Improved Approximation Guarantees through Higher Levels of SDP Hierarchies

For every fixed 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size n, finds an independent set of size n(2 ) . This improves upon a recent result of Chlamtac, which, for a fixed > 0, finds an independent set of size n in any 3-uniform hypergraph containing an independent set of size (1 2 - )n. The main feature of this algorithm is that, for fixed , it uses the (1/2 )-level of a hierarchy of semidefinite programming (SDP) relaxations. On the other hand, we show that for at least one hierarchy which gives such a guarantee, 1/ levels yield no non-trivial guarantee. Thus, this is a first SDP-based algorithm for which the approximation guarantee improves indefinitely as one uses progressively higher-level relaxations.

• Type: Conference
• Year: 2008
• Where: APPROX
• Authors: Eden Chlamtac, Gyanit Singh
• Keywords: 3-uniform Hypergraph, Algorithms, APPROX 2008, Independent Set, N-vertex 3-uniform Hypergraph