1. Computing similarity distances between rankings.
- Author
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Farnoud (Hassanzadeh), Farzad, Milenkovic, Olgica, Puleo, Gregory J., and Su, Lili
- Subjects
- *
SIMILARITY (Geometry) , *PERMUTATIONS , *GRAPH theory , *BOUNDARY value problems , *APPROXIMATION algorithms , *PATHS & cycles in graph theory - Abstract
We address the problem of computing distances between permutations that take into account similarities between elements of the ground set dictated by a graph. The problem may be summarized as follows: Given two permutations and a positive cost function on transpositions that depends on the similarity of the elements involved, find a smallest cost sequence of transpositions that converts one permutation into another. Our focus is on costs that may be described via special metric-tree structures. The presented results include a linear-time algorithm for finding a minimum cost decomposition for simple cycles and a linear-time 4 โ 3 -approximation algorithm for permutations that contain multiple cycles. The proposed methods rely on investigating a newly introduced balancing property of cycles embedded in trees, cycle-merging methods, and shortest path optimization techniques. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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