Fast distance multiplication of unit-Monge matrices

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2010, Pages 1287-1296

  Tiskin, Alexander ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

GROUP THEORY;

CIRCLE GRAPHS; LINEAR TIME; MAXIMUM CLIQUE; MONGE MATRICES; MULTIPLICATION ALGORITHMS; OPTIMISATIONS; RUNNING TIME; STRING ALGORITHMS;

MATRIX ALGEBRA;

EID: 77951685740     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973075.103     Document Type: Conference Paper

References (39)

1. A. Aggarwal, M. M. Klawe, S. Moran, P. Shor, and R. Wilber. Geometric applications of a matrix-searching algorithm. Algorithmica, 2(1):195-208, 1987.
2. M. H. Albert, R. E. L. Aldred, M. D. Atkinson, H. P. van Ditmarsch, B. D. Handley, C. C. Handley, and J. Opatrny. Longest subsequences in permutations. Australasian Journal of Combinatorics, 28:225-238, 2003.
3. M. H. Albert, M. D. Atkinson, D. Nussbaum, J.-R. Sack, and N. Santoro. On the longest increasing subsequence of a circular list. Information Processing Letters, 101:55-59, 2007.
4. A. Amir, G. Benson, and M. Farach. Let sleeping files lie: Pattern matching in Z-compressed files. Journal of Computer and System Sciences, 52(2):299-307, 1996.
5. A. Apostolico, M. J. Atallah, and S. E. Hambrusch. New clique and independent set algorithms for circle graphs. Discrete Applied Mathematics, 36:1-24, 1992.
6. A. Apostolico and C. Guerra. The longest common subsequence problem revisited. Algorithmica, 2(1):315-336, 1987. (Pubitemid 18521020)
7. N. Bourbaki. Groupes et algèbres de Lie. Chapitres 4,5 et 6. Hermann, 1968.
8. P. Cégielski, I. Guessarian, Y. Lifshits, and Y. Matiyasevich. Window subsequence problems for compressed texts. In Proceedings of CSR, volume 3967 of Lecture Notes in Computer Science, pages 127-136, 2006.
9. T. M. Chan. More algorithms for all-pairs shortest paths in weighted graphs. In Proceedings of the 39th ACM STOC, pages 590-598, 2007. (Pubitemid 47630777)
10. M. Crochemore and W. Rytter. Text Algorithms. Oxford University Press, 1994.
11. M. Demange, T. Ekim, and D. de Werra. A tutorial on the use of graph coloring for some problems in robotics. European Journal of Operational Research, 192(1):41-55, 2009.
12. M. Develin, F. Santos, and B. Sturmfels. On the rank of a tropical matrix. In Combinatorial and computational geometry, volume 52 of MSRI Publications, pages 213-242. Cambridge University Press, 2005.
13. A. Dress, J. H. Koolena, and V. Moulton. On line arrangements in the hyperbolic plane. European Journal of Combinatorics, 23(5):549-557, 2002.
14. S. Even and A. Itai. Queues, stacks and graphs. In Theory of Machines and Computations, pages 71-86. Academic Press, 1971.
15. F. Gavril. Algorithms for a maximum clique and a maximum independent set of a circle graph. Networks, 3:261-273, 1973.
16. M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Number 57 in Annals of Discrete Mathematics. Elsevier, second edition, 2004.
17. D. Gusfield. Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, 1997.
18. D. Hermelin, G. M. Landau, S. Landau, and O. Weimann. A unified algorithm for accelerating edit-distance computation via text-compression. In Proceedings of the 26th STACS, pages 529-540, 2009.
19. W.-L. Hsu. Maximum weight clique algorithms for circular-arc graphs and circle graphs. SIAM Journal on Computing, 14(1):224-231, 1985.
20. J. W. Hunt and T. G. Szymanski. A fast algorithm for computing longest common subsequences. Communications of the ACM, 20(5):350-353, 1977.
21. A. Karzanov. Combinatorial methods to solve cut-determined multi-flow problems. In Combinatorial Methods for Flow Problems, volume 3, pages 6-69. VNIISI, 1979. In Russian.
22. C. Kassel and V. Turaev. Braid Groups, volume 247 of Graduate Texts in Mathematics. Springer, 2008.
23. P. Krusche and A. Tiskin. Efficient parallel string comparison. In Proceedings of ParCo, volume 38 of NIC Series, pages 193-200. John von Neumann Institute for Computing, 2007.
24. G. Landau. Can DIST tables be merged in linear time? An open problem. In Proceedings of the Prague Stringology Conference, page 1. Czech Technical University in Prague, 2006.
25. Y. Lifshits. Processing compressed texts: A tractability border. In Proceedings of CPM, volume 4580 of Lecture Notes in Computer Science, pages 228-240, 2007.
26. Y. Lifshits and M. Lohrey. Querying and embedding compressed texts. In Proceedings of MFCS, volume 4162 of Lecture Notes in Computer Science, pages 681-692, 2006.
27. S. Masuda, K. Nakajima, T. Kashiwabara, and T. Fujisawa. Efficient algorithms for finding maximum cliques of an overlap graph. Networks, 20:157-171, 1990.
28. G. Myers. Approximately matching context-free languages. Information Processing Letters, 54:85-92, 1995.
29. R. W. Richardson and T. A. Springer. The Bruhat order on symmetric varieties. Geometriae Dedicata, 35(1-3):389-436, 1990.
30. D. Rotem and J. Urrutia. Finding maximum cliques in circle graphs. Networks, 11:269-278, 1981.
31. W. Rytter. Algorithms on compressed strings and arrays. In Proceeedings of SOFSEM, volume 1725 of Lecture notes in Computer Science, pages 48-65, 1999.
32. A. Tiskin. All semi-local longest common subsequences in subquadratic time. In Proceedings of CSR, volume 3967 of Lecture Notes in Computer Science, pages 352-363, 2006.
33. A. Tiskin. Semi-local longest common subsequences in subquadratic time. Journal of Discrete Algorithms, 6(4):570-581, 2008.
34. A. Tiskin. Semi-local string comparison: Algorithmic techniques and applications. Mathematics in Computer Science, 1(4):571-603, 2008.
35. A. Tiskin. Faster subsequence recognition in compressed strings. Journal of Mathematical Sciences, 158(5):759-769, 2009.
36. A. Tiskin. Semi-local string comparison: Algorithmic techniques and applications. Technical Report 0707.3619, arXiv, 2009.
37. S. Tsaranov. Representation and classification of Coxeter monoids. European Journal of Combinatorics, 11(2):189-204, 1990.
38. T. A. Welch. A technique for high-performance data compression. Computer, 17(6):8-19, 1984.
39. G. Ziv and A. Lempel. Compression of individual sequences via variable-rate coding. IEEE Transactions on Information Theory, 24:530-536, 1978.