A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics

Authors Laurent Bulteau , Bertrand Marchand , Yann Ponty

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Author Details

Laurent Bulteau
  • LIGM, CNRS, Univ Gustave Eiffel, F77454 Marne-la-vallée, France
Bertrand Marchand
  • LIX, CNRS UMR 7161, Ecole Polytechnique, Institut Polytechique de Paris, France
  • LIGM, Marne-la-Valée, France
Yann Ponty
  • LIX, CNRS UMR 7161, Ecole Polytechnique, Institut Polytechique de Paris, France


The authors would like to thank H. Tamaki and Y. Kobayashi for fruitful email exchanges.

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Laurent Bulteau, Bertrand Marchand, and Yann Ponty. A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold. We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n²)-space, O(n^{2ρ+2.5})-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n^{ρ+1})-space, O(n^{ρ+2})-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [Tamaki, 2011]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph. We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n^{ρ+2}) for the energy barrier problem, improving upon a partial O(n^{2ρ+2.5}) algorithm for the problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Applied computing → Bioinformatics
  • reconfiguration problems - parameterized algorithms - RNA bioinformatics - directed pathwidth


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