Theoretical and practical improvements on the RMQ-problem, with applications to LCA and LCE

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4009 LNCS, Issue , 2006, Pages 36-48

  Fischer, Johannes ^a   Heun, Volker ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; MEDICAL COMPUTING; QUERY LANGUAGES; VARIATIONAL TECHNIQUES;

CONSTANT QUERY TIME; DYNAMIC DATA STRUCTURE; LINEAR PREPROCESSING TIME; RANGE-MINIMUM-QUERY-PROBLEM;

PROBLEM SOLVING;

EID: 33746034182     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11780441_5     Document Type: Conference Paper

References (26)

1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: On finding lowest common ancestors in trees. SIAM J. Comput. 5 (1976) 115-132
2. Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM J. Comput. 13 (1984) 338-355
3. Schieber, B., Vishkin, U.: On finding lowest common ancestors: Simplification and parallelization. SIAM J. Comput. 17 (1988) 1253-1262
4. Berkman, O., Vishkin, U.: Recursive star-tree parallel data structure. SIAM J. Comput. 22 (1993)
5. Bender, M.A., Farach- Colton, M.: The LCA problem revisited. In: Proc. LATIN, LNCS 1776, Springer (2000) 88-94
6. Bender, M.A., Farach-Colton, M., Pemmasani, G., Skiena, S., Sumazin, P.: Lowest common ancestors in trees and directed acyclic graphs. J. Algorithms 57 (2005) 75-94
7. Gabow, H.N., Bentley, J.L., Tarjan, R.E.: Scaling and related techniques for geometry problems. In: Proc. of the ACM STOC, ACM Press (1984) 135-143
8. Gonnet, G.H., Baeza-Yates, R.A., Snider, T.: Now indices for text: PAT trees and PAT arrays. In Frakes, W.B., Baeza-Yates, R.A., eds.: Information Retrieval: Data Structures and Algorithms. Prentice-Hall (1992) 66-82
9. Manber, U., Myers, E.W.: Suffix arrays: A new method for on-line string searches, SIAM J. Comput. 22 (1993) 935-948
10. Kasai, T., Lee, G., Arimura, H., Arikawa, S., Park, K.: Linear-time longest-common-prefix computation in suffix arrays and its applications. In: Proc. CPM, LNCS 2089, Springer (2001) 181-192
11. Abouelhoda, M.I., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. J. Discrete Algorithms 2 (2004) 53-86
12. Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: A survey and a new distributed algorithm. In: Proc. SPAA, ACM Press (2002) 258-264
13. Vuillemin, J.: A unifying look at data structures. Comm. ACM 23 (1980) 229-239
14. Tarjan, R.E., Vishkin, U.: An efficient parallel biconnectivity algorithm. SIAM J. Comput. 14 (1985) 862-874
15. Arlazarov, V.L., Dinic, E.A., Kronrod, M.A., Faradzev, I.A.: On economic construction of the transitive closure of a directed graph. Dokl. Acad. Nauk. SSSR 194 (1970, in Russian) 487-488
16. Engl. transl, in Soviet Math. Dokl., 11 1209-1210, 1975
17. Knuth, D.E.: The Art of Computer Programming Vol. 4, Fasc. 4: Generating All Trees; History of Combinatorial Generation. Addison-Wesley (2006)
18. Main, M.G., Lorentz, R.J.: An O(n log n) algorithm for finding all repetitions in a string. J. Algorithms 5 (1984) 422-432
19. Gusfield, D., Stoye, J.: Linear time algorithm for finding and representing all tandem repeats in a string. J. Comput. Syst. Sci. 69 (2004) 525-546
20. Landau, G., Schmidt, J.P., Sokol, D.: An algorithm for approximate tandem repeats. J. Comput. Biol. 8 (2001) 1-18
21. Myers, E.W.: An O(nd) difference algorithm and its variations. Algorithmica 1 (1986) 251-266
22. Landau, G., Vishkin, U.: Introducing efficient parallelism into approximate string matching and a new serial algorithm. In: Proc. STOC, ACM Press (1986) 220-230
23. Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press (1997)
24. Schürmann, K.B., Stoye, J.: An incomplex algorithm for fast suffix array construction. In: Proc, ALENEX/ANALCO, SIAM Press (2005) 77-85.
25. Manzini, G.: Two space saving tricks for linear time lcp array computation. In: Proc. SWAT. LNCS 3111, Springer (2004) 372-383
26. Sadakane, K.: Succinct representations of Icp information and improvements in the compressed suffix arrays. In: Proc. SODA, ACM/SIAM (2002) 225-237