Optimal distance labeling for interval graphs and related graph families

SIAM Journal on Discrete Mathematics

Volumn 22, Issue 3, 2008, Pages 1239-1258

  Gavoille, Cyril ^a   Paul, Christophe ^b  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b LIRMM   (France)

Author keywords

Distance in graphs; Distributed data structure; Graph representation

Indexed keywords

CONSTANT TIME; DISTANCE IN GRAPHS; DISTANCE LABELING; DISTRIBUTED DATA-STRUCTURE; GRAPH CLASS; GRAPH REPRESENTATION; INPUT GRAPHS; INTERVAL GRAPH; LECTURE NOTES; LOWER BOUNDS; THEORETICAL ASPECTS; UPPER BOUND;

CONTROL THEORY; LABELS;

GRAPH THEORY;

EID: 69649106080     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635006     Document Type: Article

References (37)

1. S. Alstrup and T. Rauhe, Improved labeling scheme for ancestor queries, in Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms (SODA), ACM, New York, SIAM, Philadelphia, 2002, pp. 947-953.
2. F. Bazzaro and C. Gavoille, Localized and compact data-structure for comparability graphs, Discrete Math., (2008), to appear.
3. O. Berkman and U. Vishkin, Finding level-ancestors in trees, J. Comput. System Sci., 48 (1994), pp. 214-230.
4. A. Brandstädt, V. B. Le, and J. Spinrad, Graph Classes, A Survey, SIAM Monogr. Discrete Math. Appl. 3, SIAM, Philadelphia, 1999.
5. D. Z. Chen, D. T. Lee, R. Sridhar, and C. N. Sekharan, Solving the all-pair shortest path query problem on interval and circular-arc graphs, Networks, 31 (1998), pp. 249-257.
6. F. R. K. Chung, Universal graphs and induced-universal graphs, J. Graph Theory, 14 (1990), pp. 443-454.
7. J. E. Cohen, J. Komlós, and T. Mueller, The probability of an interval graph, and why it matters, in Relations Between Combinatorics and Other Parts of Mathematics, Sympos. Pure Math. 34, AMS, Providence, RI, 1979, pp. 97-115.
8. D. G. Corneil, H. Kim, S. Natarajan, S. Olariu, and A. P. Sprague, Simple linear time algorithm of unit interval graphs, Inform. Process. Lett., 55 (1995), pp. 99-104.
9. B. Courcelle and R. Vanicat, Query efficient implementation of graphs of bounded clique width, Discrete Appl. Math., 131 (2003), pp. 129-150.
10. C. M. Herrera de Figueiredo, J. Meidanis, and C. Picinin de Mello, A linear-time algorithm for proper interval recognition, Inform. Process. Lett., 56 (1995), pp. 179-184.
11. B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math., 63 (1941), pp. 600-610.
12. C. Gavoille, M. Katz, N. A. Katz, C. Paul, and D. Peleg, Approximate distance labeling schemes, in Proceedings of the 9th Annual European Symposium on Algorithms (ESA), Lecture Notes in Comput. Sci. 2161, Springer-Verlag, New York, 2001, pp. 476-488.
13. C. Gavoille and C. Paul, Distance labeling scheme and split decomposition, Discrete Math., 273 (2003), pp. 115-130.
14. C. Gavoille and D. Peleg, Compact and localized distributed data structures, Distributed Computing, 16 (2003), pp. 111-120.
15. C. Gavoille, D. Peleg, S. Pérennes, and R. Raz, Distance labeling in graphs, in Proceedings of the 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), ACM, New York, SIAM, Philadelphia, 2001, pp. 210-219.
16. A. Gupta, A. Kumar, and R. Rastogi, Traveling with a pez dispenser (or, routing issues in MPLS), SIAM J. Comput., 34 (2005), pp. 453-474.
17. P. Hanlon, Counting interval graphs, Trans. Amer. Math. Soc, 272 (1982), pp. 383-426.
18. P. Hell, J. Bang-Jensen, and J. Huang, Local tournaments and proper circular arc graphs, in Algorithms, Lecture Notes in Comput. Sci. 450, Springer-Verlag, Berlin, 1990, pp. 101-108.
19. S. Kannan, M. Naor, and S. Rudich, Implicit representation of graphs, SIAM J. Discrete Math., 5 (1992), pp. 596-603.
20. M. Katz, N. A. Katz, and D. Peleg, Distance labeling schemes for well-separated graph classes, in Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS), Lecture Notes in Comput. Sci. 1770, Springer-Verlag, Berlin, 2000, pp. 516-528.
21. A. Korman, General compact labeling schemes for dynamic trees, in Proceedings of the 19th International Symposium on Distributed Computing (DISC), Lecture Notes in Comput. Sci. 3724, Springer-Verlag, Berlin, 2005, pp. 457-471.
22. A. Korman and D. Peleg, Labeling schemes for weighted dynamic tree, in Proceedings of the 30th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Comput. Sci. 2719, Springer-Verlag, Berlin, 2003, pp. 369-383.
23. A. Korman, D. Peleg, and Y. Rodeh, Labeling schemes for dynamic tree networks, in Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science (STACS), Lecture Notes in Comput. Sci. 2285, Springer-Verlag, Berlin, 2002, pp. 76-87.
24. A. Korman, D. Peleg, and Y. Rodeh, Labeling schemes for dynamic tree networks, Theory Comput. Syst., 37 (2004), pp. 49-75.
25. M. Mendel and S. Har-Peled, Fast construction of nets in low-dimensional metrics and their applications, SIAM J. Comput., 35 (2006), pp. 1148-1184.
26. D. Peleg, Informative labeling schemes for graphs, in Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science (MFCS), Lecture Notes in Comput. Sci. 1893, Springer-Verlag, Berlin, 2000, pp. 579-588.
27. D. Peleg, Proximity-preserving labeling schemes, J. Graph Theory, 33 (2000), pp. 167-176.
28. F. S. Roberts, Indifference graphs, in Proof Techniques in Graph Theory, Academic Press, New York, 1969, pp. 139-146.
29. A. Slivkins, Distance estimation and object location via rings of neighbors, in Proceedings of the 24th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM, New York, 2005, pp. 41-50.
30. J. P. Spinrad, Efficient Graph Representations, Fields Inst. Monogr. 19, AMS, Providence, RI, 2003.
31. K. Talwar, Bypassing the embedding: Algorithms for low dimensional metrics, in Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC), ACM, New York, 2004, pp. 281-290.
32. M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, in Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society, Los Alamitos, CA, 2001, pp. 242-251.
33. M. Thorup, Compact oracles for reachability and approximate distances in planar digraphs, J. ACM, 51 (2004), pp. 993-1024.
34. M. Thorup and U. Zwick, Approximate distance oracles, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), ACM, New York, 2001, pp. 183-192.
35. M. Thorup and U. Zwick, Approximate distance oracles, J. ACM, 52 (2005), pp. 1-24.
36. W. T. Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory, The Johns Hopkins University Press, Baltimore, MD, 1992.
37. n, Ph. D. thesis, University of Gottingen, Gottingen, Germany, 1967.