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Main Title: On Minimum Monotone and Unimodal Partitions of Permutations
Author(s): Stefano, Gabriele Di
Krause, Stefan
Lübbecke, Marco E.
Zimmermann, Uwe T.
Type: Research Paper
Abstract: Partitioning a permutation into a minimum number of monotone subsequences is NP-hard. We extend this complexity result to minimum partitions into unimodal subsequences. In graph theoretical terms these problems are cocoloring and what we call split-coloring of permutation graphs. Based on a network flow interpretation of both problems we introduce mixed integer programs; this is the first approach to obtain optimal partitions for these problems in general. We derive an LP rounding algorithm which is a 2-approximation for both coloring problems. It performs much better in practice. In an online situation the permutation becomes known to an algorithm sequentially, and we give a logarithmic lower bound on the competitive ratio and analyze two online algorithms.
Subject(s): permutation
monotone sequence
unimodal sequence
mixed integer program
LP rounding
approximation algorithm
online algorithm
Issue Date: 2005
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 90C27 Combinatorial optimization
90C11 Mixed integer programming
05A05 Combinatorial choice problems
68Q25 Analysis of algorithms and problem complexity
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2005, 07
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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