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An Optimal Labeling for Node Connectivity

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Algorithms and Computation (ISAAC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5878))

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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(2klogn) bits per node. The best previously known solution, due to Korman, requires O(k 2logn) 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 Ω(klogn) proved by Katz, Katz, Korman, and Peleg.

Research supported in part by NSC grants 97-2221-E-002-122 and 98-2221-E-002-079-MY3.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University,  

    Tai-Hsin Hsu & Hsueh-I Lu

Authors
  1. Tai-Hsin Hsu
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  2. Hsueh-I Lu
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Editor information

Editors and Affiliations

  1. Dept. of Electrical and Computer Engineering, University of Hawaii, Holmes Hall 483, 2540 Dole Street, 96822, Honolulu, HI, USA

    Yingfei Dong

  2. Department of Computer Science, University of Texas at Dallas, 75083, Dallas, TX, USA

    Ding-Zhu Du

  3. Department of Computer Science, University of California, 93106, Santa Barbara, CA, USA

    Oscar Ibarra

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Hsu, TH., Lu, HI. (2009). An Optimal Labeling for Node Connectivity. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_32

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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10630-9

  • Online ISBN: 978-3-642-10631-6

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