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Knapsack Cover Subject to a Matroid Constraint Chakaravarthy, Venkatesan T. Choudhury, Anamitra Roy Natarajan, Sivaramakrishnan R. Roy, Sambuddha Approximation Algorithms LP rounding Matroid Constraints Knapsack problems We consider the Knapsack Covering problem subject to a matroid constraint. In this problem, we are given an universe U of n items where item i has attributes: a cost c(i) and a size s(i). We also have a demand D. We are also given a matroid M = (U, I) on the set U. A feasible solution S to the problem is one such that (i) the cumulative size of the items chosen is at least D, and (ii) the set S is independent in the matroid M (i.e. S is in I). The objective is to minimize the total cost of the items selected, sum_{i in S}c(i). Our main result proves a 2-factor approximation for this problem. The problem described above falls in the realm of mixed packing covering problems. We also consider packing extensions of certain other covering problems and prove that in such cases it is not possible to derive any constant factor pproximations. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Venkatesan T. Chakaravarthy and Anamitra Roy Choudhury and Sivaramakrishnan R. Natarajan and Sambuddha Roy 2013 Is Part Of LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2013.275 urn:nbn:de:0030-drops-43795 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.275 eng https://creativecommons.org/licenses/by/3.0/legalcode