Easy identification of generalized common and conserved nested intervals

TL;DR

This paper introduces simple algorithms for efficiently identifying generalized nested gene clusters, called b-nested common and conserved intervals, across multiple genomes represented as permutations.

Contribution

It presents two straightforward algorithms to compute all b-nested common or conserved intervals with optimal time complexity, extending classical nested interval concepts.

Findings

Algorithms run in O(Kn + nocc) time for listing intervals.

Counting all b-nested intervals is achievable in O(Kn) time.

New properties of conserved intervals facilitate these computations.

Abstract

In this paper we explain how to easily compute gene clusters, formalized by classical or generalized nested common or conserved intervals, between a set of K genomes represented as K permutations. A b-nested common (resp. conserved) interval I of size |I| is either an interval of size 1 or a common (resp. conserved) interval that contains another b-nested common (resp. conserved) interval of size at least |I|-b. When b=1, this corresponds to the classical notion of nested interval. We exhibit two simple algorithms to output all b-nested common or conserved intervals between K permutations in O(Kn+nocc) time, where nocc is the total number of such intervals. We also explain how to count all b-nested intervals in O(Kn) time. New properties of the family of conserved intervals are proposed to do so.