Article

An Optimal Labeling for Node Connectivity

Authors:

Hsueh-I LuAuthors Info & Claims

ISAAC '09: Proceedings of the 20th International Symposium on Algorithms and Computation

Pages 303 - 310

https://doi.org/10.1007/978-3-642-10631-6_32

Published: 05 December 2009 Publication History

Abstract

Given an n -node undirected simple graph G and a positive integer k , the k-connectivity labeling problem for G seeks short labels for the nodes of G such that whether any two nodes are k -connected in G can be determined merely by their labels. For k = 1, an optimal solution to the problem is to give each node in the same connected component of G a common log₂ n -bit label, uniquely chosen for this connected component. For k 2, Katz, Katz, Korman, and Peleg gave the first nontrivial solution to the problem, requiring O (2^klog n ) bits per node. The best previously known solution, due to Korman, requires O ( k ²log n ) bits per node. We give the first asymptotically optimal solution to the problem, requiring only $(2k-1)\left\lceil\log_2 n\right\rceil$ bits per node, which matches a lower bound ( k log n ) proved by Katz, Katz, Korman, and Peleg.

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Cited By

Pettie SSaranurak TYin LLeonardi SGupta A(2022)Optimal vertex connectivity oraclesProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519945(151-161)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519945
Bar-Natan ACharalampopoulos PGawrychowski PMozes SWeimann O(2022)Fault-tolerant distance labeling for planar graphsTheoretical Computer Science10.1016/j.tcs.2022.03.020918:C(48-59)Online publication date: 29-May-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.03.020
Gawrychowski PJanczewski WŁopuszański JMarx D(2021)Shorter labels for routing in treesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458194(2174-2193)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458194
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cover image Guide Proceedings

ISAAC '09: Proceedings of the 20th International Symposium on Algorithms and Computation

December 2009

1224 pages

ISBN:9783642106309

Editors:
Yingfei Dong
Dept. of Electrical and Computer Engineering, University of Hawaii, Honolulu, USA 96822
,
Ding-Zhu Du
Department of Computer Science, University of Texas at Dallas, Dallas, USA 75083
,
Oscar Ibarra
Department of Computer Science, University of California, Santa Barbara, USA 93106

Copyright © Springer-Verlag Berlin Heidelberg.

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Springer-Verlag

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Publication History

Published: 05 December 2009

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Cited By

Pettie SSaranurak TYin LLeonardi SGupta A(2022)Optimal vertex connectivity oraclesProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519945(151-161)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519945
Bar-Natan ACharalampopoulos PGawrychowski PMozes SWeimann O(2022)Fault-tolerant distance labeling for planar graphsTheoretical Computer Science10.1016/j.tcs.2022.03.020918:C(48-59)Online publication date: 29-May-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.03.020
Gawrychowski PJanczewski WŁopuszański JMarx D(2021)Shorter labels for routing in treesProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458194(2174-2193)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458194
Gawrychowski PUznański P(2021)Better Distance Labeling for Unweighted Planar GraphsAlgorithms and Data Structures10.1007/978-3-030-83508-8_31(428-441)Online publication date: 9-Aug-2021
https://dl.acm.org/doi/10.1007/978-3-030-83508-8_31
Fraigniaud PKorman A(2016)An Optimal Ancestry Labeling Scheme with Applications to XML Trees and Universal PosetsJournal of the ACM10.1145/279407663:1(1-31)Online publication date: 12-Feb-2016
https://dl.acm.org/doi/10.1145/2794076

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