Efficient algorithms for enumerating maximal common subsequences of two strings

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.