Summary: Improved parallel approximation of a class of integer
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 and a gener-
alization of telephone network planning in SONET rings. 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, due to Berger & Rompel and Motwani, Naor & Naor.
Keywords. De-randomization, integer programming, parallel algorithms, approximation algo-
rithms, rounding theorems, randomized rounding, linear programming, linear relaxation, com-
A preliminary version of this work appeared in the Proc. International Colloquium on Automata, Languages
and Programming, 1996, pages 562573.