Distance and routing labeling schemes for non-positively curved plane graphs

Journal of Algorithms

Volumn 61, Issue 2, 2006, Pages 60-88

  Chepoi, Victor ^a   Dragan, Feodor F ^b   Vaxès, Yann ^a  

^a AIX MARSEILLE UNIVERSITY   (France)

^b KENT STATE UNIVERSITY   (United States)

Author keywords

Distance labeling scheme; Efficient algorithms; Planar graphs; Routing labeling scheme

Indexed keywords

ALGORITHMS; BIOMEDICAL ENGINEERING; COMPUTATION THEORY; ROUTERS;

DISTANCE LABELING SCHEME; PLANAR GRAPHS; ROUTING LABELING SCHEME;

GRAPH THEORY;

EID: 37849187097     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgor.2004.07.011     Document Type: Article

References (33)

1. Bakker E.M., van Leeuwen J., and Tan R.B. Linear interval routing. Algorithms Rev. 2 (1991) 45-61
2. 1-embedding of weakly median graphs. European J. Combin. 21 (2000) 701-714
3. H.-J. Bandelt, V. Chepoi, Unpublished manuscript
4. Baues O., and Peyerimhoff N. Curvature and geometry of tessellating plane graphs. Discrete Comput. Geom. 25 (2001) 141-159
5. Breuer M.A. Coding the vertices of a graph. IEEE Trans. Inform. Theory IT-12 (1966) 148-153
6. Breuer M.A., and Folkman J. An unexpected result on coding the vertices of a graph. J. Math. Anal. Appl. 20 (1967) 583-600
7. 1-embeddable planar graphs. Discrete Appl. Math. 80 (1997) 3-19
8. Chepoi V., Dragan F., and Vaxès Y. Distance and routing labeling schemes for non-positively curved plane graphs. Technical report 13-2003, Laboratoire d'Informatique Fondamentale de Marseille. http://www.lim.univ-mrs.fr/Rapports/13-2003-Chepoi-Dragan-Vaxes.pdf
9. Chepoi V., and Rollin A. Interval routing in some planar networks. Theoret. Comput. Sci. 290 (2003) 1503-1540
10. Dress A.W.M., and Scharlau R. Gated sets in metric spaces. Aequationes Math. 34 (1987) 112-120
11. Fraigniaud P., and Gavoille C. Routing in trees. Proc. 28th Int. Colloquium on Automata, Languages and Programming. ICALP 2001. Lecture Notes in Comput. Sci. vol. 2076 (2001) 757-772
12. Fraigniaud P., and Gavoille C. A space lower bound for routing in trees. Proc. 19th Ann. Symp. Theoret. Aspects Comput. Sci. STACS 2002. Lecture Notes in Comput. Sci. vol. 2285 (2002) 65-75
13. Frederickson G.N., and Janardan R. Designing networks with compact routing tables. Algorithmica 3 (1988) 171-190
14. Gavoille C. A survey on interval routing schemes. Theoret. Comput. Sci. 245 (1999) 217-253
15. Gavoille C., and Hanusse N. Compact routing tables for graphs of bounded genus. Proc. 26th Int. Colloquium on Automata, Languages and Programming. ICALP 1999. Lecture Notes in Comput. Sci. vol. 1644 (1999) 351-360
16. Gavoille C., and Paul C. Optimal distance labeling schemes. Proc. 11th Annual European Symp. Algorithms. ESA 2003. Lecture Notes in Comput. Sci. vol. 2832 (2003) 254-265
17. Gavoille C., Peleg D., Pérennes S., and Raz R. Distance labeling in graphs. Proc. 12th Ann. ACM-SIAM Symp. Discrete Algorithms. SODA 2001 (2001), ACM-SIAM 210-219
18. Harel D., and Tarjan R. Fast algorithms for finding nearest common ancestor. SIAM J. Comput. 13 (1984) 338-355
19. Kannan S., Naor M., and Rudich S. Implicit representation of graphs. Proc. 20th Symp. Theory of Computing. STOC 1988 (1988), ACM 334-343
20. Katz M., Katz N.A., and Peleg D. Distance labeling schemes for well-separated graph classes. Proc. 17th Ann. Symp. Theoret. Aspects of Comput. Sci. STACS 2000. Lecture Notes in Comput. Sci. vol. 1770 (2000) 516-528
21. van Leeuwen J., and Tan R.B. Interval routing. The Computer J. 30 (1987) 298-307
22. Lyndon R.C. On Dehn's algorithm. Math. Ann. 166 (1966) 208-228
23. Lyndon R.C. A maximum principle for graphs. J. Combin. Theory 3 (1967) 34-37
24. Lyndon R.C., and Schupp P.E. Combinatorial Group Theory (1977), Springer-Verlag, Berlin
25. Narayanan L., and Shende S. Partial characterizations of networks supporting shortest path interval labeling schemes. Networks 32 (1998) 103-113
26. Peleg D. Proximity-preserving labeling schemes and their applications. Proc. 25th Int. Workshop on Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Comput. Sci. vol. 1665 (1999) 30-41
27. Peleg D. Informative labeling schemes for graphs. Proc. 25th Int. Symp. on Math. Foundations of Computer Science. MFCS 2000. Lecture Notes in Comput. Sci. vol. 1893 (2000) 579-588
28. Peleg D. Distributed Computing - A locality-sensitive approach (2000), Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
29. Prisǎcaru C., Soltan P., and Chepoi V. On embedding of planar graphs into hypercubes. Proc. Moldavian Acad. Sci., Ser. Math. 1 (1990) 43-50 (in Russian)
30. Santoro N., and Khatib R. Labeling and implicit routing in networks. The Computer J. 28 (1985) 5-8
31. Spinrad J.P. Efficient Graph Representations. Fields Institute Monographs vol. 19 (2003), AMS
32. Soltan P., Zambitski D., and Prisǎcaru C. Extremal Problems on Graphs and Algorithms of Their Solution (1973), Stiinţa Chişinǎu (in Russian)
33. Thorup M., and Zwick U. Compact routing schemes. Proc. 13th Ann. ACM Symp. on Par. Alg. and Arch. SPAA 2001 (2001), ACM 1-10