General compact labeling schemes for dynamic trees

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


An F- labeling scheme is composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute F(u, v) of any two vertices u and v directly from their labels. As applications for labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes. A general method for constructing labeling schemes for dynamic trees was previously developed in [28]. This method is based on extending an existing static tree labeling scheme to the dynamic setting. This approach fits many natural functions on trees, such as distance, routing, nearest common ancestor etc.. The resulted dynamic schemes incur overheads (over the static scheme) on the label size and on the communication complexity. In particular, all their schemes yield a multiplicative over-head factor of Ω(log n) on the label sizes of the static schemes. Following [28], we develop a different general method for extending static labeling schemes to the dynamic tree settings. Our method fits the same class of tree functions. In contrast to the above paper, our trade-off is designed to minimize the label size on expense of communication. Informally, for any k we present a dynamic labeling scheme incurring multiplicative overhead factors (over the static scheme) of O(log k n) on the label size and O(k logk n) on the amortized message complexity. In particular, by setting k = √n, we obtain dynamic labeling schemes with asymptotically optimal label sizes and sublinear amortized message complexity for the routing and the nearest common ancestor functions.

Original languageEnglish
Title of host publicationDistributed Computing - 19th International Conference, DISC 2005, Proceedings
Number of pages15
StatePublished - 2005
Externally publishedYes
Event19th International Conference on Distributed Computing, DISC 2005 - Cracow, Poland
Duration: 26 Sep 200529 Sep 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3724 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Distributed Computing, DISC 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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