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Labeling schemes for vertex connectivity

2010
*
ACM Transactions on Algorithms
*

This paper studies

doi:10.1145/1721837.1721855
fatcat:5skjeocl5fd3naa56cad3ruzx4
*labeling**schemes**for*the*vertex**connectivity*function on general graphs. ... 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. ... In this section we present a k-*vertex**connectivity**labeling**scheme**for*the graph family G n using less than k 2 log n-bit*labels*. ...##
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Labeling Schemes for Vertex Connectivity
[chapter]

*
Lecture Notes in Computer Science
*

This paper studies

doi:10.1007/978-3-540-73420-8_11
fatcat:5qovxlwmgjd3zlyrs7sf5pbqeu
*labeling**schemes**for*the*vertex**connectivity*function on general graphs. ... 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. ... In this section we present a k-*vertex**connectivity**labeling**scheme**for*the graph family G n using less than k 2 log n-bit*labels*. ...##
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Proximity-Preserving Labeling Schemes and Their Applications
[chapter]

1999
*
Lecture Notes in Computer Science
*

This paper considers informative

doi:10.1007/3-540-46784-x_5
fatcat:foltucx5ejdodb4enkkgbyjsyq
*labeling**schemes**for*graphs. ... It is shown that*for*the class of n-*vertex*weighted trees with M -bit edge weights, there exists such a proximity-preserving*labeling**scheme*using O(M log n + log 2 n) bit*labels*. ... Acknowledgements I am grateful to Cyril Gavoille, Yehuda Hassin and Richard Tan*for*helpful discussions. ...##
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Fault-Tolerant Labeling and Compact Routing Schemes
[article]

2021
*
arXiv
*
pre-print

Our main results

arXiv:2106.00374v1
fatcat:wfgpkcdqdzb5zkh4crwjk65loa
*for*an n-*vertex*graph and a fault bound f are: – There is a randomized FT*connectivity**labeling**scheme*with a*label*length of O(f+log n) bits, hence optimal*for*f=O(log n). ...*For*a given n-*vertex*graph G and a bound f on the number of faults, an f-FT*connectivity**labeling**scheme*is a distributed data structure that assigns each of the graph edges and vertices a short*label*, ...*For*example, in routing applications the*label*of the*vertex*is treated as its "address". It is quite immediate to provide*connectivity**labeling**schemes*of logarithmic length. ...##
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A dynamic distributed approach to representing proper interval graphs

2009
*
Discrete Mathematics
*

*scheme*

*for*proper interval graphs. ... The

*scheme*is dynamic in the sense that only a small adjustment must be made to the

*vertex*

*labels*when a small change is made to the graph. ... Specifically, our

*labelling*

*scheme*is as follows. •

*For*each

*vertex*v, we maintain the following. -A unique identifier

*for*each

*vertex*. ...

##
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Isometric universal graphs
[article]

2021
*
arXiv
*
pre-print

Our main tool is a new type of distance

arXiv:2103.08570v2
fatcat:kpbg6r3pnze2xesksw5xzhqrjm
*labelling**scheme*, whose study might be of independent interest. ... We show that*for*any integer n≥ 1, there is a graph on 3^n+O(log^2 n) vertices that contains isometric copies of all n-*vertex*graphs. ...*For*any integer n 1, the class of all*connected*n-*vertex*graphs has a distance-vector*labelling**scheme*with*labels*of at most 4n + O(log n) bits. Proof. Let G be a*connected*n-*vertex*graph. ...##
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Compact and localized distributed data structures

2003
*
Distributed computing
*

The survey concentrates mainly on combinatorial and algorithmic techniques, such as adjacency and distance

doi:10.1007/s00446-002-0073-5
fatcat:bqydpls23ncnnm57nnhmctnz3m
*labeling**schemes*and interval*schemes**for*routing, and covers complexity results on various applications ... , focusing on compact localized*schemes**for*message routing in communication networks. ...*For*edge-*connectivity*, this yields a tight bound of Θ(log 2 n) bits. Also, a k-*vertex**connectivity**labeling**scheme*is given*for*general n-*vertex*graphs using O(log n) bit*labels**for*fixed k. ...##
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Forbidden-Set Distance Labels for Graphs of Bounded Doubling Dimension

2016
*
ACM Transactions on Algorithms
*

*For*an n-

*vertex*graph G in this family, and

*for*any desired precision parameter > 0, the

*labeling*

*scheme*stores an O(1+ −1 ) 2α log 2 n-bit

*label*at each

*vertex*. ... The

*labeling*

*scheme*can be extended into a forbiddenset

*labeled*routing

*scheme*with stretch 1 +

*for*graphs of bounded doubling dimension. ... Courcelle

*for*helpful discussions about

*labeling*

*schemes*in the forbidden-set setting. ...

