doi:10.1007/s00453-010-9431-z
ISI:000291481900005
ArXiv:0904.0859
Pritchard, David
Chakrabarty, Deeparnab
Approximability of Sparse Integer Programs
Springer-Verlag
http://infoscience.epfl.ch/record/150507/files/453_2010_Article_9431.pdf
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.
2010-08-21T15:15:13Z
http://infoscience.epfl.ch/record/150507
http://infoscience.epfl.ch/record/150507
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