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A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2125)

Abstract

Hannenhalli and Pevzner gave the first polynomial-time algorithm for computing the inversion distance between two signed permutations, as part of the larger task of determining the shortest sequence of inversions needed to transform one permutation into the other. Their algorithm (restricted to distance calculation) proceeds in two stages: in the first stage, the overlap graph induced by the permutation is decomposed into connected components, then in the second stage certain graph structures (hurdles and others) are identified. Berman and Hannenhalli avoided the explicit computation of the overlap graph and gavean O(na(n)) algorithm, based on a Union-Find structure, to find its connected components, where a is the inverse Ackerman function. Since for all practical purposes a(n) is a constant no larger than four, this algorithm has been the fastest practical algorithm to date. In this paper, we present a new linear-time algorithm for computing the connected components, which is more efficient than that of Berman and Hannenhalli in both theory and practice. Our algorithm uses only a stack and is very easy to implement. We give the results of computational experiments over a large range of permutation pairs produced through simulated evolution; our experiments show a speed-up by a factor of 2 to 5 in the computation of the connected components and by a factor of 1.3 to 2 in the overall distance computation.

Keywords

  • Evolutionary Rate
  • Distance Computation
  • Cycle Graph
  • Signed Permutation
  • Computational Molecular Biology

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported in part by NSF Grants CAREER 00-93039, NSF ITR 00-81404 and NSF DEB 99-10123 and by DOE SUNAPP AX-3006 and DOE-CSRI-14968.

Supported in part by NSF Grant ITR 00-81404.

Supported by the UNM Albuquerque High Performance Computing Center.

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Bader, D.A., Moret, B.M.E., Yan, M. (2001). A Linear-Time Algorithm for Computing Inversion Distance between Signed Permutations with an Experimental Study. In: Dehne, F., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 2001. Lecture Notes in Computer Science, vol 2125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44634-6_34

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  • DOI: https://doi.org/10.1007/3-540-44634-6_34

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