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Optimal Distance Labeling Schemes for Trees
[article]

2017
*
arXiv
*
pre-print

Prior to our work, all

arXiv:1608.00212v2
fatcat:pziujxmqafd55dratk57wte57e
*distance**labeling**schemes**for**trees*could be reinterpreted as universal*trees*. A*tree*T is said to be universal if any*tree*on n nodes can be found as a subtree of T. ...*For*the particular case of*trees*,*optimal*bounds (up to low order terms) were recently obtained*for*adjacency*labeling*[FOCS'15], nearest common ancestor*labeling*[SODA'14], and ancestry*labeling*[SICOMP ... In particular, it means that*for*level-ancestor queries, the*scheme*of Alstrup et al. [8] is*optimal*(after some modifications described in Section 3.6).*Labeling**schemes**for*bounded*distances*. ...##
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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

doi:10.1007/s00446-002-0073-5
fatcat:bqydpls23ncnnm57nnhmctnz3m
*distance**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. ... Hence Θ(n) bits is the*optimal**distance**label*length*for*general unweighted graphs. ...##
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Distance Labeling for Permutation Graphs

2005
*
Electronic Notes in Discrete Mathematics
*

The datastructure is localized and given as a

doi:10.1016/j.endm.2005.06.098
fatcat:qh6ijtinbbc6dj556hqndgspdu
*distance**labeling*, that is each vertex receives a*label*of O(log n) bits so that*distance*queries between any two vertices are answered by inspecting on their ...*labels*only. ...*Trees*, bounded*tree*-width and bounded clique-width graphs have O(log 2 n) bit*distance**labeling**schemes*. ...##
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Compact Multicast Routing
[chapter]

2009
*
Lecture Notes in Computer Science
*

*For*

*trees*, routing requires (log 2 / log log ) memory and header size, and this is known to be

*optimal*[6]. ... So a complete information

*scheme*should maintain at each node the next step(s) of the shortest spanning

*tree*,

*for*all possible subsets. ... It is an interesting open question to find the

*optimal*trade-offs between storage and space

*for*the various problems considered in this paper. ...

##
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Approximate Distance Labeling Schemes

2000
*
Electronic Notes in Discrete Mathematics
*

We develop such constant approximate

doi:10.1016/s1571-0653(05)80145-3
fatcat:zpns4qhc55fmbo4hqu7jfgvjrq
*distance**labeling**schemes**for*the classes of*trees*, bounded treewidth graphs, planar graphs, k-chordal graphs, and graphs with a dominating pair (including*for*instance ... We also establish lower bounds, and prove that most of our*schemes*are*optimal*in terms of the length of the*labels*generated and the quality of the approximation. ... We would like to thank Stéphane Pérennes*for*his help in developing the upper bound*for**trees*, and Douglas West*for*his bibliographic support. ...##
###
Informative Labeling Schemes for Graphs
[chapter]

2000
*
Lecture Notes in Computer Science
*

Considering the class of n-vertex

doi:10.1007/3-540-44612-5_53
fatcat:tr3wjlnap5azzmjazyv2x2dqpq
*trees*with M-bit edge weights, it is shown that*for*this class there exists a Steiner*labeling**scheme*using O((M + log n) log n) bit*labels*, which is asymptotically*optimal*... We begin by developing f*labeling**schemes**for*three functions f over the class of n-vertex*trees*. ... 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
*

Considering the class of n-vertex

doi:10.1016/j.tcs.2005.03.015
fatcat:aigpwzyhorh3rpueyf4ita7iwu
*trees*with M-bit edge weights, it is shown that*for*this class there exists a Steiner*labeling**scheme*using O((M + log n) log n) bit*labels*, which is asymptotically*optimal*... We begin by developing f*labeling**schemes**for*three functions f over the class of n-vertex*trees*. ... Acknowledgements I am grateful to Michal Katz and Nir Katz*for*their helpful comments and suggestions. ...##
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Proximity-Preserving Labeling Schemes and Their Applications
[chapter]

1999
*
Lecture Notes in Computer Science
*

It is shown that

doi:10.1007/3-540-46784-x_5
fatcat:foltucx5ejdodb4enkkgbyjsyq
*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*. ... This paper considers informative*labeling**schemes**for*graphs. ... Acknowledgements I am grateful to Cyril Gavoille, Yehuda Hassin and Richard Tan*for*helpful discussions. ...##
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Space-Optimal Time-Efficient Silent Self-Stabilizing Constructions of Constrained Spanning Trees

