TY - CHAP
T1 - On k-Column Sparse Packing Programs
T2 - Integer Programming and Combinatorial OptimizationInteger Programming and Combinatorial Optimization
Y1 - 2010
A1 - Bansal,Nikhil
A1 - Korula,Nitish
A1 - Nagarajan,Viswanath
A1 - Srinivasan, Aravind
ED - Eisenbrand,Friedrich
ED - Shepherd,F.
AB - 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 (klogk)-hard to approximate.We generalize our result to the case of maximizing monotone submodular functions over k-column sparse packing constraints, and obtain an e2ke−1+o(k) -approximation algorithm. In obtaining this result, we prove a new property of submodular functions that generalizes the fractionally subadditive property, which might be of independent interest.
JA - Integer Programming and Combinatorial OptimizationInteger Programming and Combinatorial Optimization
T3 - Lecture Notes in Computer Science
PB - Springer Berlin / Heidelberg
VL - 6080
SN - 978-3-642-13035-9
UR - http://dx.doi.org/10.1007/978-3-642-13036-6_28
ER -