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- W200045149 abstract "Free AccessAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to SectionFree Access HomeINFORMS TutORials in Operations ResearchEmerging Theory, Methods, and Applications Branch and Tree Decomposition Techniques for Discrete OptimizationIllya V. Hicks, Arie M. C. A. Koster, Elif KolotoğluIllya V. Hicks, Arie M. C. A. Koster, Elif KolotoğluPublished Online:14 Oct 2014https://doi.org/10.1287/educ.1053.0017Abstract This chapter gives a general overview of two emerging techniques for discrete optimization that have footholds in mathematics, computer science, and operations research: branch decompositions and tree decompositions. Branch decompositions and tree decompositions, along with their respective connectivity invariants, branchwidth and treewidth, were first introduced to aid in proving the graph minors theorem, a well-known conjecture (Wagner's conjecture Robertson and Seymour [N. Robertson and P. D. Seymour. Graph minors: A survey. I. Anderson, ed. Surveys in Combinatorics. London Mathematical Society Lecture Note Series, Vol. 103. Cambridge University Press, Cambridge, UK, 153--171, 1985.]) in graph theory. The algorithmic importance of branch decompositions and tree decompositions for solving 𝒩𝒫-hard problems modeled on graphs was first realized by computer scientists in relation to formulating graph problems in monadic second-order logic. The dynamic programming techniques utilizing branch decompositions and tree decompositions, called branch decomposition- and tree decomposition-based algorithms, fall into a class of algorithms known as fixed-parameter tractable algorithms and have been shown to be effective in a practical setting for 𝒩𝒫-hard problems such as minimum domination, the traveling salesman problem, general minor containment, and frequency assignment problems. This publication has no references to display. Previous Back to Top Next FiguresReferencesRelatedInformation Emerging Theory, Methods, and ApplicationsSeptember 2005 Article Information Metrics Downloaded 88 times in the past 12 months Information Published Online:October 14, 2014 Copyright © 2005, INFORMSCite asIllya V. HicksArie M. C. A. KosterElif Kolotoğlu (2014) Branch and Tree Decomposition Techniques for Discrete Optimization. INFORMS TutORials in Operations Research null(null):1-29. https://doi.org/10.1287/educ.1053.0017 Keywordsbranchwidthtreewidthgraph algorithmscombinatorial optimizationPDF download" @default.
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- W200045149 title "Branch and Tree Decomposition Techniques for Discrete Optimization" @default.
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