On improving the approximation ratio of the r-shortest common superstring problem

Tristan Braquelaire , Marie Gasparoux (1) , Mathieu Raffinot (2) , Raluca Uricaru (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 MAB - Méthodes et Algorithmes pour la Bioinformatique

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently been published, the general objective is now to break the conceptual lower bound barrier of 2. This paper is a step ahead in this direction. Here we focus on a particular instance of the SCS problem, meaning the r-SCS problem, which requires all input strings to be of the same length, r. Golonev et al. proved an approximation ratio which is better than the general one for r<= 6. Here we extend their approach and improve their approximation ratio, which is now better than the general one for r<= 7, and less than or equal to 2 up to r = 6.

Domaines: Informatique [cs]; Complexité [cs.CC]; Bio-informatique [q-bio.QM]

Tristan Braquelaire, Marie Gasparoux, Mathieu Raffinot, Raluca Uricaru. On improving the approximation ratio of the r-shortest common superstring problem. 2019. ⟨hal-02414032⟩