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.

Original languageEnglish
Pages (from-to)421-425
Number of pages5
JournalInformation Processing Letters
Volume114
Issue number8
DOIs
StatePublished - Aug 2014

    Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

    Research areas

  • Algorithms, Exact algorithm, Exponential-time algorithm, NP-hard problem, Shortest common superstring, Traveling salesman problem

ID: 49826155