Greedy Δ-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

Greedy Δ-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

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Article ID: iaor20132084
Volume: 66
Issue: 1
Start Page Number: 113
End Page Number: 152
Publication Date: May 2013
Journal: Algorithmica
Authors: ,
Keywords: approximation, covering problems, greedy algorithms, caching algorithm
Abstract:

This paper describes a simple greedy Δ‐approximation algorithm for any covering problem whose objective function is submodular and non‐decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering constraints, each of which constrains at most Δ variables of the problem. (A simple example is Vertex Cover, with Δ=2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems.

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