eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-12-10
275
286
10.4230/LIPIcs.FSTTCS.2013.275
article
Knapsack Cover Subject to a Matroid Constraint
Chakaravarthy, Venkatesan T.
Choudhury, Anamitra Roy
Natarajan, Sivaramakrishnan R.
Roy, Sambuddha
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol024-fsttcs2013/LIPIcs.FSTTCS.2013.275/LIPIcs.FSTTCS.2013.275.pdf
Approximation Algorithms
LP rounding
Matroid Constraints
Knapsack problems