2015
*
2015 IEEE 35th International Conference on Distributed Computing Systems
*

known algorithms designed and

doi:10.1109/icdcs.2015.66
dblp:conf/icdcs/BlinF15
fatcat:r4od2ao7gbdhpbub7tjoksvhfq
*optimized*specifically*for*solving each of these two tasks. ... In this paper, we make a first attempt*for*answering the question of whether such an efficient algorithm exists*for*every task, by focussing on constrained spanning*tree*construction tasks. ... As*for*the*distance*-based*labeling**scheme*using the pairs (ID, d), the pairs (ID, s) alone provide a proof-*labeling**scheme**for*spanning*trees*. ...##
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Average Case Analysis for Tree Labelling Schemes
[chapter]

2005
*
Lecture Notes in Computer Science
*

*For*

*trees*, Gavoille et al. [7] proved that

*for*any such

*distance*

*labelling*

*scheme*, the maximum

*label*length is at least 1 8 log 2 n − O(log n) bits. ... In this paper, we present two new

*distance*

*labelling*

*schemes*that not only achieve the

*optimal*

*label*length Θ(log n · log(H n (T ))), but also have a much smaller expected

*label*length under certain

*tree*... In this paper, we study

*distance*

*labelling*

*schemes*

*for*unweighted

*trees*.

*For*

*trees*, Gavoille et al. ...

##
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On rotation distance between binary coupling trees and applications for 3nj-coefficients

1999
*
Computer Physics Communications
*

This is the graph of rooted (unordered) binary

doi:10.1016/s0010-4655(99)00216-7
fatcat:wilbt4vdmbfezlmdziikmnov5i
*trees*with*labelled*leaves, and has order (2n − 1)!!. ... The vertices of this graph G n consist of binary coupling*trees*, representing the coupling*schemes*in the bra/kets of the 3nj-coefficients. ... A binary coupling*tree*on n + 1 leaves is a rooted binary*tree*such that • the n + 1 leaves are*labelled*1, 2, . . . , n + 1; • the internal vertices are not*labelled*; •*for*each internal vertex, one can ...##
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A highway-centric labeling approach for answering distance queries on large sparse graphs

2012
*
Proceedings of the 2012 international conference on Management of Data - SIGMOD '12
*

Here, we propose a novel

doi:10.1145/2213836.2213887
dblp:conf/sigmod/JinRXL12
fatcat:dzuxwapr4zfbvmhjhnrwauifzy
*labeling**scheme*, referred to as Highway-Centric*Labeling*,*for*answering*distance*queries in a large sparse graph. ... It empowers the*distance**labeling*with a highway structure and leverages a novel bipartite set cover framework/algorithm. ... There are several interval-*labeling**schemes*[25]*for*a rooted directed*tree*. A simple*scheme*is as follows. ...##
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Additive Spanners and Distance and Routing Labeling Schemes for Hyperbolic Graphs

2010
*
Algorithmica
*

routing protocol, and a

doi:10.1007/s00453-010-9478-x
fatcat:6dtmgfdgjnh4zdnut7jddioppq
*distance**labeling**scheme*with O(log 2 n) bit*labels*, O(δ log n) additive error and constant time*distance*decoder. ... As a consequence, we show that the family of n-vertex δ-hyperbolic graphs with δ ≥ 1/2 admits a routing*labeling**scheme*with O(δ log 2 n) bit*labels*, O(δ log n) additive stretch and O(log 2 (4δ)) time ... We would like to thank the referees*for*many useful suggestions and remarks. ...##
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Distance labeling schemes for trees
[article]

2015
*
arXiv
*
pre-print

We consider

arXiv:1507.04046v1
fatcat:ritscusvkbde7bhmbezfmj443i
*distance**labeling**schemes**for**trees*: given a*tree*with n nodes,*label*the nodes with binary strings such that, given the*labels*of any two nodes, one can determine, by looking only at the*labels*... We also give (1+ϵ)-stretch*labeling**schemes*using Θ( n) bits*for*constant ϵ>0. (1+ϵ)-stretch*labeling**schemes*with polylogarithmic*label*size have previously been established*for*doubling dimension graphs ... Fix an*optimal*leaf*distance**labeling**scheme*σ which produces exactly g(h, W, a) distinct*labels**for*the family of (h, W, a)-*trees*. ...##
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Distance labeling scheme and split decomposition

2003
*
Discrete Mathematics
*

This yields to

doi:10.1016/s0012-365x(03)00232-2
fatcat:blqilrue4nfanms7lpnvxal5ey
*optimal**label*length*schemes**for*the family of*distance*-hereditary graphs and*for*other families of graphs, allowing*distance*estimation in constant time once the*labels*have been constructed ... A*distance**labeling**scheme*is a distributed data-structure designed to answer queries about*distance*between any two vertices of a graph G. ... Applying this technique, we show that the*optimal**schemes**for**trees*obtained by [17, 19] can be generalized to*distance*-hereditary graphs. ...
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