Abstract
This paper studies β-approximate distance labeling schemes, which are composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute a β-approximation of the distance between any two vertices directly from their labels (without using any additional information). As most applications for informative labeling schemes in general, and distance labeling schemes in particular, concern large and dynamically changing networks, it is of interest to focus on distributed dynamic labeling schemes. The paper considers the problem on dynamic weighted trees and cycles where the vertices of the tree (or the cycle) are fixed but the (positive integral) weights of the edges may change. The two models considered are the fully dynamic model, where from time to time some edge changes its weight by a fixed quanta, and the increasing dynamic model in which edge weights can only grow. The paper presents distributed β-approximate distance labeling schemes for the two models, for β > 1, and establishes upper and lower bounds on the required label size and the communication complexity involved in updating the labels following a weight change.
Supported in part by a grant from the Israel Science Foundation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Abiteboul, H. Kaplan and T. Milo. Compact labeling schemes for ancestor queries. In Proc. 12th ACM-SIAM Symp. on Discrete Algorithms, Jan. 2001.
Y. Afek, B. Awerbuch, S.A. Plotkin and M. Saks. Local management of a global resource in a communication. J. of the ACM, pages 1–19, 1989.
S. Alstrup, C. Gavoille, H. Kaplan and T. Rauhe. Identifying nearest common ancestors in a distributed environment. IT-C Technical Report 2001-6, The IT University, Copenhagen, Denmark, Aug. 2001.
S. Alstrup and T. Rauhe. Improved Labeling Scheme for Ancestor Queries. In Proc. 19th ACM-SIAM Symp. on Discrete Algorithms, Jan. 2002.
M.A. Breuer and J. Folkman. An unexpected result on coding the vertices of a graph. J. of Mathematical Analysis and Applications, 20:583–600, 1967.
M.A. Breuer. Coding the vertexes of a graph. IEEE Trans. on Information Theory, IT-12:148–153, 1966.
E. Cohen, E. Halperin, H. Kaplan and U. Zwick. Reachability and Distance Queries via 2-hop Labels. In Proc. 19th ACM-SIAM Symp. on Discrete Algorithms, Jan. 2002.
P. Fraigniaud and C. Gavoille. Routing in trees. In Proc. 28th Int. Colloq. on Automata, Languages & Prog., LNCS 2076, pages 757–772, July 2001.
C. Gavoille and C. Paul. Split decomposition and distance labelling: an optimal scheme for distance hereditary graphs. In Proc. European Conf. on Combinatorics, Graph Theory and Applications, Sept. 2001.
C. Gavoille and D. Peleg. Compact and Localized Distributed Data Structures. Research Report RR-1261-01, LaBRI, Univ. of Bordeaux, France, Aug. 2001.
C. Gavoille, M. Katz, N.A. Katz, C. Paul and D. Peleg. Approximate Distance Labeling Schemes. In 9th European Symp. on Algorithms, Aug. 2001, Aarhus, Denmark, SV-LNCS 2161, 476–488.
C. Gavoille, D. Peleg, S. Pérennes and R. Raz. Distance labeling in graphs. In Proc. 12th ACM-SIAM Symp. on Discrete Algorithms, pages 210–219, Jan. 2001.
S. Kannan, M. Naor, and S. Rudich. Implicit representation of graphs. In Proc. 20th ACM Symp. on Theory of Computing, pages 334–343, May 1988.
H. Kaplan and T. Milo. Short and simple labels for small distances and other functions. In Workshop on Algorithms and Data Structures, Aug. 2001.
H. Kaplan, T. Milo and R. Shabo. A Comparison of Labeling Schemes for Ancestor Queries. In Proc. 19th ACM-SIAM Symp. on Discrete Algorithms, Jan. 2002.
M. Katz, N.A. Katz, A. Korman and D. Peleg. Labeling schemes for flow and connectivity. In Proc. 19th ACM-SIAM Symp. on Discrete Algorithms, Jan. 2002.
M. Katz, N.A. Katz, and D. Peleg. Distance labeling schemes for well-separated graph classes. In Proc. 17th Symp. on Theoretical Aspects of Computer Science, pages 516–528, February 2000.
A. Korman, D. Peleg, and Y. Rodeh. Labeling schemes for dynamic tree networks. In Proc. 19th STACS Symp. on Theoretical Aspects of Computer Science, March. 2002.
D. Peleg. Proximity-preserving labeling schemes and their applications. In Proc. 25th Int. Workshop on Graph-Theoretic Concepts in Computer Science, pages 30–41, June 1999.
D. Peleg. Informative labeling schemes for graphs. In Proc. 25th Symp. on Mathematical Foundations of Computer Science, volume LNCS-1893, pages 579–588. Springer-Verlag, Aug. 2000.
M. Thorup. Compact oracles for reachability and approximate distances in planar digraphs. In Proc. 42nd IEEE Symp. on Foundations of Computer Science, Oct. 2001.
M. Thorup and U. Zwick. Compact routing schemes. In Proc. 13th ACM Symp. on Parallel Algorithms and Architecture, pages 1–10, Hersonissos, Crete, Greece, July 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Korman, A., Peleg, D. (2003). Labeling Schemes for Weighted Dynamic Trees. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_31
Download citation
DOI: https://doi.org/10.1007/3-540-45061-0_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40493-4
Online ISBN: 978-3-540-45061-0
eBook Packages: Springer Book Archive