@article{Pritchard:150507,
title = {Approximability of Sparse Integer Programs},
author = {Pritchard, David and Chakrabarty, Deeparnab},
publisher = {Springer-Verlag},
journal = {Algorithmica},
number = {1},
volume = {61},
pages = {75-93},
year = {2011},
note = {Preliminary version appeared in Proc. European Symposium on Algorithms (ESA) 2009.},
abstract = {The main focus of this paper is a pair of new approximation algorithms for certain integer programs. First, for covering integer programs {min cx:Ax≥b,0≤x≤d} where A has at most k nonzeroes per row, we give a k-approximation algorithm. (We assume A,b,c,d are nonnegative.) For any k≥2 and ε>0, if P≠NP this ratio cannot be improved to k−1−ε, and under the unique games conjecture this ratio cannot be improved to k−ε. One key idea is to replace individual constraints by others that have better rounding properties but the same nonnegative integral solutions; another critical ingredient is knapsack-cover inequalities. Second, for packing integer programs {max cx:Ax≤b,0≤x≤d} where A has at most k nonzeroes per column, we give a (2k 2+2)-approximation algorithm. Our approach builds on the iterated LP relaxation framework. In addition, we obtain improved approximations for the second problem when k=2, and for both problems when every A ij is small compared to b i . Finally, we demonstrate a 17/16-inapproximability for covering integer programs with at most two nonzeroes per column.},
url = {http://infoscience.epfl.ch/record/150507},
doi = {10.1007/s00453-010-9431-z},
}