2016
DOI: 10.48550/arxiv.1601.03521
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Similarity-First Search: a new algorithm with application to Robinsonian matrix recognition

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Cited by 2 publications
(6 citation statements)
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“…Corneil [5] gives an algorithm for recognizing unit interval graphs based on three sweeps of Lex-BFS. In [18] a weighted generalization of Lex-BFS, called Similarity First Search (SFS), is introduced, which applies to symmetric matrices. It is shown in [18] that n sweeps of SFS can recognize Robinsonian matrices of size n by returning a Robinson ordering.…”
Section: Outlook About Other Structured Matrices and Recognition Algo...mentioning
confidence: 99%
See 1 more Smart Citation
“…Corneil [5] gives an algorithm for recognizing unit interval graphs based on three sweeps of Lex-BFS. In [18] a weighted generalization of Lex-BFS, called Similarity First Search (SFS), is introduced, which applies to symmetric matrices. It is shown in [18] that n sweeps of SFS can recognize Robinsonian matrices of size n by returning a Robinson ordering.…”
Section: Outlook About Other Structured Matrices and Recognition Algo...mentioning
confidence: 99%
“…In [18] a weighted generalization of Lex-BFS, called Similarity First Search (SFS), is introduced, which applies to symmetric matrices. It is shown in [18] that n sweeps of SFS can recognize Robinsonian matrices of size n by returning a Robinson ordering. It is natural to ask whether SFS can also be used to find perfect elimination orderings.…”
Section: Outlook About Other Structured Matrices and Recognition Algo...mentioning
confidence: 99%
“…Different algorithms were recently introduced in [14,15], based on a link between Robinsonian matrices and unit interval graphs (pointed out in [23]) and exploiting the fact that unit interval graphs can be recognized efficiently using a simple graph search algorithm, namely Lexicographic Breadth-First Search (Lex-BFS) (see [3,4]). The algorithm of [14] is based on expressing Robinsonian matrices as conic combinations of (adjacency matrices of) unit interval graphs and iteratively using Lex-BFS to check whether these are unit interval graphs; its overall running time is O(L(m + n)), where L is the number of distinct values in the matrix and m is its number of nonzero entries.…”
Section: Introduction 1backgroundmentioning
confidence: 99%
“…The algorithm of [14] is based on expressing Robinsonian matrices as conic combinations of (adjacency matrices of) unit interval graphs and iteratively using Lex-BFS to check whether these are unit interval graphs; its overall running time is O(L(m + n)), where L is the number of distinct values in the matrix and m is its number of nonzero entries. The algorithm of [15] relies on a new search algorithm, Similarity-First Search (SFS), which can be seen as a generalization of Lexicographic Breadth-First Search (Lex-BFS) to the setting of weighted graphs. The SFS algorithm runs in O(n + m log n) time and the recognition algorithm for Robinsonian matrices terminates after at most n iterations of SFS, thus with overall running time O(n 2 + nm log n) [15].…”
Section: Introduction 1backgroundmentioning
confidence: 99%
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