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A Lex-BFS-based recognition algorithm for Robinsonian matrices

Monique Laurent(monique***at***cwi.nl)
Matteo Seminaroti(matteo.seminaroti***at***cwi.nl)

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 $n\times n$ 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 of $A$

Keywords: Robinson (dis)similarity; unit interval graph; Lex-BFS; seriation; partition refinement; straight enumeration

Category 1: Combinatorial Optimization

Citation:

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Entry Submitted: 04/29/2015
Entry Accepted: 04/30/2015
Entry Last Modified: 04/29/2015

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