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Compact and Localized Distributed Data Structures
 JOURNAL OF DISTRIBUTED COMPUTING
, 2001
"... This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sou ..."
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Cited by 72 (23 self)
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This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sought information involves only a small and local set of entities. In contrast, localized data representation schemes are based on breaking the information into small local pieces, or labels, selected in a way that allows one to infer information regarding a small set of entities directly from their labels, without using any additional (global) information. The survey focuses on combinatorial and algorithmic techniques, and covers complexity results on various applications, including compact localized schemes for message routing in communication networks, and adjacency and distance labeling schemes.
Labeling Schemes for Weighted Dynamic Trees
 In Proc. 30th Int. Colloq. on Automata, Languages & Prog
, 2003
"... A Distance labeling scheme is a type of localized network representation in which short labels are assigned to the vertices, allowing one to infer the distance between any two vertices directly from their labels, without using any additional information sources. As most applications for network repr ..."
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Cited by 21 (16 self)
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A Distance labeling scheme is a type of localized network representation in which short labels are assigned to the vertices, allowing one to infer the distance between any two vertices directly from their labels, without using any additional information sources. As most applications for network representations in general, and distance labeling schemes in particular, concern large and dynamically changing networks, it is of interest to focus on distributed dynamic labeling schemes. The paper considers dynamic weighted trees where the vertices of the trees are fixed but the (positive integral) weights of the edges may change. The two models considered are the edgedynamic model, where from time to time some edge changes its weight by a fixed quanta, and the increasingdynamic model in which edge weights can only grow. The paper presents distributed approximate distance labeling schemes for the two dynamic models, which are efficient in terms of the required label size and communication complexity involved in updating the labels following the weight changes.
Labeling Schemes for Dynamic Tree Networks
 Theory of Computing Systems
, 2002
"... Distance labeling schemes are composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute the distance between any two vertices directly from their labels (without using any additional information). As applications f ..."
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Cited by 20 (16 self)
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Distance labeling schemes are composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute the distance between any two vertices directly from their labels (without using any additional information). As applications for distance labeling schemes concern mainly large and dynamically changing networks, it is of interest to study distributed dynamic labeling schemes. The current paper considers the problem on dynamic trees, and proposes efficient distributed schemes for it. The paper first presents a labeling scheme for distances in the dynamic tree model, with amortized message complexity O(log 2 n) per operation, where n is the size of the tree at the time the operation takes place. The protocol maintains O(log 2 n) bit labels. This label size is known to be optimal even in the static scenario. A more general labeling scheme is then introduced for the dynamic tree model, based on extending an existing static tree labeling scheme to the dynamic setting. The approach fits a number of natural tree functions, such as distance, separation level and flow. The main resulting scheme incurs an overhead of a O(log n) multiplicative factor in both the label size and amortized message complexity in the case of dynamically growing trees (with no vertex deletions). If an upper bound on n is known in advance, this method yields a different tradeoff, with an O(log 2 n / log log n) multiplicative overhead on the label size but only an O(log n / log log n) overhead on the amortized message complexity. In the fullydynamic model the scheme incurs also an increased additive overhead in amortized communication, of O(log 2 n) messages per operation.
Distance labeling scheme and split decomposition
 Discrete Mathematics
, 2003
"... A distance labeling scheme is a distributed datastructure designed to answer queries about distance between any two vertices of a graph G. The datastructure consists in a label L(x; G) assigned to each vertex x of G such that the distance dG(x; y) between any two vertices x and y can be estimated ..."
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Cited by 13 (6 self)
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A distance labeling scheme is a distributed datastructure designed to answer queries about distance between any two vertices of a graph G. The datastructure consists in a label L(x; G) assigned to each vertex x of G such that the distance dG(x; y) between any two vertices x and y can be estimated as a function f(L(x; G); L(y; G)). In this paper we combine several types of distance labeling schemes and split decomposition of graphs. This yields to optimal label length schemes for the family of distancehereditary graphs and for other families of graphs, allowing distance estimation in constant time once the labels have been constructed.
Labeling Schemes for Weighted Dynamic Trees (Extended Abstract)
"... Abstract. This paper studies βapproximate distance labeling schemes, which are composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute a βapproximation of the distance between any two vertices directly from the ..."
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Cited by 2 (0 self)
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Abstract. This paper studies βapproximate distance labeling schemes, which are composed of a marker algorithm for labeling the vertices of a graph with short labels, coupled with a decoder algorithm allowing one to compute a βapproximation of the distance between any two vertices directly from their labels (without using any additional information). As most applications for informative labeling schemes in general, and distance labeling schemes in particular, concern large and dynamically changing networks, it is of interest to focus on distributed dynamic labeling schemes. The paper considers the problem on dynamic weighted trees and cycles where the vertices of the tree (or the cycle) are fixed but the (positive integral) weights of the edges may change. The two models considered are the fully dynamic model, where from time to time some edge changes its weight by a fixed quanta, and the increasing dynamic model in which edge weights can only grow. The paper presents distributed βapproximate distance labeling schemes for the two models, for β> 1, and establishes upper and lower bounds on the required label size and the communication complexity involved in updating the labels following a weight change. 1
Distance Labeling Scheme and Split Decomposition
, 2001
"... Abstract A distance labeling scheme is a distributed datastructure designed to answer queries about distance between any two vertices of a graph G. The datastructure consists in a label L(x; G) assigned to each vertex x of G such that the distance dG(x; y) between any two vertices x and y can be e ..."
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Abstract A distance labeling scheme is a distributed datastructure designed to answer queries about distance between any two vertices of a graph G. The datastructure consists in a label L(x; G) assigned to each vertex x of G such that the distance dG(x; y) between any two vertices x and y can be estimated as a function f(L(x; G); L(y; G)). In this paper we combine several types of distance labeling schemes and split decomposition of graphs. This yields to optimal label length schemes for the family of distancehereditary graphs and for other families of graphs, allowing distance estimation in constant time once the labels have been constructed.