Betweenness parameterized above tight lower bound

Gregory Gutin*, Eun Jung Kim, Matthias Mnich, Anders Yeo

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We study ordinal embedding relaxations in the realm of parameterized complexity. We prove the existence of a quadratic kernel for the betweenness problem parameterized above its tight lower bound, which is stated as follows. For a set v of variables and set c of constraints “vi is between vj and vk”, decide whether there is a bijection from v to the set {1,…,|v|} satisfying at least |c|/3+? of the constraints in c. Our result solves an open problem attributed to benny chor in niedermeier's monograph “invitation to fixed-parameter algorithms”. The betweenness problem is of interest in molecular biology. An approach developed in this paper can be used to determine parameterized complexity of a number of other optimization problems on permutations parameterized above or below tight bounds.
Original languageEnglish
Pages (from-to)872-878
JournalJournal of Computer and System Sciences
Issue number8
Publication statusPublished - 2010
Externally publishedYes


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