##
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Forbidden-set distance labels for graphs of bounded doubling dimension

2010
*
Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10
*

*For*an n-

*vertex*graph G in this family, and

*for*any desired precision parameter > 0, the

*labeling*

*scheme*stores an O(1+ −1 ) 2α log 2 n-bit

*label*at each

*vertex*. ... The

*labeling*

*scheme*can be extended into a forbiddenset

*labeled*routing

*scheme*with stretch 1 +

*for*graphs of bounded doubling dimension. ... Courcelle

*for*helpful discussions about

*labeling*

*schemes*in the forbidden-set setting. ...

##
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Informative Labeling Schemes for Graphs
[chapter]

2000
*
Lecture Notes in Computer Science
*

We begin by developing f

doi:10.1007/3-540-44612-5_53
fatcat:tr3wjlnap5azzmjazyv2x2dqpq
*labeling**schemes**for*three functions f over the class of n-*vertex*trees. ... An f*labeling**scheme**labels*the vertices of a weighted graph G in such a way that f (W ) can be inferred (or at least approximated) efficiently*for*any*vertex*subset W of G by merely inspecting the*labels*... Acknowledgements I am grateful to Michal Katz and Nir Katz*for*their helpful comments and suggestions. ...##
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Informative labeling schemes for graphs

2005
*
Theoretical Computer Science
*

We begin by developing f

doi:10.1016/j.tcs.2005.03.015
fatcat:aigpwzyhorh3rpueyf4ita7iwu
*labeling**schemes**for*three functions f over the class of n-*vertex*trees. ... An f*labeling**scheme**labels*the vertices of a weighted graph G in such a way that f (W ) can be inferred (or at least approximated) efficiently*for*any*vertex*subset W of G by merely inspecting the*labels*... Acknowledgements I am grateful to Michal Katz and Nir Katz*for*their helpful comments and suggestions. ...##
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The vertex-transitive TLF-planar graphs
[article]

2004
*
arXiv
*
pre-print

We characterize these graphs with a finite local representation and a special kind of finite state automaton named

arXiv:cs/0412078v1
fatcat:gpavzsicobfvhgyzdcoy3r2nn4
*labeling**scheme*. ... We consider the class of the topologically locally finite (in short TLF) planar*vertex*-transitive graphs, a class containing in particular all the one-ended planar Cayley graphs and the normal transitive ...*For*the larger degrees, we enumerate all possible*labeling**schemes*, each one corresponding to an enumerable family of planar*vertex*-transitive graphs. ...##
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Labeling Schemes with Queries
[article]

2006
*
arXiv
*
pre-print

We show that inspecting the

arXiv:cs/0609163v1
fatcat:adtz2ulsufcrzddgmzrxjlim4q
*label*of a single additional*vertex*(one query) enables us to reduce the*label*size of many*labeling**schemes*significantly. ... An f-*labeling**scheme**for*a family of graphs*labels*the vertices of all graphs in such that*for*every graph G∈ and every two vertices u,v∈ G, the value f(u,v) can be inferred by merely inspecting the*labels*... They also show a*labeling**scheme*supporting the k-*vertex*-*connectivity*function on general graphs using O(2 k log n)-bit*labels*. See [30]*for*a survey on (static)*labeling**schemes*. ...##
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Enumerating planar locally finite Cayley graphs
[article]

2003
*
arXiv
*
pre-print

Keywords:

arXiv:cs/0309017v1
fatcat:m4pdgbgujndq5gytl3cjfbnewa
*vertex*-transitive, Cayley graph, planar graph, tiling,*labeling**scheme*... We characterize the set of planar locally finite Cayley graphs, and give a finite representation of these graphs by a special kind of finite state automata called*labeling**schemes*. ... The*labeling**scheme*describes how the edges must be*labeled*: take a*vertex*s and an edge*labeled*by the generator a i pointing towards s. ...##
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Proof labeling schemes

2005
*
Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '05
*

On the other hand, approaches are presented

doi:10.1145/1073814.1073817
dblp:conf/podc/KormanKP05
fatcat:r6owxmlic5ampjl55u5lymvl3e
*for*the efficient construction of*schemes*, and upper and lower bounds are established on the cost of*schemes**for*multiple basic problems. ... Our approach thus allows*for*a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures*for*maintaining them was done without ... Note that the upper bound*for*k*vertex**connectivity*is independent of k. Using similar methods we can construct proof*labeling**scheme**for*k-the flow between s and t, with size O(k log n). ...
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