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A Lex-BFS-based recognition algorithm for Robinsonian matrices

Laurent,Monique
; 
Seminaroti,M.
Abstract
Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be reordered. We present a new polynomial time algorithm to recognize Robinsonian matrices based on a new characterization of Robinsonian matrices in terms of straight enumerations of unit interval graphs. The algorithm is simple and is based essentially on lexicographic breadth-first search (Lex-BFS), using a divide-and-conquer strategy. When applied to a nonnegative symmetric n×n matrix with m nonzero entries and given as a weighted adjacency list, it runs in O(d(n+m)) time, where d is the depth of the recursion tree, which is at most the number of distinct nonzero entries
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Date
2017-05
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Tilburg University Research Output Collection
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Keywords
Robinson (dis)similarity, Unit interval graph, Lex-BFS, Seriation, Partition refinement, Straight enumeration
Citation
Laurent, M & Seminaroti, M 2017, 'A Lex-BFS-based recognition algorithm for Robinsonian matrices', Discrete Applied Mathematics, vol. 222, pp. 151-165. https://doi.org/10.1016/j.dam.2017.01.027
URI
https://hdl.handle.net/20.500.14602/67497
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