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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Bibliographic Details
Published in:Information processing letters Vol. 113; no. 12; pp. 447 - 451
Main Authors: Karpinski, Marek, Lingas, Andrzej, Sledneu, Dzmitry
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 30.06.2013
Elsevier Sequoia S.A
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2013.03.009