LNCS 2764 On the Complexity of Approximating k Dimensional Matching 1st Edition by Elad Hazan, Shmuel Safra, Oded Schwartz ISBN 3540380450 9783540380450

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Product details:

ISBN 10: 3540380450

ISBN 13: 9783540380450

Author:  Elad Hazan, Shmuel Safra, Oded Schwartz 

LNCS 2764 – On the Complexity of Approximating k-Dimensional Matching 1st Edition: 

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 
 unless P = NP. This improves the previous factor of 
 by Trevisan [Tre01]. For low k values we prove NP-hardness factors of 
 and 
 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.

 

LNCS 2764 – On the Complexity of Approximating k-Dimensional Matching 1st Edition Table of contents:

1 Introduction

1.1 Bounded Variants of Set-Packing

1.2 Previous Results

1.3 Our Contribution

1.4 Outline

2 Preliminarie

3 Hyper Dispersers

4 Proof of the Asymptotic Inapproximability Factor for k-SP

4.1 The Construction

5 Extending the Proof for k-DM

6 Hyper-Dispersers

6.1 Optimality of Hyper-Disperser Constructio

7 Discussion

8 Acknowledgements

 

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