Open access
Date
2016Type
- Conference Paper
ETH Bibliography
yes
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Abstract
Random Edge is the most natural randomized pivot rule for the simplex algorithm. Considerable progress has been made recently towards fully understanding its behavior. Back in 2001, Welzl introduced the concepts of reachmaps and niceness of Unique Sink Orientations (USO), in an effort to better understand the behavior of Random Edge. In this paper, we initiate the systematic study of these concepts. We settle the questions that were asked by Welzl about the niceness of (acyclic) USO. Niceness implies natural upper bounds for Random Edge and we provide evidence that these are tight or almost tight in many interesting cases. Moreover, we show that Random Edge is polynomial on at least n^{Omega(2^n)} many (possibly cyclic) USO. As a bonus, we describe a derandomization of Random Edge which achieves the same asymptotic upper bounds with respect to niceness. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000126567Publication status
publishedExternal links
Book title
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)Journal / series
Leibniz International Proceedings in Informatics (LIPIcs)Volume
Pages / Article No.
Publisher
Schloss Dagstuhl - Leibniz-Zentrum für InformatikEvent
Subject
Random edge; Unique sink orientation; Random walk; Reachmap; NicenessOrganisational unit
03457 - Welzl, Emo (emeritus) / Welzl, Emo (emeritus)
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ETH Bibliography
yes
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