Independent Sets in Semi-random Hypergraphs
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A set of vertices in a hypergraph is called an independent set if no hyperedge is completely contained inside the set. Given a hypergraph, computing its largest size independent set is an NP-hard problem. In this work, we study the independent set problem on hypergraphs in a natural semi-random family of instances. Our semi-random model is inspired by the Feige-Kilian model [FK01]. This popular model has also been studied in the works of [FK01, Ste17, MMT20] etc. McKenzie, Mehta, and Trevisan [MMT20] gave algorithms for computing independent sets in such a semi-random family of graphs. The algorithms by McKenzie et al. [MMT20] are based on rounding a "crude-SDP". We generalize their results and techniques to hypergraphs for an analogous family of hypergraph instances. Our algorithms are based on rounding the "crude-SDP" of McKenzie et al. [MMT20], augmented with "Lasserre/SoS like" hierarchy of constraints. Analogous to the results of McKenzie et al. [MMT20], we study the ranges of input parameters where we can recover the planted independent set or a large independent set.
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