A fast algorithm for multiplying min-sum permutations

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6 Citations (Scopus)


The present article considers the problem for determining, for given two permutations over indices from 1 to n, the permutation whose distribution matrix is identical to the min-sum product of the distribution matrices of the given permutations. This problem has several applications in computing the similarity between strings. The fastest known algorithm to date for solving this problem executes in O(n1.5) time, or very recently, in O(nlogn) time. The present article independently proposes another O(nlogn)-time algorithm for the same problem, which can also be used to partially solve the problem efficiently with respect to time in the sense that, for given indices g and i with 1≤g<i≤n+1, the proposed algorithm outputs the values R(h) for all indices h with g≤h<i in O(n+(i-g)log(i-g)) time, where R is the solution of the problem.

Original languageEnglish
Pages (from-to)2175-2183
Number of pages9
JournalDiscrete Applied Mathematics
Issue number17
Publication statusPublished - 2011 Oct 28


  • Algorithms
  • Matrix multiplication
  • Semi-local string comparison


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