Near-perfect token distribution

Andrei Z. Broder; Alan M. Frieze; E. Shamir; E. Upfal

doi:10.1007/3-540-55719-9_83

Near-perfect token distribution

Andrei Z. Broder, Alan M. Frieze, E. Shamir, E. Upfal

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

12 Scopus citations

Abstract

Suppose that n tokens are arbitrarily placed on the n nodes of a graph. At each parallel step one token may be moved from each node to an adjacent node. An algorithm for the near-perfect token distribution problem redistributes the tokens in a minimum number of steps, so that, at the end, no more than O(1) tokens reside at each node. (In perfect distribution, at the end, exactly one token resides at each node.) In this paper we present a simple algorithm that works for all extrovert graphs, a new property which we define and study. In terms of connectivity requirements, extrovert graphs are in-between expanders and compressors. Our results lead to an optimal solution for the near-perfect token distribution problem on almost all cubic graphs. The new solution is conceptually simpler than previous algorithms, and applies to graphs of minimum possible degree.

Original language	English
Title of host publication	Automata, Languages and Programming - 19th International Colloquium, Proceedings
Editors	Werner Kuich
Publisher	Springer Verlag
Pages	308-317
Number of pages	10
ISBN (Print)	9783540557197
DOIs	https://doi.org/10.1007/3-540-55719-9_83
State	Published - 1992
Event	19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 - Wien, Austria Duration: 13 Jul 1992 → 17 Jul 1992

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	623 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th International Colloquium on Automata, Languages, and Programming, ICALP 1992
Country/Territory	Austria
City	Wien
Period	13/07/92 → 17/07/92

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

Access to Document

10.1007/3-540-55719-9_83

Cite this

Broder, A. Z., Frieze, A. M., Shamir, E., & Upfal, E. (1992). Near-perfect token distribution. In W. Kuich (Ed.), Automata, Languages and Programming - 19th International Colloquium, Proceedings (pp. 308-317). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 623 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55719-9_83

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Broder, AZ, Frieze, AM, Shamir, E & Upfal, E 1992, Near-perfect token distribution. in W Kuich (ed.), Automata, Languages and Programming - 19th International Colloquium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 623 LNCS, Springer Verlag, pp. 308-317, 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992, Wien, Austria, 13/07/92. https://doi.org/10.1007/3-540-55719-9_83

Near-perfect token distribution. / Broder, Andrei Z.; Frieze, Alan M.; Shamir, E. et al.
Automata, Languages and Programming - 19th International Colloquium, Proceedings. ed. / Werner Kuich. Springer Verlag, 1992. p. 308-317 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 623 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Broder AZ, Frieze AM, Shamir E, Upfal E. Near-perfect token distribution. In Kuich W, editor, Automata, Languages and Programming - 19th International Colloquium, Proceedings. Springer Verlag. 1992. p. 308-317. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-55719-9_83

Near-perfect token distribution

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