The complexity of Shortest Common Supersequence for inputs with no identical consecutive letters

Aurélie Lagoutte (1) , Sébastien Tavenas (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

The Shortest Common Supersequence problem (SCS for short) consists in finding a shortest common supersequence of a finite set of words on a fixed alphabet Σ. It is well-known that its decision version denoted [SR8] in [4] is NP-complete. Many variants have been studied in the literature. In this paper we settle the complexity of two such variants of SCS where inputs do not contain identical consecutive letters. We prove that those variants denoted ϕSCS and MSCS both have a decision version which remains NP-complete when |Σ| ≥ 3. Note that it was known for MSCS when |Σ| ≥ 4 [3].

Mots clés: words; shortest common super sequence; flooding games

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Aurélie Lagoutte, Sébastien Tavenas. The complexity of Shortest Common Supersequence for inputs with no identical consecutive letters. 2017. ⟨hal-01508495⟩