On Almost Monge All Scores Matrices

Research output: Contribution to journalArticlepeer-review


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 its 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 apply these properties to obtain an O(r(nm+ n2)) time algorithm for constructing the all scores matrix of an m× n grid graph with r bridges and bounded integer weights.

Original languageEnglish
Pages (from-to)47-68
Number of pages22
Issue number1
StatePublished - 15 Jan 2019


  • All path score computations
  • DIST matrices
  • Longest common subsequences
  • Monge matrices
  • Multiple-source shortest-paths
  • Sequence alignment

ASJC Scopus subject areas

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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