Improved parallel approximation of a class of integer programming problems

We present a method to derandomizeRNC algorithms, converting them toNC algorithms. Using it, we show how to approximate a class of NP-hard integer programming problems inNC, to within factors better than the current-bestNC algorithms (of Berger and Rompel and Motwaniet al.); 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 generalization of telephone network planning in SONET rings. Also for a subfamily of the “packing” integer programs, we provide the firstNC 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 ofsuperpolynomially many terms, which can however be computed inNC; this superpolynomiality is the bottleneck for some earlier approaches, due to Berger and Rompel and Motwaniet al. A preliminary version of this work appeared inProc. International Colloquim on Automata, Languages and Programming, 1996, pages 562–573. Work done in parts at DIMACS (supported in part by NSF-STC91-19999 and by support from the N.J. Commission on Science and Technology), at the Institute for Advanced Study, Princeton (supported in part by Grant 93-6-6 of the Alfred P. Sloan Foundation), and at the National University of Singapore.