Sorting by Prefix Block-Interchanges

Author Anthony Labarre

Thumbnail PDF


  • Filesize: 0.52 MB
  • 15 pages

Document Identifiers

Author Details

Anthony Labarre
  • Laboratoire d'Informatique Gaspard Monge, Université Gustave Eiffel, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, 77454, Marne-la-Vallée, France

Cite AsGet BibTex

Anthony Labarre. Sorting by Prefix Block-Interchanges. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation using as few such operations as possible. We give a 2-approximation algorithm for this problem, show how to obtain improved lower and upper bounds on the corresponding distance, and determine the largest possible value for that distance.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • permutations
  • genome rearrangements
  • interconnection network
  • sorting
  • edit distance
  • prefix block-interchange


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Sheldon B. Akers, Balakrishnan Krishnamurthy, and Dov Harel. The star graph: An attractive alternative to the n-cube. In Proceedings of the Fourth International Conference on Parallel Processing, pages 393-400. Pennsylvania State University Press, August 1987. URL:
  2. Vineet Bafna and Pavel A. Pevzner. Sorting by transpositions. SIAM Journal on Discrete Mathematics, 11(2):224-240 (electronic), May 1998. URL:
  3. Piotr Berman, Sridhar Hannenhalli, and Marek Karpinski. 1.375-approximation algorithm for sorting by reversals. In Rolf H. Möhring and Rajeev Raman, editors, Proceedings of the 10th Annual European Symposium on Algorithms, volume 2461 of Lecture Notes in Computer Science, pages 200-210, Rome, Italy, September 2002. Springer. URL:
  4. Laurent Bulteau, Guillaume Fertin, and Irena Rusu. Sorting by transpositions is difficult. SIAM Journal on Discrete Mathematics, 26(3):1148-1180, 2012. URL:
  5. Laurent Bulteau, Guillaume Fertin, and Irena Rusu. Pancake flipping is hard. Journal of Computer and System Sciences, 81(8):1556-1574, 2015. URL:
  6. Liming Cai, Jianer Chen, Rodney G. Downey, and Michael R. Fellows. On the parameterized complexity of short computation and factorization. Archive for Mathematical Logic, 36(4-5):321-337, 1997. URL:
  7. Alberto Caprara. Sorting permutations by reversals and Eulerian cycle decompositions. SIAM Journal on Discrete Mathematics, 12(1):91-110 (electronic), January 1999. URL:
  8. Xin Chen. On sorting unsigned permutations by double-cut-and-joins. Journal of Combinatorial Optimization, 25(3):339-351, 2013. URL:
  9. Shih-Wen Chou, Chung-Han Yang, Kun-Tze Chen, and Chin Lung Lu. Prefix block-interchanges on binary strings. In William Cheng-Chung Chu, Han-Chieh Chao, and Stephen Jenn-Hwa Yang, editors, Proceedings of the International Computer Symposium on Intelligent Systems and Applications, volume 274 of Frontiers in Artificial Intelligence and Applications, pages 1960-1969, Taichung, Taiwan, December 2014. IOS Press. URL:
  10. David A. Christie. Sorting permutations by block-interchanges. Information Processing Letters, 60(4):165-169, 1996. URL:
  11. Zanoni Dias and João Meidanis. Sorting by prefix transpositions. In Alberto H. F. Laender and Arlindo L. Oliveira, editors, Proceedings of the Ninth International Symposium on String Processing and Information Retrieval, volume 2476 of Lecture Notes in Computer Science, pages 65-76, Lisbon, Portugal, September 2002. Springer-Verlag. URL:
  12. Isaac Elias and Tzvika Hartman. A 1.375-approximation algorithm for sorting by transpositions. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 3(4):369-379, 2006. URL:
  13. Guillaume Fertin, Anthony Labarre, Irena Rusu, Eric Tannier, and Stéphane Vialette. Combinatorics of Genome Rearrangements. Computational Molecular Biology. The MIT Press, 2009. URL:
  14. Sridhar Hannenhalli and Pavel A. Pevzner. Transforming cabbage into turnip: Polynomial algorithm for sorting signed permutations by reversals. Journal of the ACM, 46(1):1-27, 1999. URL:
  15. Mark R. Jerrum. The complexity of finding minimum-length generator sequences. Theoretical Computer Science, 36(2-3):265-289, June 1985. URL:
  16. D. J. Kleitman, Edvard Kramer, J. H. Conway, Stroughton Bell, and Harry Dweighter. Elementary problems: E2564-E2569. The American Mathematical Monthly, 82(10):1009-1010, 1975. URL:
  17. Donald E. Knuth. Sorting and Searching, volume 3 of The art of Computer Programming. Addison-Wesley, 1995. Google Scholar
  18. Anthony Labarre. New bounds and tractable instances for the transposition distance. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 3(4):380-394, October 2006. URL:
  19. Anthony Labarre. Lower bounding edit distances between permutations. SIAM Journal on Discrete Mathematics, 27(3):1410-1428, 2013. URL:
  20. Anthony Labarre and Josef Cibulka. Polynomial-time sortable stacks of burnt pancakes. Theoretical Computer Science, 412(8-10):695-702, March 2011. URL:
  21. S. Lakshmivarahan, Jung-Sing Jwo, and S. K. Dhall. Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey. Parallel Computing, 19(4):361-407, April 1993. URL:
  22. Sophia Yancopoulos, Oliver Attie, and Richard Friedberg. Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics, 21(16):3340-3346, 2005. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail