Optimal cuts and partitions in tree metrics in polynomial time

We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could...

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Vydané v:	Information processing letters Ročník 113; číslo 12; s. 447 - 451
Hlavní autori:	Karpinski, Marek, Lingas, Andrzej, Sledneu, Dzmitry
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 30.06.2013 Elsevier Sequoia S.A
Predmet:	Algorithms Computational complexity Computer and Information Sciences Computer science Computer Sciences Data processing Data- och informationsvetenskap (Datateknik) Datavetenskap (Datalogi) Dynamic programming Geometric metric Geometry Graph theory Graphs Matematik Mathematical Sciences Natural Sciences Naturvetenskap Optimal bisection Optimal cut Optimization Partitions Polynomial time Polynomials Shortest path algorithms Shortest-path problems Studies Tree metric Trees Optimal bisection Tree metric Optimal cut Computational complexity Geometric metric Polynomial time
ISSN:	0020-0190, 1872-6119
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Abstract	We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. •A novel polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree.•A resolution of the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings.•A discussion of an extension of our method to the class of metrics induced by the bounded treewidth graphs.
AbstractList	We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. [PUBLICATION ABSTRACT] We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. (C) 2013 Elsevier B.V. All rights reserved. We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. •A novel polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree.•A resolution of the exact complexity status of the optimal partition problems in one-dimensional geometric metric settings.•A discussion of an extension of our method to the class of metrics induced by the bounded treewidth graphs.
Author	Lingas, Andrzej Sledneu, Dzmitry Karpinski, Marek
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SubjectTerms	Algorithms Computational complexity Computer and Information Sciences Computer science Computer Sciences Data processing Data- och informationsvetenskap (Datateknik) Datavetenskap (Datalogi) Dynamic programming Geometric metric Geometry Graph theory Graphs Matematik Mathematical Sciences Natural Sciences Naturvetenskap Optimal bisection Optimal cut Optimization Partitions Polynomial time Polynomials Shortest path algorithms Shortest-path problems Studies Tree metric Trees
Title	Optimal cuts and partitions in tree metrics in polynomial time
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