Khanna, Y and Louis, A and Paul, R (2021) Independent Sets in Semi-random Hypergraphs. In: Lecture Notes in Computer Science, 9 August - 11 August 2021, Virtual, Online, pp. 528-542.
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Abstract
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 [9]. This popular model has also been studied in the works of [9, 30, 35] etc. McKenzie, Mehta, and Trevisan [30] gave algorithms for computing independent sets in such a semi-random family of graphs. The algorithms by McKenzie et al. [30] 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. [30], augmented with “Lasserre/SoS like” hierarchy of constraints. Analogous to the results of McKenzie et al. [30], we study the ranges of input parameters where we can recover the planted independent set or a large independent set.
| Item Type: | Conference Paper |
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| Publication: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH. |
| Keywords: | Approximation algorithms; Beyond worst-case analysis; Hypergraphs; Lasserre/SoS hierarchy; Planted independent sets; Semi-random models; Semidefinite programming |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 09 Jun 2023 08:57 |
| Last Modified: | 09 Jun 2023 08:57 |
| URI: | https://eprints.iisc.ac.in/id/eprint/81820 |
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