research-article

Labeling schemes for vertex connectivity

Author:

Amos KormanAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 6, Issue 2

Article No.: 39, Pages 1 - 10

https://doi.org/10.1145/1721837.1721855

Published: 06 April 2010 Publication History

Abstract

This article studies labeling schemes for the vertex connectivity function on general graphs. We consider the problem of assigning short labels to the nodes of any n-node graph is such a way that given the labels of any two nodes u and v, one can decide whether u and v are k-vertex connected in G, that is, whether there exist k vertex disjoint paths connecting u and v. This article establishes an upper bound of k²log n on the number of bits used in a label. The best previous upper bound for the label size of such a labeling scheme is 2^klog n.

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Cited By

Gawrychowski PUznański P(2023)Better Distance Labeling for Unweighted Planar GraphsAlgorithmica10.1007/s00453-023-01133-z85:6(1805-1823)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1007/s00453-023-01133-z
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
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Labeling schemes for vertex connectivity

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 6, Issue 2

March 2010

373 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1721837

Issue’s Table of Contents

Copyright © 2010 ACM.

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Association for Computing Machinery

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Publication History

Published: 06 April 2010

Accepted: 01 September 2008

Revised: 01 September 2008

Received: 01 July 2007

Published in TALG Volume 6, Issue 2

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Cited By

Gawrychowski PUznański P(2023)Better Distance Labeling for Unweighted Planar GraphsAlgorithmica10.1007/s00453-023-01133-z85:6(1805-1823)Online publication date: 1-Jun-2023
https://dl.acm.org/doi/10.1007/s00453-023-01133-z
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
Radha RRilwan N(2021)Frequency Assignment Model of Zero Divisor GraphJournal of Applied Mathematics10.1155/2021/66988152021(1-8)Online publication date: 9-Mar-2021
https://doi.org/10.1155/2021/6698815
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
Bar-Natan ACharalampopoulos PGawrychowski PMozes SWeimann O(2021)Fault-Tolerant Distance Labeling for Planar GraphsStructural Information and Communication Complexity10.1007/978-3-030-79527-6_18(315-333)Online publication date: 20-Jun-2021
https://doi.org/10.1007/978-3-030-79527-6_18
Abrahamsen MAlstrup SHolm JKnudsen MStöckel M(2020)Near-optimal induced universal graphs for cycles and pathsDiscrete Applied Mathematics10.1016/j.dam.2019.10.030282(1-13)Online publication date: Aug-2020
https://doi.org/10.1016/j.dam.2019.10.030
Alstrup SKaplan HThorup MZwick U(2019)Adjacency Labeling Schemes and Induced-Universal GraphsSIAM Journal on Discrete Mathematics10.1137/16M110596733:1(116-137)Online publication date: 15-Jan-2019
https://doi.org/10.1137/16M1105967
Fraigniaud PPatt-Shamir BPerry M(2019)Randomized proof-labeling schemesDistributed Computing10.1007/s00446-018-0340-832:3(217-234)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s00446-018-0340-8
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