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This paper describes a simple greedy D-approximation algorithm for anycovering problem whose objective function is submodular and non-decreasing, andwhose feasible region can be expressed as the intersection of arbitrary (closedupwards) covering constraints, each of which constrains at most D variables ofthe problem. (A simple example is Vertex Cover, with D = 2.) The algorithmgeneralizes previous approximation algorithms for fundamental covering problemsand online paging and caching problems.

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