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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 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...
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.
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...
Linear Interval Routing
 The Computer Journal
, 1991
"... We study a variant of Interval Routing [SK85, LT86] where the routing range associated with every link is represented by a linear (i.e., contiguous) interval with no wrap around. This kind of routing schemes arises naturally in the study of dynamic Prefix Routing [BLT90]. Linear Interval Routing sch ..."
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Cited by 70 (3 self)
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We study a variant of Interval Routing [SK85, LT86] where the routing range associated with every link is represented by a linear (i.e., contiguous) interval with no wrap around. This kind of routing schemes arises naturally in the study of dynamic Prefix Routing [BLT90]. Linear Interval Routing schemes are precisely the Prefix Routing schemes that use an alphabet of one symbol. We characterize the type of networks that admit optimum Linear Interval Routing schemes. It is shown that several wellknown interconnection networks such as hypercubes, certain ntori, and ndimensional grids all with unitcost links, have optimum Linear Interval Routing schemes. We also introduce the multilabel Linear Interval Routing schemes where each link may contain more than one label, and we prove several characterization results for these schemes. 1 Introduction In communication networks routing algorithms are employed for selecting suitable routes from origin to destination nodes and ensuring that m...
On Hierarchical Routing in Doubling Metrics
, 2005
"... We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α ..."
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Cited by 58 (8 self)
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We study the problem of routing in doubling metrics, and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(X) at most α if every set of diameter D can be covered by 2 α sets of diameter D/2. (A doubling metric is one whose doubling dimension dim(X) is a constant.) We show how to perform (1 + τ)stretch routing on metrics for any 0 < τ ≤ 1 with routing tables of size at most (α/τ) O(α) log 2 ∆ bits with only (α/τ) O(α) log ∆ entries, where ∆ is the diameter of the graph; hence the number of routing table entries is just τ −O(1) log ∆ for doubling metrics. These results extend and improve on those of Talwar (2004). We also give better constructions of sparse spanners for doubling metrics than those obtained from the routing tables above; for τ> 0, we give algorithms to construct (1 + τ)stretch spanners for a metric (X, d) with maximum degree at most (2 + 1/τ) O(dim(X)) , matching the results of Das et al. for Euclidean metrics.
Routing in Distributed Networks: Overview and Open Problems
 ACM SIGACT News  Distributed Computing Column
, 2001
"... This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems. ..."
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Cited by 49 (12 self)
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This article focuses on routing messages in distributed networks with efficient data structures. After an overview of the various results of the literature, we point some interestingly open problems.
Memory Requirement for Routing in Distributed Networks
 IN 15 TH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING (PODC
, 1995
"... In this paper, we deal with the compact routing problem on distributed networks, that is implementing routing schemes that use a minimum memory size on each node. We prove that for every shortest path routing scheme, for any constant ", 0 ! " ! 1, and for every integer d such that 3 d "n, there ..."
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Cited by 36 (7 self)
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In this paper, we deal with the compact routing problem on distributed networks, that is implementing routing schemes that use a minimum memory size on each node. We prove that for every shortest path routing scheme, for any constant ", 0 ! " ! 1, and for every integer d such that 3 d "n, there exists a nnode network of maximum degree d that locally requires at least \Theta(n log d) bits of memory on \Theta(n) nodes. This optimal lower bound means that whatever the routing scheme (interval routing, boolean routing, prefix routing, : : : ), there exists a network on which one can not do better than routing tables. Moreover, we prove that, for the wellknown interval routing scheme, there exists a nnode network of bounded degree d, for every d 3, that requires \Theta(n) intervals on \Theta(n) links to code any shortest path routing function. This tight lower bound shows that, for networks of bounded degree, the interval routing scheme can be worst than the routing tables ...