Labeling Schemes for Flow and Connectivity

Katz, Michal; Katz, Nir A.; Korman, Amos; Peleg, David

doi:10.1137/s0097539703433912

Cited by 107 publications

(130 citation statements)

References 5 publications

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“…Distance labelling. A distance labelling of a graph G is an assignment of unique labels to vertices of G so that the distance between any two vertices can be inferred from their labels alone [16,20].…”

Section: Other Related Workmentioning

confidence: 99%

Ephemeral networks with random availability of links: The case of fast networks

Akrida

Gąsieniec

Mertzios

et al. 2016

Journal of Parallel and Distributed Computing

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights• We define the Temporal Diameter (TD) and the expected TD of temporal networks with random availabilities of links• We define fast and slow random temporal networks, according to their expected TD• Random temporal networks on instances of dense (directed) random graphs G n,p are fast• We introduce the critical availability as a measure of periodic availability of links• We give a lower and an upper bound on the critical availability AbstractWe consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We then provide a partial characterisation of fast random temporal networks. We also define the critical availability as a measure of periodic random availability of the links of a network, required to make the network fast. We finally give a lower bound as well as an upper bound on the (critical) availability.

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Section: Other Related Workmentioning

confidence: 99%

Ephemeral networks with random availability of links: The case of fast networks

Akrida

Gąsieniec

Mertzios

et al. 2016

Journal of Parallel and Distributed Computing

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“…Our focus is thus on informative labeling schemes using relatively short labels (say, of length polylogarithmic in n). Labeling schemes of this type were recently developed for different graph families and for a variety information types, including vertex adjacency [Alstrup and Rauhe 2002;Breuer 1966;Breuer and Folkman 1967;Kannan et al 1992;Korman et al 2006], distance [Alstrup et al 2005;Katz et al 2000;Kaplan and Milo 2001;Korman et al 2006;Peleg 1999;Thorup 2004], tree routing [Fraigniaud and Gavoille 2001;Fraigniaud and Gavoille 2002;Thorup and Zwick 2001], vertex-connectivity [Alstrup and Rauhe 2002;Katz et al 2004], flow Katz et al 2004], tree ancestry [Abiteboul at al. 2001;Abiteboul at al.…”

Section: Problem and Motivationmentioning

confidence: 99%

“…The general idea used in [Katz et al 2004] for labeling adjacency for some G ∈ C n (k), is to partition the edges of G into a 'simple' graph in A n (k) and two other graphs belonging to C n (k − 1). The labeling algorithm of [Katz et al 2004] recursively labels subgraphs of G that belong to C n (t) for t < k. Since adjacency for a graph in A n (k) can be encoded using roughly k log n-bit labels, the resulted labels in the recursive labeling use at most 2 k log n bits.…”

Section: · 115mentioning

confidence: 99%

“…The labeling algorithm of [Katz et al 2004] recursively labels subgraphs of G that belong to C n (t) for t < k. Since adjacency for a graph in A n (k) can be encoded using roughly k log n-bit labels, the resulted labels in the recursive labeling use at most 2 k log n bits. Our main technical contribution in this paper is to show that the edge set of any graph G ∈ C n (k) can be partitioned into a 'simple' graph in A n (k−1) and (only) one other graph belonging to C n (k−1).…”

Section: · 115mentioning

confidence: 99%

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Labeling Schemes for Vertex Connectivity

Korman

2007

Automata, Languages and Programming

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This paper 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, i.e., whether there exist k vertex disjoint paths connecting u and v. The paper establishes an upper bound of k 2 log 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 k log n.

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“…This problem has been studied by Katz et al [15], Alstrup et al [2], and Lewenstein et al [16]. Lewenstein et al [16] showed that with no auxiliary data structure, a label space of size n i=1 n i is necessary and sufficient to represent the equivalence relation.…”

Section: Introductionmentioning

confidence: 99%