Large Edit Distance with Multiple Block Operations

  • Dana Shapira
  • James A. Storer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2857)


We consider the addition of some or all of the operations block move, block delete, block copy, block reversals, and block copy reversals, to the traditional edit distance problem (finding the minimum number of insert-character and delete-character operations to convert one string to another). When all of the above operations are allowed, the problem, called the nearest neighbors problem, is NP hard, and the best known approximation is O(logn log* n), which was achieved by Muthukrishnan and Sahinalp [2000,2002a]. In this paper we show that this problem can be approximated by a constant factor of 3.5 using a simple sliding window method. When eliminating reversals, the same method reduces the best known approximation of 12, achieved by Ergun, Muthukrishnan and Sahinalp [2003], down to a factor of 4. Both constant factors are proved to be tight. Allowing only subsets of these operations does not necessarily make the problem easier. Shapira and Storer [2002] present a logn factor approximation algorithm for edit distance with block moves (which is also an NP-complete problem). Here, we show that edit distance with block deletions can be solved optimally, but edit distance with block moves and block deletions remains NP-complete and can be reduced to the problem of block moves only, keeping the same logn factor approximation.


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  1. Bafna, V., Pevzner, P.A.: Sorting by Transpositions. SIAM Journal Discrete Mathematics 11(2), 124–240 (1998)MathSciNetGoogle Scholar
  2. Bafna, V., Pevzner, P.A.: Genome Rearrangements and Sorting by Reversals. In: IEEE Sym. on Foundations of Computer Science, pp. 148–157 (1993)Google Scholar
  3. Cormode, G., Paterson, M., Sahinalp, S.C., Vishkin, U.: Communication Complexity of Document Exchange. In: SODA, pp. 197–206 (2000)Google Scholar
  4. Cormode, G., Muthukrishnan, S.: The String Edit Distance Problem with Moves. In: SODA, pp. 667–676 (2002)Google Scholar
  5. Durand, D., Farach, M., Ravi, R., Singh, M.: A Short Course in Computational Molecular Biology. DIMACS Technical Report 97–63 (1997)Google Scholar
  6. Ergun, F., Muthukrishnan, S., Sahinalp, S.C.: Comparing Sequences with Segment Rearrangements, DIMACS Technical Report (2003)Google Scholar
  7. Hannenhalli, S.: Polynomial-Time Algorithm for Computing Translocation Distance Between Genomes. In: Hirschberg, D.S., Meyers, G. (eds.) CPM 1996. LNCS, vol. 1075, pp. 162–176. Springer, Heidelberg (1996)Google Scholar
  8. Lopresti, D., Tomkins, A.: Block Edit Models for Approximate String Matching. Theoretical Computer Science 181, 159–179 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  9. Masek, W.J., Paterson, M.S.: A Faster Algorithm for Computing String Edit Distances. J. Computer and System Sciences 20, 18–31 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  10. Muthukrishnan, S., Sahinalp, S.C.: Approximate Nearest Neighbors and Sequence Comparison with Block Operations. In: ACM STOC, pp. 416–424 (2000)Google Scholar
  11. Muthukrishnan, S., Sahinalp, S.C.: Simple and Practical Sequence Nearest Neighbors with Block Operations. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 262–278. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. Muthukrishnan, S., Sahinalp, S.C.: An Improved Algorithm for Sequence Comparison with Block Reversals. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 372–386. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. Shapira, D., Storer, J.A.: Edit Distance with Move Operations. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 85–98. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. Shapira, D., Storer, J.A.: In-Place Differential File Compression. In: DCC, pp. 263–272 (2003a)Google Scholar
  15. Shapira, D., Storer, J.A.: Edit Distance with Multiple Block Operations, Technical Report CS-03-236 (2003b)Google Scholar
  16. Smith, T.F., Waterman, M.S.: Identification of Common Molecular Sequences. Journal of Molecular Biology 147, 195–197 (1981)CrossRefGoogle Scholar
  17. Tichy, W.F.: The String to String Correction Problem with Block Moves. ACM Transactions on Computer Systems 2(4), 309–321 (1984)CrossRefMathSciNetGoogle Scholar
  18. Vingron, M., Waterman, M.S.: Sequence Alignment and Penalty Choice. Journal of Molecular Biology 235, 1–12 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dana Shapira
    • 1
  • James A. Storer
    • 1
  1. 1.Computer Science DepartmentBrandeis University 

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