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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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 157; no. 5; pp. 991 - 1008
Main Authors: Lari, Isabella, Maravalle, Maurizio, Simeone, Bruno
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 06.03.2009
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2008.03.032