Efficient algorithms for enumerating maximal common subsequences of two strings

TL;DR

This paper introduces multiple efficient algorithms for enumerating all maximal common subsequences of two strings, optimizing preprocessing time, space, and delay for practical applications.

Contribution

It presents three novel algorithms with different space-time trade-offs for enumerating MCSs, including data structures for targeted search without full enumeration.

Findings

Cubic-space algorithm preprocesses in cubic time, outputs MCSs in linear time.

Quadratic-space algorithm preprocesses in quadratic time, outputs MCSs in linear time.

Linear-space algorithm preprocesses in quadratic time, outputs MCSs in linearithmic time.

Abstract

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a cubic-space data structure in cubic time to output each MCS in linear time. This data structure can be used to search for particular MCSs satisfying some condition without performing an explicit enumeration. Another prepares a quadratic-space data structure in quadratic time to output each MCS in linear time, and the other prepares a linear-space data structure in quadratic time to output each MCS in linearithmic time.