# Improved parallel approximation of a class of integer programming problems

## Abstract

We present a method to derandomize *RNC* algorithms, converting them to *NC* algorithms. Using it, we show how to approximate a class of *NP*-hard integer programming problems in *NC*, to within factors better than the current-best *NC* algorithms (of Berger & Rompel and Motwani, Naor & Naor); in some cases, the approximation factors are as good as the best-known sequential algorithms, due to Raghavan. This class includes problems such as global wire-routing in VLSI gate arrays. Also for a subfamily of the “packing” integer programs, we provide the first *NC* approximation algorithms; this includes problems such as maximum matchings in hypergraphs, and generalizations. The key to the utility of our method is that it involves sums of *superpolynomially many* terms, which can however be computed in *NC*; this superpolynomiality is the bottleneck for some earlier approaches.

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