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SODA
2010
ACM

On linear and semidefinite programming relaxations for hypergraph matching

11 years 10 months ago
On linear and semidefinite programming relaxations for hypergraph matching
The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a well-studied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method. Our main results are the following: ? We consider the standard linear programming relaxation of the problem. We provide an algorithmic proof of a result of F?uredi, Kahn and Seymour, showing that the integrality gap is exactly k - 1 + 1/k for k-uniform hypergraphs, and is exactly k - 1 for k-partite hypergraphs. This yields an improved approximation algorithm for the weighted 3-dimensional matching problem. Our algorithm combines the use of the iterative rounding method and the fractional local ratio method, showing a ...
Yuk Hei Chan, Lap Chi Lau
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Yuk Hei Chan, Lap Chi Lau
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