A generic algorithm to find all common intervals of two permutations

• Published in: 2005 IEEE Computational Systems Bioinformatics Conference - Workshops (CSBW'05) pp. 85 - 86
• Main Authors: Feng, G., Shan, Y.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 2005
• Subjects: Bioinformatics; Computer science; Conferences; Genomics; Proteins; Upper bound
• ISBN: 0769524427; 9780769524429
• DOI: 10.1109/CSBW.2005.9

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.