SDP-Based Algorithms for Maximum Independent Set Problems on Hypergraphs

Authors:
Geir Agnarsson;Magnús M. Halldórsson;Elena Losievskaja
Affiliations:
Dept. of Mathematical Sciences, George Mason University, Fairfax, USA;School of Computer Science, Reykjavík University, Reykjavik, Iceland IS-103;Faculty of Industrial, Mechanical Engineering and Computer Science, University of Iceland, Reykjavik, Iceland IS-107
Venue:
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Year:
2009

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Abstract

This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a $O(\bar{D} \log\log \bar{D}/\log \bar{D})$ bound, where $\bar{D}$ is the average weighted degree in a hypergraph, matching the best bounds known for the special case of graphs. Our approach is to use an semi-definite technique to sparsify a given hypergraph and then apply combinatorial algorithms to find a large independent set in the resulting sparser instance.