Exploiting pseudo-locality of interchange distance

Abstract

The goal of this paper is to examine how to exploit pseudo-locality in order to transform tools designed for the Hamming distance into tools adequate for the interchange distance, which is a pseudo-local metric. Intuitively, operators of pseudo-local string rearrangement distance measures have a bounded effect on the Hamming distance between the string prior to the operator application and after it. Specifically, we demonstrate a way to exploit pseudo-locality of the interchange distance combined with additional techniques to derive:

• 1.
  The first efficient approximate nearest-neighbor (ANN) data structure for the interchange distance, which is $\mathrm{NP}$-hard to compute for general strings.
• 2.
  The first linear-time approximation algorithm to compute approximate pattern matching with interchanges, which is a vast improvement from the $\Theta \left(nm\right)$-time known algorithm, where n and m are the text and the pattern length, respectively.