A generic algorithm to find all common intervals of two permutations

Abstract

Let K he the set of {1,2,....,m}, [x, y] denote the set of [x,x+1,...,y], where 1/spl les/x,y/spl les/m. Given two permutations /spl sigma//sub A/ and /spl sigma//sub B/ of a set /spl aleph/, A 2-tuple of intervals ([x/sub 1/, y/sub 1/], [x/sub 2/, y/sub 2/]) is called common intervals if /spl sigma//sub A/([x/sub 1/, y/sub 1/])=([x/sub 2/, y/sub 2/]). In this paper, we propose a sufficient and necessary condition for a 2-tuple of intervals to be common intervals. Based on these conditions, we present a generic algorithm that finds all common intervals of these two permutations.