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98
Compass Routing on Geometric Networks
 IN PROC. 11 TH CANADIAN CONFERENCE ON COMPUTATIONAL GEOMETRY
, 1999
"... In this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions: ..."
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Cited by 266 (14 self)
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In this paper we study local routing algorithms on geometric networks. Formally speaking, suppose that we want to travel from a vertex s to a vertex t of a geometric network. A routing algorithm is called a local routing algorithm if it satisfies the following conditions:
Compact routing schemes
 in SPAA ’01: Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
"... We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extrem ..."
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Cited by 196 (7 self)
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We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes constant time. Yet, the stretch of these routing schemes, i.e., the worst ratio between the cost of the path on which a packet is routed and the cost of the cheapest path from source to destination, is a small constant. Our schemes achieve a nearoptimal tradeoff between the size of the routing tables used and the resulting stretch. More specifically, we obtain: 1. A routing scheme that uses only ~ O(n 1=2) bits of memory at each node of an nnode network that has stretch 3. The space is optimal, up to logarithmic factors, in the sense that
Compact Routing with Minimum Stretch
 Journal of Algorithms
"... We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all node ..."
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Cited by 112 (5 self)
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We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use\Omega\Gamma n) local space at some vertex. 1 Introduction Let G = (V; E) with jV j = n be a labeled undirected network. Assuming that a positive cost, or distance is assigned with each edge, the stretch of path p(u; v) from node u to node v is defined as jp(u;v)j jd(u;v)j , where jd(u; v)j is the length of the shortest u \Gamma v path. The approximate allpairs shortest path problem involves a tradeoff of stretch against time short paths with stretch bounded by a constant are com...
Distance Labeling in Graphs
, 2000
"... We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases. We obtain upper a ..."
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Cited by 102 (26 self)
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We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases. We obtain upper and lower bounds for several interesting families of graphs. In particular, our main results are the following. For general graphs, we show that the length needed is (n). For trees, we show that the length needed is (log 2 n). For planar graphs, we show an upper bound of O( p n log n) and a lower bound of n 1=3 ). For bounded degree graphs, we show a lower bound of p n). The upper bounds for planar graphs and for trees follow by a more general upper bound for graphs with a r(n)separator. The two lower bounds, however, are obtained by two different arguments that may be interesting in their own right. We also show some lower bounds on the length of the labels, even if it is only...
Routing in Trees
 IN 28 TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP
, 2001
"... This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that nnode trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing d ..."
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Cited by 87 (26 self)
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This article focuses on routing messages along shortest paths in tree networks, using compact distributed data structures. We mainly prove that nnode trees support routing schemes with message headers, node addresses, and local memory space of size O(log n) bits, and such that every local routing decision is taken in constant time. This improves the best known routing scheme by a factor of O(log n) in term of both memory requirements and routing time. Our routing scheme requires headers and addresses of size slightly larger than log n, motivated by an inherent tradeoff between addresssize and memory space, i.e., any routing scheme with addresses on log n bits requires n) bits of local memoryspace. This shows that a little variation of the address size, e.g., by an additive O(log n) bits factor, has a significant impact on the local memory space.
Nearest Common Ancestors: A survey and a new distributed algorithm
, 2002
"... Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete ba ..."
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Cited by 76 (12 self)
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Several papers describe linear time algorithms to preprocess a tree, such that one can answer subsequent nearest common ancestor queries in constant time. Here, we survey these algorithms and related results. A common idea used by all the algorithms for the problem is that a solution for complete balanced binary trees is straightforward. Furthermore, for complete balanced binary trees we can easily solve the problem in a distributed way by labeling the nodes of the tree such that from the labels of two nodes alone one can compute the label of their nearest common ancestor. Whether it is possible to distribute the data structure into short labels associated with the nodes is important for several applications such as routing. Therefore, related labeling problems have received a lot of attention recently.
Routing with Polynomial CommunicationSpace Tradeoff
 SIAM Journal on Discrete Mathematics
, 1993
"... This paper presents a family of memorybalanced routing schemes that use relatively short paths while storing relatively little routing information. The hierarchical schemes H k (for every integer k 1) guarantee a stretch factor of O(k 2 ) on the length of the routes and require storing at most O ..."
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Cited by 75 (13 self)
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This paper presents a family of memorybalanced routing schemes that use relatively short paths while storing relatively little routing information. The hierarchical schemes H k (for every integer k 1) guarantee a stretch factor of O(k 2 ) on the length of the routes and require storing at most O(kn 1 k log n log D) bits of routing information per vertex in an nprocessor network with diameter D. The schemes are nameindependent and applicable to general networks with arbitrary edge weights. This improves on previous designs whose stretch bound was exponential in k. Key words: Communication networks, routing tables, communicationspace tradeoffs, graph covers. Dept. of Mathematics and Lab. for Computer Science, M.I.T., Cambridge, MA 02139; ARPANET: baruch@theory.lcs.mit.edu. Supported by Air Force Contract TNDGAFOSR860078, ARO contract DAAL0386K0171, NSF contract CCR8611442, DARPA contract N0001489J1988, and a special grant from IBM. y Department of Applied Mathemati...
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.
Implicit Representation of Graphs
 SIAM Journal On Discrete Mathematics
, 1992
"... How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place h ..."
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Cited by 72 (0 self)
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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an nvertex graph, the names of the vertices (i.e. integers from 1 to n) betray nothing about the graph itself. Indeed, the names (or labels) on the n vertices are just log n bit place holders to allow data on the edges to encode the structure of the graph. In our scenario, there is no such waste. By assigning O(log n) bit labels to the vertices, we completely encode the structure of the graph, so that given the labels of two vertices we can test if they are adjacent in time linear in the size of the labels. Furthermore, given an arbitrary original labeling of the vertices, we can find structure coding labels (as above) that are no more than a small constant factor larger than the original labels. These notions are intimately related to vertex induced universal graphs of polynomial size. For example, we can label planar graphs with structure coding labels of size ! 4 log n, which implies the existence of a graph with n 4 vertices that contains all nvertex planar graphs as vertex induced subgraphs.
Compact Distributed Data Structures for Adaptive Routing
 In Proc. 21st ACM Symp. on Theory of Computing
, 1989
"... In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stret ..."
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Cited by 71 (7 self)
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In designing a routing scheme for a communication network it is desirable to use as short as possible paths for routing messages, while keeping the routing information stored in the processors' local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factor  the maximum ratio between the cost of a route computed by the scheme and that of a cheapest path connecting the same pair of vertices. This paper presents a family of adaptive routing schemes for general networks. The hierarchical schemes HS k (for every fixed k 1) guarantee a stretch factor of O(k 2 \Delta 3 k ) and require storing at most O \Gamma kn 2 k log n \Delta bits of routing information per vertex. The new important features, that make the schemes appropriate for adaptive use, are ffl applicability to networks with arbitrary edge costs; ffl nameindependence, i.e., usage of original names; ffl a balanced distribution of the memory; ffl an efficient onli...