Computing sharp bounds for hard clustering problems on trees

Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging, communication and distribution networks, districting, biological taxonomy, and others. They are formulated here as optimal tree partitioning prob...

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Vydáno v:Discrete Applied Mathematics Ročník 157; číslo 5; s. 991 - 1008
Hlavní autoři: Lari, Isabella, Maravalle, Maurizio, Simeone, Bruno
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier B.V 06.03.2009
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computational complexity
Computer science; control theory; systems
Contiguity-constrained clustering
Exact sciences and technology
Graph theory
Heuristics
Integer programming
Linear programming
Mathematics
Sciences and techniques of general use
Theoretical computing
Trees
Trees
Integer programming
Contiguity-constrained clustering
Linear programming
Computational complexity
Heuristics
Tree(graph)
Taxonomy
Computing
Optimization
Relaxation
Database
Distribution function
Combinatorics
Data communication
Partition
Computer theory
Paging
Communication network
Integer
Experimental result
Distribution
Objective function
Application
Variety
ISSN:0166-218X, 1872-6771
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Abstract Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging, communication and distribution networks, districting, biological taxonomy, and others. They are formulated here as optimal tree partitioning problems. In a previous paper, it was shown that their computational complexity strongly depends on the nature of the objective function and, in particular, that minimizing the total within-cluster dissimilarity or the diameter is computationally hard. We propose heuristics that find good partitions within a reasonable time, even for instances of relatively large size. Such heuristics are based on the solution of continuous relaxations of certain integer (or almost integer) linear programs. Experimental results on over 2000 randomly generated instances with up to 500 entities show that the values (total within-cluster dissimilarity or diameter) of the solutions provided by these heuristics are quite close to the minimum one.
AbstractList Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging, communication and distribution networks, districting, biological taxonomy, and others. They are formulated here as optimal tree partitioning problems. In a previous paper, it was shown that their computational complexity strongly depends on the nature of the objective function and, in particular, that minimizing the total within-cluster dissimilarity or the diameter is computationally hard. We propose heuristics that find good partitions within a reasonable time, even for instances of relatively large size. Such heuristics are based on the solution of continuous relaxations of certain integer (or almost integer) linear programs. Experimental results on over 2000 randomly generated instances with up to 500 entities show that the values (total within-cluster dissimilarity or diameter) of the solutions provided by these heuristics are quite close to the minimum one.
Author Maravalle, Maurizio
Simeone, Bruno
Lari, Isabella
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Cites_doi 10.1007/BF02293706
10.1080/14786440109462720
10.1287/mnsc.25.4.329
10.1093/comjnl/28.1.82
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10.1109/TPAMI.1984.4767503
10.1016/S0167-9473(96)00062-X
10.1037/h0071325
10.1145/320521.320531
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10.1109/TPAMI.1980.4767027
10.1137/S1052623498342186
10.1080/1055678021000060829a
10.1007/s00357-003-0011-7
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Issue 5
Keywords Trees
Integer programming
Contiguity-constrained clustering
Linear programming
Computational complexity
Heuristics
Tree(graph)
Taxonomy
Computing
Optimization
Relaxation
Database
Distribution function
Combinatorics
Data communication
Partition
Computer theory
Paging
Communication network
Integer
Experimental result
Distribution
Objective function
Application
Variety
Language English
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Snippet Clustering problems with relational constraints in which the underlying graph is a tree arise in a variety of applications: hierarchical data base paging,...
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SubjectTerms Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computational complexity
Computer science; control theory; systems
Contiguity-constrained clustering
Exact sciences and technology
Graph theory
Heuristics
Integer programming
Linear programming
Mathematics
Sciences and techniques of general use
Theoretical computing
Trees
Title Computing sharp bounds for hard clustering problems on trees
URI https://dx.doi.org/10.1016/j.dam.2008.03.032
Volume 157
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