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- W2768402024 abstract "We study the following basic problem called Bi-Covering. Given a graph $G(V,E)$, find two (not necessarily disjoint) sets $Asubseteq V$ and $Bsubseteq V$ such that $Acup B = V$ and such that every edge $e$ belongs to either the graph induced by $A$ or the graph induced by $B$. The goal is to minimize $max{|A|,|B|}$. This is the most simple case of the Channel Allocation problem [R. Gandhi et al., Networks, 47 (2006), pp. 225--236]. A solution that outputs $V,emptyset$ gives ratio at most 2. We show that under a similar strong Unique Games Conjecture by Bansal and Khot [Optimal long code test with one free bit, in Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS'09, IEEE, 2009, pp. 453--462] there is no $2-epsilon$ ratio algorithm for the problem, for any constant $epsilon>0$. Given a bipartite graph, Max-Bi-Clique is a problem of finding the largest $ktimes k$ complete bipartite subgraph. For the Max-Bi-Clique problem, a constant factor hardness was known un..." @default.
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- W2768402024 date "2017-01-01" @default.
- W2768402024 modified "2023-10-17" @default.
- W2768402024 title "Bi-Covering: Covering Edges with Two Small Subsets of Vertices" @default.
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- W2768402024 doi "https://doi.org/10.1137/16m1082421" @default.
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