Elsevier

Discrete Applied Mathematics

Volume 232, 11 December 2017, Pages 157-175
Discrete Applied Mathematics

Computing similarity distances between rankings

https://doi.org/10.1016/j.dam.2017.07.038Get rights and content
Under an Elsevier user license
open archive

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 43-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.

Keywords

Permutations
Similarity distance
Transposition distance

Cited by (0)

This work was supported in part by the NSF STC Class 2010 CCF 0939370 grant. Research of the third author is supported by the IC Postdoctoral Research Fellowship (grant number 2014-14081100005). Farzad Farnoud was with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA.