On dependent randomized rounding algorithms

Authors:
Dimitris Bertsimas;Chungpiaw Teo;Rakesh Vohra
Affiliations:
Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Room E53-363, 50 Memorial Drive, Cambridge, MA 02139-1347, USA;Department of Decision Sciences, Faculty of Business Administration, National University of Singapore, Singapore;Department of Managerial Economics and Management Sciences, Northwestern University, Evanston, Illinois, USA
Venue:
Operations Research Letters
Year:
1999

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Abstract

In recent years, approximation algorithms based on randomized rounding of fractional optimal solutions have been applied to several classes of discrete optimization problems. In this paper, we describe a class of rounding methods that exploits the structure and geometry of the underlying problem to round fractional solution to 0-1 solution. This is achieved by introducing dependencies in the rounding process. We show that this technique can be used to establish the integrality of several classical polyhedra (min cut, uncapacitated lot-sizing, Boolean optimization, k-median on cycle) and produces an improved approximation bound for the min-k-sat problem.