TY - GEN

T1 - Distributed set cover approximation

AU - Even, Guy

AU - Ghaffari, Mohsen

AU - Medina, Moti

N1 - Publisher Copyright:
© Guy Even, Mohsen Ghaffari, and Moti Medina.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - This paper presents a deterministic distributed algorithm for computing an f(1+ε) approximation of the well-studied minimum set cover problem, for any constant ε > 0, in O(log(f∆)/log log(f∆)) rounds. Here, f denotes the maximum element frequency and ∆ denotes the cardinality of the largest set. This f(1 + ε) 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 Ω(log(∆)/log log(∆)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM’16], which holds for even f = 2 and for any poly(log ∆) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+ε)-approximation of vertex cover, with round complexity O(log ∆/log log ∆), 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).

AB - This paper presents a deterministic distributed algorithm for computing an f(1+ε) approximation of the well-studied minimum set cover problem, for any constant ε > 0, in O(log(f∆)/log log(f∆)) rounds. Here, f denotes the maximum element frequency and ∆ denotes the cardinality of the largest set. This f(1 + ε) 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 Ω(log(∆)/log log(∆)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM’16], which holds for even f = 2 and for any poly(log ∆) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+ε)-approximation of vertex cover, with round complexity O(log ∆/log log ∆), 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).

KW - And phrases Distributed Algorithms

KW - Approximation Algorithms

KW - Set Cover

KW - Vertex Cover

UR - http://www.scopus.com/inward/record.url?scp=85059649359&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.DISC.2018.22

DO - 10.4230/LIPIcs.DISC.2018.22

M3 - פרסום בספר כנס

AN - SCOPUS:85059649359

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 32nd International Symposium on Distributed Computing, DISC 2018

A2 - Schmid, Ulrich

A2 - Widder, Josef

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 15 October 2018 through 19 October 2018

ER -