eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-10-04
22:1
22:14
10.4230/LIPIcs.DISC.2018.22
article
Distributed Set Cover Approximation: Primal-Dual with Optimal Locality
Even, Guy
1
Ghaffari, Mohsen
2
Medina, Moti
3
https://orcid.org/0000-0002-5572-3754
Tel-Aviv University, Israel
ETH Zurich, Switzerland
Ben-Gurion University, Israel
This paper presents a deterministic distributed algorithm for computing an f(1+epsilon) approximation of the well-studied minimum set cover problem, for any constant epsilon>0, in O(log (f Delta)/log log (f Delta)) rounds. Here, f denotes the maximum element frequency and Delta denotes the cardinality of the largest set. This f(1+epsilon) approximation almost matches the f-approximation guarantee of standard centralized primal-dual algorithms, which is known to be essentially the best possible approximation for polynomial-time computations. The round complexity almost matches the Omega(log (Delta)/log log (Delta)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM'16], which holds for even f=2 and for any poly(log Delta) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+epsilon)-approximation of vertex cover, with round complexity O(log Delta/log log Delta), as presented by Bar-Yehuda, Censor-Hillel, and Schwartzman [PODC'17] for weighted vertex cover. Our method is quite different and it can be viewed as a locality-optimal way of performing primal-dual for the more general case of set cover. We note that the vertex cover algorithm of Bar-Yehuda et al. does not extend to set cover (when f >= 3).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol121-disc2018/LIPIcs.DISC.2018.22/LIPIcs.DISC.2018.22.pdf
Distributed Algorithms
Approximation Algorithms
Set Cover
Vertex Cover