Linear-work greedy parallel approximate set cover and variants

Authors:
Guy E. Blelloch;Richard Peng;Kanat Tangwongsan
Affiliations:
Carnegie Mellon University, Pittsburgh, PA, USA;Carnegie Mellon University, Pittsburgh, PA, USA;Carnegie Mellon University, Pittsburgh, PA, USA
Venue:
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Year:
2011

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Abstract

We present parallel greedy approximation algorithms for set cover and related problems. These algorithms build on an algorithm for solving a graph problem we formulate and study called Maximal Nearly Independent Set (MaNIS)---a graph abstraction of a key component in existing work on parallel set cover. We derive a randomized algorithm for MaNIS that has O(m) work and O(log2 m) depth on input with m edges. Using MaNIS, we obtain RNC algorithms that yield a (1+ε)Hn-approximation for set cover, a (1 - 1/e -ε)-approximation for max cover and a (4 + ε)-approximation for min-sum set cover all in linear work; and an O(log* n)-approximation for asymmetric k-center for k ≤ logO(1) n and a (1.861+ε)-approximation for metric facility location both in essentially the same work bounds as their sequential counterparts.