Knapsack Cover Subject to a Matroid Constraint
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.
Approximation Algorithms
LP rounding
Matroid Constraints
Knapsack problems
275-286
Regular Paper
Venkatesan T.
Chakaravarthy
Venkatesan T. Chakaravarthy
Anamitra Roy
Choudhury
Anamitra Roy Choudhury
Sivaramakrishnan R.
Natarajan
Sivaramakrishnan R. Natarajan
Sambuddha
Roy
Sambuddha Roy
10.4230/LIPIcs.FSTTCS.2013.275
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