What makes the arc-preserving subsequence problem hard?

Authors:
Guillaume Blin;Guillaume Fertin;Romeo Rizzi;Stéphane Vialette
Affiliations:
LINA – FRE CNRS 2729, Université de Nantes, Nantes Cedex 3, France;LINA – FRE CNRS 2729, Université de Nantes, Nantes Cedex 3, France;Dipartimento di Informatica e Telecomunicazioni, Università degli Studi di Trento Facoltà di Scienze, Povo – Trento, (TN), Italy;LRI – UMR CNRS 8623 Faculté des Sciences d'Orsay, Université Paris-Sud Bât 490, Orsay Cedex, France
Venue:
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Year:
2005

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Abstract

Given two arc-annotated sequences (S,P) and (T,Q) representing RNA structures, the Arc-Preserving Subsequence (APS) problem asks whether (T,Q) can be obtained from (S, P) by deleting some of its bases (together with their incident arcs, if any). In previous studies [3, 6], this problem has been naturally divided into subproblems reflecting intrinsic complexity of arc structures. We show that APS(Crossing, Plain) is NP-Complete, thereby answering an open problem [6]. Furthermore, to get more insight into where actual border of APS hardness is, we refine APS classical subproblems in much the same way as in [11] and give a complete categorization among various restrictions of APS problem complexity.