On an alternative sequence comparison statistic of Steele

TL;DR

This paper analyzes Steele's string comparison statistic, providing asymptotic results for its moments and distribution in random words and permutations, offering an alternative to the longest common subsequence measure.

Contribution

It offers new asymptotic analyses of Steele's statistic and its variation, addressing variance issues in string similarity measures.

Findings

Derived moment asymptotics for Steele's statistic

Established distributional asymptotics in random models

Proposed an alternative to the longest common subsequence measure

Abstract

The purpose of this paper is to study a statistic that is used to compare the similarity between two strings, which is first introduced by Michael Steele in 1982. It was proposed as an alternative to the length of the longest common subsequences, for which the variance problem is still open. Our results include moment asymptotics and distributional asymptotics for Steele's statistic and a variation of it in random words and random permutations.