- A Lex-BFS-based recognition algorithm for Robinsonian matrices Monique Laurent(moniquecwi.nl) Matteo Seminaroti(matteo.seminaroticwi.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: Download: [PDF]Entry Submitted: 04/29/2015Entry Accepted: 04/30/2015Entry Last Modified: 04/29/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.