Solving SCS for bounded length strings in fewer than [formula omitted] steps

Abstract

It is still not known whether a shortest common superstring (SCS) of n input strings can be found faster than in O⁎(2n) time (O⁎(⋅) suppresses polynomial factors of the input length). In this short note, we show that for any constant r, SCS for strings of length at most r can be solved in time O⁎(2(1−c(r))n) where c(r)=(1+2r2)−1. For this, we introduce so-called hierarchical graphs that allow us to reduce SCS on strings of length at most r to the directed rural postman problem on a graph with at most k=(1−c(r))n weakly connected components. One can then use a recent O⁎(2k) time algorithm by Gutin, Wahlström, and Yeo.