On almost Monge all scores matrices

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The all scores matrix of a grid graph is a matrix containing the optimal scores of paths from every vertex on the first row of the graph to every vertex on the last row. This matrix is commonly used to solve diverse string comparison problems. All scores matrices have the Monge property, and this was exploited by previous works that used all scores matrices for solving various problems. In this paper, we study an extension of grid graphs that contain an additional set of edges, called bridges. Our main result is to show several properties of the all scores matrices of such graphs. We also give an O(r(nm + n2)) time algorithm for constructing the all scores matrix of an m x n grid graph with r bridges.

Original languageEnglish
Title of host publication27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016
EditorsRoberto Grossi, Moshe Lewenstein
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770125
StatePublished - 1 Jun 2016
Event27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016 - Tel Aviv, Israel
Duration: 27 Jun 201629 Jun 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference27th Annual Symposium on Combinatorial Pattern Matching, CPM 2016
CityTel Aviv


  • All path score computations
  • DIST matrices
  • Longest common subsequences
  • Monge matrices
  • Sequence alignment

ASJC Scopus subject areas

  • Software

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