan
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  2. Shmuel Safra
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  3. Oded Schwartz
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Editor information

Editors and Affiliations

  1. Computer Science Department, Princeton University, 35 Olden Street, 08540, Princeton, NJ

    Sanjeev Arora

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. University of California, Los Angeles

    Amit Sahai

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© 2003 Springer-Verlag Berlin Heidelberg

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Hazan, E., Safra, S., Schwartz, O. (2003). On the Complexity of Approximating k-Dimensional Matching. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds) Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. RANDOM APPROX 2003 2003. Lecture Notes in Computer Science, vol 2764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45198-3_8

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  • DOI: https://doi.org/10.1007/978-3-540-45198-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40770-6

  • Online ISBN: 978-3-540-45198-3

  • eBook Packages: Springer Book Archive

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