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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