Improved parallel approximation of a class of integer programming problems

N. Alon, A. Srinivasan
1997 Algorithmica  
We present a method to derandomize RN C algorithms, converting them to N C algorithms. Using it, we show how to approximate a class of N P -hard integer programming problems in N C, to within factors better than the current-best N C 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 generalization
more » ... of telephone network planning in SONET rings. Also for a subfamily of the "packing" integer programs, we provide the first N C 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 N C; this superpolynomiality is the bottleneck for some earlier approaches, due to Berger & Rompel and Motwani, Naor & Naor.
doi:10.1007/bf02523683 fatcat:7mmkyhnnbrbafldjieg5r55hxa