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Improved local computation algorithm for set cover via sparsification

Author(s)
Mitrović, Slobodan; Rubinfeld, Ronitt
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Abstract
We design a Local Computation Algorithm (LCA) for the set cover problem. Given a set system where each set has size at most s and each element is contained in at most t sets, the algorithm reports whether a given set is in some fixed set cover whose expected size is O(log s) times the minimum fractional set cover value. Our algorithm requires s (log s t (log s·(log log s+log log t)) queries. This result improves upon the application of the reduction of [Parnas and Ron, TCS'07] on the result of [Kuhn et al., SODA'06], which leads to a query complexity of (st) (log s·log t . To obtain this result, we design a parallel set cover algorithm that admits an efficient simulation in the LCA model by using a sparsification technique introduced in [Ghaffari and Uitto, SODA'19] for the maximal independent set problem. The parallel algorithm adds a random subset of the sets to the solution in a style similar to the PRAM algorithm of [Berger et al., FOCS'89]. However, our algorithm differs in the way that it never revokes its decisions, which results in a fewer number of adaptive rounds. This requires a novel approximation analysis which might be of independent interest. O ) O O )
Date issued
2020-01
URI
https://hdl.handle.net/1721.1/130417
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Grunau, Christoph et al. “Improved local computation algorithm for set cover via sparsification.” Paper in the Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (SODA20), Salt Lake City, Utah, January 5-8 2020, Society for Industrial and Applied Mathematics © 2020 The Author(s)
Version: Original manuscript

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