Knapsack Cover Subject to a Matroid Constraint

Chakaravarthy, Venkatesan T.; Choudhury, Anamitra Roy; Natarajan, Sivaramakrishnan R.; Roy, Sambuddha

doi:10.4230/LIPIcs.FSTTCS.2013.275

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Knapsack Cover Subject to a Matroid Constraint

Authors Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, Sambuddha Roy

Part of: Volume: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-12-10

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Document Identifiers

DOI: 10.4230/LIPIcs.FSTTCS.2013.275
URN: urn:nbn:de:0030-drops-43795

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Keywords

Approximation Algorithms
LP rounding
Matroid Constraints
Knapsack problems

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Abstract

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.

Cite As Get BibTex

Venkatesan T. Chakaravarthy, Anamitra Roy Choudhury, Sivaramakrishnan R. Natarajan, and Sambuddha Roy. Knapsack Cover Subject to a Matroid Constraint. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013) https://doi.org/10.4230/LIPIcs.FSTTCS.2013.275

Author Details

Venkatesan T. Chakaravarthy

Anamitra Roy Choudhury

Sivaramakrishnan R. Natarajan

Sambuddha Roy

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