Greedy δ-Approximation algorithm for covering with arbitrary constraints and submodular cost

Abstract

This paper describes a greedy -approximation algorithm for monotone covering, a generalization of many fundamental NP-hard covering problems. The approximation ratio is the maximum number of variables on which any constraint depends. (For example, for vertex cover, is 2.) The algorithm unifies, generalizes, and improves many previous algorithms for fundamental covering problems such as vertex cover, set cover, facilities location, and integer and mixed-integer covering linear programs with upper bound on the variables. The algorithm is also the first -competitive algorithm for online monotone covering, which generalizes online versions of the above-mentioned covering problems as well as many fundamental online paging and caching problems. As such it also generalizes many classical online algorithms, including lru, fifo, fwf, balance, greedy-dual, greedy-dual size (a.k.a. landlord), and algorithms for connection caching, where is the cache size. It also gives new -competitive algorithms for upgradable variants of these problems, which model choosing the caching strategy and an appropriate hardware configuration (cache size, CPU, bus, network, etc.). © 2009 Springer Berlin Heidelberg.