Showing papers by "Aravind Srinivasan published in 1996"
TL;DR: The bounds for computing a network decomposition distributively and deterministically are improved and it is shown that the class of graphs G whose maximum degree isnO(?(n))where ?
225 citations
28 Jan 1996
TL;DR: The Lovasz Local Lemma due to Erdős et al. as mentioned in this paper is a powerful tool in proving the existence of rare events, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean.
Abstract: The Lovasz Local Lemma due to Erdős and Lovasz (in Infinite and Finite Sets, Colloq. Math. Soc. J. Bolyai 11, 1975, pp. 609–627) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean. As applications, we consider two classes of NP-hard integer programs: minimax and covering integer programs. A key technique, randomized rounding of linear relaxations, was developed by Raghavan & Thompson (Combinatorica, 7 (1987), pp. 365–374 ) to derive good approximation algorithms for such problems. We use our extension of the Local Lemma to prove that randomized rounding produces, with non-zero probability, much better feasible solutions than known before, if the constraint matrices of these integer programs are column-sparse (e.g., routing using short paths, problems on hypergraphs with small dimension/degree). This complements certain well-known results from discrepancy theory. We also generalize the method of pessimistic estimators due to Raghavan (J. Computer and System Sciences, 37 (1988), pp. 130–143 ), to obtain constructive (algorithmic) versions of our results for covering integer programs.
61 citations
08 Jul 1996
TL;DR: In this article, the authors present a method to derandomize RNC algorithms, converting them to NC algorithms, and show how to approximate a class of NP-hard integer programming problems in NC, to within factors better than the current best NC algorithms.
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.
7 citations
Proceedings Article•
08 Jul 1996
TL;DR: A method to derandomize RNC algorithms, converting them to NC algorithms, and provides the first NC approximation algorithms; this includes problems such as maximum matchings in hypergraphs, and generalizations.
2 citations