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- W1593162480 abstract "For every fixed γ ≥ 0, we give an algorithm that, given an n-vertex 3-uniform hypergraph containing an independent set of size γn, finds an independent set of size $n^{Omega(gamma^2)}$ . This improves upon a recent result of Chlamtac, which, for a fixed ε> 0, finds an independent set of size n ε in any 3-uniform hypergraph containing an independent set of size $(frac12-varepsilon)n$ . The main feature of this algorithm is that, for fixed γ, it uses the Θ(1/γ 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/γ 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." @default.
- W1593162480 created "2016-06-24" @default.
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- W1593162480 date "2008-08-27" @default.
- W1593162480 modified "2023-09-23" @default.
- W1593162480 title "Improved Approximation Guarantees through Higher Levels of SDP Hierarchies" @default.
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- W1593162480 doi "https://doi.org/10.1007/978-3-540-85363-3_5" @default.
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