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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| Veröffentlicht in: | Discrete Applied Mathematics Jg. 157; H. 5; S. 991 - 1008 |
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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. |
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| 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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| 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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| 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 |
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