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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 (25 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.
Shortest Paths in Digraphs of Small Treewidth. Part I: Sequential Algorithms
, 1995
"... We consider the problem of preprocessing an nvertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a consta ..."
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Cited by 35 (4 self)
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We consider the problem of preprocessing an nvertex digraph with real edge weights so that subsequent queries for the shortest path or distance between any two vertices can be efficiently answered. We give algorithms that depend on the treewidth of the input graph. When the treewidth is a constant, our algorithms can answer distance queries in O(ff(n)) time after O(n) preprocessing. This improves upon previously known results for the same problem. We also give a dynamic algorithm which, after a change in an edge weight, updates the data structure in time O(n fi ), for any constant 0 ! fi ! 1. Furthermore, an algorithm of independent interest is given: computing a shortest path tree, or finding a negative cycle in linear time.
The Complexity of Interval Routing on Random Graphs
 THE COMPUTER JOURNAL
, 1995
"... Several methods exist for routing messages in a network without using complete routing tables (compact routing). In kinterval routing schemes (kIR.S), links carry up to k intervals each. A message is routed over certain link if its destination belongs to one of the intervals of the link. We giv ..."
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Cited by 32 (4 self)
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Several methods exist for routing messages in a network without using complete routing tables (compact routing). In kinterval routing schemes (kIR.S), links carry up to k intervals each. A message is routed over certain link if its destination belongs to one of the intervals of the link. We give some results for the necessary value of k in order to achieve shortest path routing. Even though for very structured networks low values of suce, we show that for 'general graphs' interval routing cannot significantly reduce the spacerequirements for shortest path routing. In particular we show that for suitably large n, there are suitable values of p such that for randomly chosen graphs G 6 ,p the following holds, with high probability: if G admits an optimal kIIS, then k = The result is obtained by means of a novel matrix representation for the shortest paths in a network.
Materialization TradeOffs in Hierarchical Shortest Path Algorithms
 In Symposium on Large Spatial Databases
, 1997
"... Materialization and hierarchical routing algorithms are becoming important tools in querying databases for the shortest paths in timecritical applications like Intelligent Transportation Systems (ITS), due to the growing size of their spatial graph databases [16]. A hierarchical routing algorithm d ..."
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Cited by 28 (3 self)
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Materialization and hierarchical routing algorithms are becoming important tools in querying databases for the shortest paths in timecritical applications like Intelligent Transportation Systems (ITS), due to the growing size of their spatial graph databases [16]. A hierarchical routing algorithm decomposes the original graph into a set of fragment graphs and a boundary graph which summarizes the fragment graphs. A fully materialized hierarchical routing algorithm precomputes and stores the shortestpath view and the shortestpathcost view for the graph fragments as well as for the boundary graph [9]. The storage cost of the fully materialized approach can be reduced by a virtual or a hybrid materialization approach, where few or none of the relevant views are precomputed. This paper explores the effect of materializing individual views for the storage overhead and computation time of hierarchical routing algorithms. Our experiments with the Twin Cities metropolitan roadmap show...
Improved Algorithms for Dynamic Shortest Paths
 Algorithmica
, 1996
"... We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can ..."
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Cited by 15 (3 self)
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We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time and a distance query is answered also in logarithmic time. In the case of planar digraphs, we give an interesting tradeoff between preprocessing, query and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to nvertex digraphs of genus O(n 1\Gamma" ) for any " ? 0. Keywords: Shortest path, dynamic algorithm, planar digraph, outerplanar digraph. This work was partially supported by the NSF grant No. CCR9409191 and by the EU ESPRIT LTR Project No. 20244 (ALCOMIT). 1 Introduction 1.1 The prob...
Two Lower Bounds for MultiLabel Interval Routing
, 1997
"... Interval routing is a spaceefficient method for pointtopoint networks. The method has been incorporated in the design of a commercially available routing chip [7], and is a basic element in some compact routing methods (e.g., [4]). With up to one interval label per edge, the method has been shown ..."
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Cited by 13 (6 self)
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Interval routing is a spaceefficient method for pointtopoint networks. The method has been incorporated in the design of a commercially available routing chip [7], and is a basic element in some compact routing methods (e.g., [4]). With up to one interval label per edge, the method has been shown to be nonoptimal for arbitrary graphs [9, 13], where optimality is measured in terms of the longest (routing) path in a graph. It is intuitive to think that the longest path would depend on the number of interval labels used. In this paper, using some nonplanar graphs, we prove that even with a relatively large number of labels, interval routing still falls short of being optimal for arbitrary graphs. The bounds on the longest path we prove are 3 2 D, independent of any number of labels up to \Theta(log n), where D is the diameter of the graph; and 5 4 D, independent of any number of labels from \Theta(log n) to \Theta( p n). Our lower bound results suggest that a large increase, a fac...
Interval Routing Schemes allow Broadcasting with Linear MessageComplexity
, 2000
"... The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we an ..."
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Cited by 11 (4 self)
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The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we answer a longstanding conjecture by showing that compact routing can also help to perform distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows to broadcast with an O(n) messagecomplexity, where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suce to solve leaderelection for any graph labeled by a shortest path interval routing scheme, improving therefore the O(m + n) previous known bound.
Online and Dynamic Algorithms for Shortest Path Problems
 Proc. 12th Symp. on Theor. Aspects of Comp. Sc. (STACS'95), LNCS 900
, 1995
"... Abstract. We describe algorithms for finding shortest paths and distances in a planar digraph which exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be ..."
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Cited by 10 (9 self)
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Abstract. We describe algorithms for finding shortest paths and distances in a planar digraph which exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. Our data structures can be updated after any such change in only polylogarithmic time, while a singlepair query is answered in sublinear time. We also describe the first parallel algorithms for solving the dynamic version of the shortest path problem. 1
HammockonEars Decomposition: A Technique for the Efficient Parallel Solution of Shortest Paths and Other Problems
 Theoretical Computer Science
, 1996
"... We show how to decompose efficiently in parallel any graph into a number, ~ fl, of outerplanar subgraphs (called hammocks) satisfying certain separator properties. Our work combines and extends the sequential hammock decomposition technique introduced by G. Frederickson and the parallel ear decom ..."
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Cited by 8 (5 self)
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We show how to decompose efficiently in parallel any graph into a number, ~ fl, of outerplanar subgraphs (called hammocks) satisfying certain separator properties. Our work combines and extends the sequential hammock decomposition technique introduced by G. Frederickson and the parallel ear decomposition technique, thus we call it the hammockonears decomposition. We mention that hammockonears decomposition also draws from techniques in computational geometry and that an embedding of the graph does not need to be provided with the input. We achieve this decomposition in O(logn log log n) time using O(n + m) CREW PRAM processors, for an nvertex, medge graph or digraph. The hammockonears decomposition implies a general framework for solving graph problems efficiently. Its value is demonstrated by a variety of applications on a significant class of (di)graphs, namely that of sparse (di)graphs. This class consists of all (di)graphs which have a ~ fl between 1 and \Theta(n...