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A Branch-and-Bound Algorithm for Fitting Anti-Robinson Structures to Symmetric Dissimilarity Matrices

Published online by Cambridge University Press:  01 January 2025

Michael J. Brusco
Michael J. Brusco*
Affiliation:
Florida State University
*
Requests for reprints should be sent to Michael J. Brusco, Department of Marketing, Florida State University, Tallahassee, FL 32306-1110. E-Mail: mbrusco@cob.fsu.edu
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Abstract

The seriation of proximity matrices is an important problem in combinatorial data analysis and can be conducted using a variety of objective criteria. Some of the most popular criteria for evaluating an ordering of objects are based on (anti-) Robinson forms, which reflect the pattern of elements within each row and/or column of the reordered matrix when moving away from the main diagonal. This paper presents a branch-and-bound algorithm that can be used to seriate a symmetric dissimilarity matrix by identifying a reordering of rows and columns of the matrix optimizing an anti-Robinson criterion. Computational results are provided for several proximity matrices from the literature using four different anti-Robinson criteria. The results suggest that with respect to computational efficiency, the branch-and-bound algorithm is generally competitive with dynamic programming. Further, because it requires much less storage than dynamic programming, the branch-and-bound algorithm can provide guaranteed optimal solutions for matrices that are too large for dynamic programming implementations.

Keywords

combinatorial optimizationbranch and boundseriationanti-Robinson form

Information

Type
Articles
Information
Psychometrika , Volume 67 , Issue 3 , September 2002 , pp. 459 - 471
Copyright
Copyright © 2002 The Psychometric Society

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