Compact labeling scheme for ancestor queries

SIAM Journal on Computing

Volumn 35, Issue 6, 2006, Pages 1295-1309

  Abiteboul, Serge ^a   Alstrup, Stephen ^b   Kaplan, Haim ^c   Milo, Tova ^c   Rauhe, Theis ^b  

^a INRIA ROCQUENCOURT   (France)

^b IT UNIVERSITY OF COPENHAGEN   (Denmark)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Alphabetic codes; Ancestor queries; Labeling algorithm; Rooted tree

Indexed keywords

ALPHABETIC CODES; ANCESTOR QUERIES; LABELING ALGORITHM; ROOTED TREE;

ALGORITHMS; COMPUTATION THEORY; PROBLEM SOLVING; TREES (MATHEMATICS);

QUERY LANGUAGES;

EID: 33845587607     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539703437211     Document Type: Article

References (34)

1. S. ABITEBOUL, P. BUNEMAN, AND D. SUCIU, Data on the Web: From Relations to Semistructured Data and XML, Morgan-Kaufmann, San Francisco, 1999.
2. S. ABITEBOUL, H. KAPLAN. AND T. MILO, Compact labeling schemes for ancestor queries, in Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Washington, DC, 2001, SIAM, Philadelphia, 2001, pp. 547-556.
3. S. ALSTRUP, P. BILLE, AND T. RAUHE, Labeling schemes for small distances in trees, in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Baltimore, MD, 2003, SIAM, Philadelphia, 2003, pp. 689-698.
4. S. ALSTRUP, C. GAVOILLE, H. KAPLAN, AND T. RAUHE, Nearest common ancestors: A survey and a new algorithm for a distributed environment, Theory Comput. Syst., 37 (2004), pp. 441-456.
5. S. ALSTRUP, J. HOLM, K. DE LICHTENBERG, AND M. THORUP, Minimizing diameters of dynamic trees, in Automata, Languages and Programming, 24th International Colloquium (ICALP), Lecture Notes in Comput. Sci. 1256, Springer-Verlag, New York, 1997, pp. 270-280.
6. S. ALSTRUP, J. HOLM, AND M. THORUP, Maintaining median and center in dynamic trees, in Proceedings of the 7th Scandinavian Workshop on Algorithm Theory (SWAT), Lecture Notes Comput. Sci. 1851, Springer-Verlag, New York, 2000, pp. 46-56.
7. S. ALSTRUP AND T. RAUHE, Improved labeling scheme for ancestor queries, in Proceedings of the Thirteen Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), San Francisco, CA, 2002, SIAM, Philadelphia, 2002, pp. 947-953.
8. Altavista, online search engine at http://www.altavista.com.
9. M. A. BREUER, Coding vertexes of a graph, IEEE Trans. Inform. Theory, IT-12 (1966), pp. 148-153.
10. M. A. BREUER AND J. FOLKMAN, An unexpected result on coding vertices of a graph, J. Math. Anal. Appl., 20 (1967), pp. 583-600.
11. T. H. CORMEN, C. E. LBISERSON, AND R. L. RIVEST, Introduction to Algorithms, MIT Press/ McGraw-Hill, New York, 1991.
12. A. DEUTSCH, M. F. FERNANDEZ, D. FLORESCU, A. Y. LEVY, AND D. SUCIU, A query language for XML, Computer Networks, 31 (1999), pp. 1155-1169.
13. G. N. FREDERICKSON, Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees, SIAM J. Comput., 26 (1997), pp. 484-538.
14. C. GAVOILLE AND D. PELEG, Compact and localized distributed data structures, J. Distributed Comput., 16 (2003), pp. 111-120.
15. C. GAVOILLE, D. PELEG, S. PÉRENNÈS, AND R. RAZ, Distance labeling in graphs, J. Algorithms, 53 (2004), pp. 85-112.
16. E. N. GILBERT AND E. F. MOORE, Variable-length binary encodings, Bell System Technical Journal, 38 (1959), pp. 933-967.
17. Google, online search engine at http://www.google.com/.
18. S. KANNAN, M. NAOR, AND S. RUDICH, Implicit representation of graphs, SIAM J. Discrete Math., 5 (1992), pp. 596-603.
19. H. KAPLAN AND T. MILO, Short and simple labels for small distances and other functions, in Proceedings of the 7th Workshop on Algorithms and Data Structures, Providence, RI, 2001, Lecture Notes in Comput. Sci. 2125, Springer, New York, 2001, pp. 246-257.
20. H. KAPLAN, T. MILO, AND R. SHABO, A comparison of labeling schemes for ancestor queries, in Proceedings of the Thirteen Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), San Francisco, CA, 2002, SIAM, Philadelphia, 2002, pp. 954-963.
21. M. KATZ, N. A. KATZ, A. KORMAN, AND D. PELEG, Labeling schemes for flow and connectivity, SIAM J. Comput., 34 (2004), pp. 23-40.
22. M. KATZ, N. A. KATZ, AND D. PELEG, Distance labeling schemes for well-separated graph classes, Discrete Appl. Math., 145 (2005), pp. 384-402.
23. Q. LI AND B. MOON, Indexing and querying xml data for regular path expression, in Proceedings of the 27th International Conference on Very Large Data Bases (VLDB), Rome, 2001, Morgan Kaufmann, San Francisco, 2001, pp. 361-370.
24. K. MEHLHORN, A best possible bound for the weighted path length of binary search trees, SIAM J. Comput., 6 (1997), pp. 235-239.
25. OASIS, Organization for the Advancement of Structures Information Standards, available online at http://www.oasis-open.org/.
26. D. PELEG, Proximity-preserving labeling schemes, J. Graph Theory, 33 (2000), pp. 167-176.
27. N. SANTORO AND R. KHATIB, Labeling and implicit routing in networks, Comput. J., 28 (1985), pp. 5-8.
28. R. TARJAN, Depth-first search and linear graph algorithms, SIAM J. Comput., 1 (1972), pp. 146-160.
29. M. THORUP AND U. ZWICK, Compact routing schemes, in Proceedings of the 13th Annual ACM Symposium on Parallel Algorithms and Architectures, Crete, Greece, 2001, ACM, New York, 2001, pp. 1-10.
30. A. K. TSAKALIDIS, Maintaining order in a generalized linked list, Acta Inform., 21 (2004), pp. 101-112.
31. W3. Extensible Markup Languange (XML) 1.0, documentation online at http://www.w3.org/XML.
32. W3C. Extensible Stylesheet Language (XSL), documentation online at http://www.w3.org/Style/XSL/.
33. HyperText Markup Language (HTML), documentation online at http://www.w3.org/MarkUp.
34. Xyleme. A dynamic data warehouse for the XML data of the web, documentation online at http://www.xyleme.com