Abstract
In this paper, we propose an efficient implicit representation of caterpillars and binary trees with n vertices. Our schemes, called Traversal & Jumping, assign to vertices of the tree distinct labels of log2 n + O(1) bits, and support constant time adjacency queries between any two vertices by using only their labels. Moreover, all the labels can be constructed in O(n) time.
The three authors are supported by the project ”GeoComp” of the ACI Masses de Données.
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Abiteboul, S., Alstrup, S., Kaplan, H., Milo, T., Rauhe, T.: Compact labeling schemes for ancestor queries. SIAM Journal on Computing (2005)
Alstrup, S., Bille, P., Rauhe, T.: Labeling schemes for small distances in trees. SIAM Journal on Discrete Mathematics 19(2), 448–462 (2005)
Alstrup, S., Gavoille, C., Kaplan, H., Rauhe, T.: Nearest common ancestors: A survey and a new algorithm for a distributed environment. Theory of Computing Systems 37, 441–456 (2004)
Abiteboul, S., Kaplan, H., Milo, T.: Compact labeling schemes for ancestor queries. In: 12th Symposium on Discrete Algorithms (SODA), pp. 547–556. ACM-SIAM, New York (2001)
Alstrup, S., Rauhe, T.: Small induced-universal graphs and compact implicit graph representations. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 53–62. IEEE Computer Society Press, Los Alamitos (2002)
Breuer, M.A., Folkman, J.: An unexpected result on coding the vertices of a graph. Journal of Mathematical Analysis and Applications 20, 583–600 (1967)
Bazzaro, F., Gavoille, C.: Localized and compact data-structure for comparability graphs. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 1122–1131. Springer, Heidelberg (2005)
Breuer, M.A.: Coding the vertexes of a graph. IEEE Transactions on Information Theory IT-12, 148–153 (1966)
Dragan, F.F., Lomonosov, I.: New routing schemes for interval graphs, circular-arc graphs, and permutation graphs. In: 14th IASTED International Conference on Parallel and Distributed Computing and Systems (PDCS), pp. 78–83 (November 2002)
Dragan, F.F., Lomonosov, I.: On compact and efficient routing in certain graph classes (Extended abstract). In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 402–414. Springer, Heidelberg (2004)
Fraigniaud, P., Gavoille, C.: Routing in trees. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 757–772. Springer, Heidelberg (2001)
Gavoille, C., Paul, C.: Optimal distance labeling for interval and circular-arc graphs. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 254–265. Springer, Heidelberg (2003)
Gavoille, C., Peleg, D.: Compact and localized distributed data structures. Journal of Distributed Computing 16, 111–120 (2003), PODC 20-Year Special Issue
Kaplan, H., Milo, T.: Short and simple labels for small distances and other functions. In: Dehne, F., Sack, J.-R., Tamassia, R. (eds.) WADS 2001. LNCS, vol. 2125, pp. 32–40. Springer, Heidelberg (2001)
Kannan, S., Naor, M., Rudich, S.: Implicit representation of graphs. In: 20th Annual ACM Symposium on Theory of Computing (STOC), pp. 334–343. ACM Press, New York (1988)
Kannan, S., Naor, M., Rudich, S.: Implicit representation of graphs. SIAM Journal on Discrete Mathematics 5, 596–603 (1992)
Norine, S., Robertson, N., Thomas, R., Wollan, P.: Proper minor-closed families are small. Journal of Combinatorial Theory, Series B (to appear, 2005)
Thorup, M., Zwick, U.: Compact routing schemes. In: 13th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA), July 2001, pp. 1–10. ACM Press, New York (2001)
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Bonichon, N., Gavoille, C., Labourel, A. (2006). Short Labels by Traversal and Jumping. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_12
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DOI: https://doi.org/10.1007/11780823_12
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