A fast algorithm for multiplying min-sum permutations

The present article considers the problem for determining, for given two permutations over indices from image to image, 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 image time, or very recently, in image time. The present article independently proposes another image-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 image and image with image, the proposed algorithm outputs the values image for all indices image with image in image time, where image is the solution of the problem.