%0 Book Section %B Integer Programming and Combinatorial OptimizationInteger Programming and Combinatorial Optimization %D 2010 %T On k-Column Sparse Packing Programs %A Bansal,Nikhil %A Korula,Nitish %A Nagarajan,Viswanath %A Srinivasan, Aravind %E Eisenbrand,Friedrich %E Shepherd,F. %X 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. %B Integer Programming and Combinatorial OptimizationInteger Programming and Combinatorial Optimization %S Lecture Notes in Computer Science %I Springer Berlin / Heidelberg %V 6080 %P 369 - 382 %8 2010/// %@ 978-3-642-13035-9 %G eng %U http://dx.doi.org/10.1007/978-3-642-13036-6_28