article

Labeling schemes for weighted dynamic trees

Authors:

David PelegAuthors Info & Claims

Information and Computation, Volume 205, Issue 12

Pages 1721 - 1740

https://doi.org/10.1016/j.ic.2007.08.004

Published: 01 December 2007 Publication History

Abstract

A Distance labeling scheme is a type of localized network representation in which short labels are assigned to the vertices, allowing one to infer the distance between any two vertices directly from their labels, without using any additional information sources. As most applications for network representations 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 dynamic weighted trees where the vertices of the trees are fixed but the (positive integral) weights of the edges may change. The two models considered are the edge-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 approximate distance labeling schemes for the two dynamic models, which are efficient in terms of the required label size and communication complexity involved in updating the labels following the weight changes.

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Cited By

Glončák VMunkstrup JGrue Simonsen J(2023)Implicit Representation of RelationsTheory of Computing Systems10.1007/s00224-023-10141-z67:6(1156-1196)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s00224-023-10141-z
Alstrup SDahlgaard SKnudsen M(2017)Optimal Induced Universal Graphs and Adjacency Labeling for TreesJournal of the ACM10.1145/308851364:4(1-22)Online publication date: 17-Aug-2017
https://dl.acm.org/doi/10.1145/3088513
Alstrup SGavoille CHalvorsen EPetersen H(2016)Simpler, faster and shorter labels for distances in graphsProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884460(338-350)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884460
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Index Terms

Labeling schemes for weighted dynamic trees
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
      2. Graph enumeration
  2. Mathematical analysis
    1. Numerical analysis
      1. Computations in finite fields
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image Information and Computation

Information and Computation Volume 205, Issue 12

December, 2007

125 pages

ISSN:0890-5401

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2007.

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Academic Press, Inc.

United States

Publication History

Published: 01 December 2007

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Cited By

Glončák VMunkstrup JGrue Simonsen J(2023)Implicit Representation of RelationsTheory of Computing Systems10.1007/s00224-023-10141-z67:6(1156-1196)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s00224-023-10141-z
Alstrup SDahlgaard SKnudsen M(2017)Optimal Induced Universal Graphs and Adjacency Labeling for TreesJournal of the ACM10.1145/308851364:4(1-22)Online publication date: 17-Aug-2017
https://dl.acm.org/doi/10.1145/3088513
Alstrup SGavoille CHalvorsen EPetersen H(2016)Simpler, faster and shorter labels for distances in graphsProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884460(338-350)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884460
Castañeda ADolev DTrehan A(2016)Compact routing messages in self-healing treesProceedings of the 17th International Conference on Distributed Computing and Networking10.1145/2833312.2833328(1-10)Online publication date: 4-Jan-2016
https://dl.acm.org/doi/10.1145/2833312.2833328
Rotbart NVaz Salles MZotos I(2014)An Evaluation of Dynamic Labeling Schemes for Tree NetworksProceedings of the 13th International Symposium on Experimental Algorithms - Volume 850410.1007/978-3-319-07959-2_17(199-210)Online publication date: 29-Jun-2014
https://dl.acm.org/doi/10.1007/978-3-319-07959-2_17
Emek YKorman A(2011)New bounds for the controller problemDistributed Computing10.1007/s00446-010-0119-z24:3-4(177-186)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1007/s00446-010-0119-z
Fraigniaud PKorman ACharikar M(2010)Compact ancestry labeling schemes for XML treesProceedings of the twenty-first annual ACM-SIAM symposium on Discrete algorithms10.5555/1873601.1873639(458-466)Online publication date: 17-Jan-2010
https://dl.acm.org/doi/10.5555/1873601.1873639
Emek YKorman ARicha AGuerraoui R(2010)Efficient threshold detection in a distributed environmentProceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing10.1145/1835698.1835742(183-191)Online publication date: 25-Jul-2010
https://dl.acm.org/doi/10.1145/1835698.1835742
Korman A(2010)Labeling schemes for vertex connectivityACM Transactions on Algorithms (TALG)10.1145/1721837.17218556:2(1-10)Online publication date: 6-Apr-2010
https://dl.acm.org/doi/10.1145/1721837.1721855
Emek YKorman A(2009)New bounds for the controller problemProceedings of the 23rd international conference on Distributed computing10.5555/1813164.1813174(22-34)Online publication date: 23-Sep-2009
https://dl.acm.org/doi/10.5555/1813164.1813174
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