The intractability of computing the Hamming distance

Theoretical Computer Science

Volumn 337, Issue 1-3, 2005, Pages 331-346

  Manthey, Bodo ^a   Reischuk, Rüdiger ^a  

^a UNIVERSITY OF LÜBECK   (Germany)

Author keywords

Computational complexity; Edit distance; Hamming distance; Inapproximability; Parameterized complexity

Indexed keywords

APPROXIMATION THEORY; BINARY CODES; COMPUTATIONAL COMPLEXITY; FORMAL LANGUAGES; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM SOLVING;

EDIT DISTANCE; HAMMING DISTANCE; INAPPROXIMABILITY; PARAMETERIZED COMPLEXITY;

COMPUTER SCIENCE;

EID: 18444366757     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.02.002     Document Type: Article

References (35)

1. K.A. Abrahamson, R.G. Downey, and M.R. Fellows Fixed-parameter tractability and completeness IV: on completeness for W[P] and PSPACE analogs Ann. Pure Appl. Logic 73 3 1995 235 276
2. A.V. Aho, and T.G. Peterson A minimum distance error-correcting parser for context-free languages SIAM J. Comput. 1 4 1972 305 312
3. E. Allender, D. Bruschi, and G. Pighizzini The complexity of computing maximal word functions Comput. Complexity 3 1993 368 391
4. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi Complexity and Approximation: Combinatorial Optimization Problems and their Approximability Properties 1999 Springer Berlin
5. Z. Bar-Yossef, T.S. Jayram, R. Krauthgamer, and R. Kumar Approximating edit distance efficiently Proc. 45th Ann. IEEE Symp. on Foundations of Computer Science (FOCS) 2004 IEEE Computer Society Silver Spring, MD 550 559
6. T. Batu, F. Ergün, J. Kilian, A. Magen, S. Raskhodnikova, R. Rubinfeld, and R. Sami A sublinear algorithm for weakly approximating edit distance Proc. 35th Ann. ACM Symp. on Theory of Computing (STOC) 2003 ACM Press New York 316 324
7. F.-J. Brandenburg, On one-way auxiliary pushdown automata, in: H. Tzschach, H. Waldschmidt, H.K.-G. Walter (Eds.), Proc. 3rd GI-Conference on Theoretical Computer Science, Lecture Notes in Computer Science, Vol. 48, Springer, Berlin, 1977, pp. 132-144.
8. L. Cai, and J. Chen On the amount of nondeterminism and the power of verifying SIAM J. Comput. 26 3 1997 733 750
9. S.C. Chan, A.K.C. Wong, and D.K.Y. Chiu A survey of multiple sequence comparison methods Bull. Math. Biol. 54 4 1992 563 598
10. S.A. Cook Characterizations of pushdown machines in terms of time-bounded computers J. ACM 18 1 1971 4 18
11. R.G. Downey, and M.R. Fellows Fixed-parameter tractability and completeness I: Basic results SIAM J. Comput. 24 4 1995 873 921
12. R.G. Downey, and M.R. Fellows Fixed-parameter tractability and completeness II: On completeness for W[1] Theoret. Comput. Sci. 141 1-2 1995 109 131
13. R.G. Downey, and M.R. Fellows Parameterized Complexity, Monographs in Computer Science 1999 Springer Berlin
14. R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, in: R.M. Karp (Ed.), Complexity of Computation, SIAM-AMS Proceedings, Vol. 7, 1974, pp. 43-73.
15. M. Furst, J.B. Saxe, and M. Sipser Parity, circuits, and the polynomial-time hierarchy Math. Systems Theory 17 1 1984 13 27
16. D.M. Gusfield Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology 1997 Cambridge University Press Cambridge
17. M.M. Halldórsson Approximating the minimum maximal independence number Inform. Process. Lett. 46 4 1993 169 172
18. R.W. Hamming Error detecting and error correcting codes Bell System Tech. J. 29 2 1950 147 160
19. L.A. Hemachandra, Algorithms from complexity theory: Polynomial-time operations for complex sets, in: T. Asano, T. Ibaraki, H. Imai, T. Nishizeki (Eds.), Proc. SIGAL Internat. Symp. on Algorithms, Lecture Notes in Computer Science, Vol. 450, Springer, Berlin, 1990, pp. 221-231.
20. D.S. Hirschberg A linear space algorithm for computing maximal common subsequences Commun. ACM 18 6 1975 341 343
21. N. Immerman Descriptive Complexity, Graduate Texts in Computer Science 1998 Springer Berlin
22. E.T. Irons An error-correcting parse algorithm Commun. ACM 6 11 1963 669 673
23. R.E. Ladner The circuit value problem is log space complete for P SIGACT News 7 1 1975 18 20
24. V.I. Levenshtein Binary codes capable of correcting deletions, insertions and reversals Sov. Phys. Dokl. 10 8 1966 707 710
25. G. Lyon Syntax-directed least-errors analysis for context-free languages: a practical approach Commun. ACM 17 1 1974 3 14
26. B. Manthey, R. Reischuk, The intractability of computing the Hamming distance, in: T. Ibaraki, N. Katoh, H. Ono (Eds.), Proc. 14th Ann. Internat. Symp. on Algorithms and Computation (ISAAC), Lecture Notes in Computer Science, Vol. 2906, Springer, Berlin, 2003, pp. 88-97.
27. W.J. Masek, and M.S. Paterson A faster algorithm computing string edit distances J. Comput. System Sci. 20 1 1980 18 31
28. G. Navarro A guided tour to approximate string matching ACM Comput. Surv. 33 1 2001 31 88
29. P.A. Pevzner Computational Molecular Biology: An Algorithmic Approach 2000 MIT Press Cambridge, MA
30. G. Pighizzini A parallel minimum distance error-correcting context-free parser A. Marchetti-Spaccamela P. Mentrasti M.V. Zilli Proc. 4th Italian Conf. on Theoretical Computer Science 1992 World Scientific Singapore 305 316
31. G. Pighizzini How hard is computing the edit distance? Inform. Comput. 165 1 2001 1 13
32. D.A. Spielman, The complexity of error-correcting codes, in: B.S. Chlebus, L. Czaja (Eds.), Proc. 11th Internat. Symp. on Fundamentals of Computation Theory (FCT), Lecture Notes in Computer Science, Vol. 1279, Springer, Berlin, 1997, pp. 67-84.
33. I.H. Sudborough On the tape complexity of deterministic context-free languages J. ACM 25 3 1978 405 414
34. A. Vardy Algorithmic complexity in coding theory and the minimum distance problem Proc. 29th Ann. ACM Symp. on Theory of Computing (STOC) 1997 ACM Press New York 92 109
35. H. Vollmer, Introduction to Circuit Complexity - A Uniform Approach, Texts in Theoretical Computer Science, An EATCS Series, Springer, Berlin, 1999.