On k-Column Sparse Packing Programs
Abstract
We consider the class of packing integer programs (PIPs) that are column sparse, where there is a specified upper bound k on the number of constraints that each variable appears in. We give an improved (ek + o(k))-approximation algorithm for k-column sparse PIPs. Our algorithm is based on a linear programming relaxation, and involves randomized rounding combined with alteration. We also show that the integrality gap of our LP relaxation is at least 2k - 1; it is known that even special cases of k-column sparse PIPs are Ω(k/log k)-hard to approximate.
- Publication:
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Lecture Notes in Computer Science
- Pub Date:
- 2010
- DOI:
- 10.1007/978-3-642-13036-6_28
- arXiv:
- arXiv:0908.2256
- Bibcode:
- 2010LNCS.6080..369B
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- F.2.2
- E-Print:
- 19 pages, v3: additional details