The RPR2 rounding technique for semidefinite programs

Uriel Feige, Michael Langberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Several combinatorial optimization problems can be approximated using algorithms based on semidefinite programming. In many of these algorithms a semidefinite relaxation of the underlying problem is solved yielding an optimal vector configuration v1 ... vn. This vector configuration is then rounded into a f0; 1g solution. We present a procedure called RPR2 (Random Projection followed by Randomized Rounding) for rounding the solution of such semidefinite programs. We show that the random hyperplane rounding technique introduced by Goemans and Williamson, and its variant that involves outward rotation are both special cases of RPR2. We illustrate the use of RPR2 by presenting two applications. For Max-Bisection we improve the approximation ratio. For Max-Cut, we improve the tradeoff curve (presented by Zwick) that relates the approximation ratio to the size of the maximum cut in a graph.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 28th International Colloquium, ICALP 2001, Proceedings
EditorsFernando Orejas, Paul G. Spirakis, Jan van Leeuwen
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540422870, 9783540422877
StatePublished - 2001
Externally publishedYes
Event28th International Colloquium on Automata, Languages and Programming, ICALP 2001 - Crete, Greece
Duration: 8 Jul 200112 Jul 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2076 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Colloquium on Automata, Languages and Programming, ICALP 2001


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