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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 111 (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...
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...
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 71 (26 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.
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.
Sparse Partitions (Extended Abstract)
 In IEEE Symposium on Foundations of Computer Science
, 1990
"... 1 ) Baruch Awerbuch David Peleg y Abstract: This abstract presents a collection of clustering and decomposition techniques enabling the construction of sparse and locality preserving representations for arbitrary networks. These new clustering techniques have already found several powerful appl ..."
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Cited by 21 (0 self)
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1 ) Baruch Awerbuch David Peleg y Abstract: This abstract presents a collection of clustering and decomposition techniques enabling the construction of sparse and locality preserving representations for arbitrary networks. These new clustering techniques have already found several powerful applications in the area of distributed network algorithms. Two of these applications are described in this abstract, namely, routing with polynomial communicationspace tradeoff and online tracking of mobile users. 1 Introduction 1.1 Motivation As networks grow larger, various control and management functions become increasingly more complex and expensive. Traditional protocols, based on a global approach, require all sites to participate in their activities, and to maintain considerable amounts of global information (e.g. topological data, status tables etc). This becomes problematic due to space considerations, the complexity of maintaining and updating this global information and the incre...
The Complexity of the Characterization of Networks Supporting ShortestPath Interval Routing (Extended Abstract)
, 1991
"... Interval Routing is a spaceefficient routing method for communication networks which has been extensively studied and implemented. Many variants of this basic routing method were proposed, such as Linear Interval Routing, strict Interval Routing and strict Linear Interval Routing. These methods wer ..."
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Cited by 16 (1 self)
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Interval Routing is a spaceefficient routing method for communication networks which has been extensively studied and implemented. Many variants of this basic routing method were proposed, such as Linear Interval Routing, strict Interval Routing and strict Linear Interval Routing. These methods were generalized to allow k intervals per edge. The question of characterizing networks which support optimal interval routing was thoroughly investigated for each of the variants above, and under different models. Only partial answers, both positive and negative, were given. In this paper we study the characterization of networks which admit optimal (strict or nonstrict) interval routing and optimal (strict or nonstrict) linear interval routing under the most basic model  the one unit cost, one interval per edge model. We prove that the characterization of these networks is NPhard...
MultiDimensional Interval Routing Schemes
, 1995
"... . Interval Routing Scheme (kIRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation INMOS Transputer Router chip. In this paper we introduce an extension of the Interval Routing Scheme kIRS to the multidimensiona ..."
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Cited by 13 (2 self)
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. Interval Routing Scheme (kIRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation INMOS Transputer Router chip. In this paper we introduce an extension of the Interval Routing Scheme kIRS to the multidimensional case hk; diMIRS, where k is the number of intervals and d is the number of dimensions. Whereas kIRS only represents compactly a single shortest path between any two nodes, with this new extension we are able to represent all shortest paths compactly. This is useful for faulttolerance and traffic distribution in a network. We study efficient representations of all shortest paths between any pair of nodes for general network topologies, for product graphs and for specific interconnection networks such as rings, grids, tori, hypercubes and chordal rings. For these interconnection networks we show that for about the same space complexity as kIRS we can represent all shortest paths in hk; ...
On The Hardness Of Devising Interval Routing Schemes
, 1996
"... The kInterval Routing Scheme (kIRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation of the INMOS transputer router chips. In this paper we investigate the time complexity of devising a minimal space kIRS and w ..."
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Cited by 8 (1 self)
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The kInterval Routing Scheme (kIRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation of the INMOS transputer router chips. In this paper we investigate the time complexity of devising a minimal space kIRS and we prove that the problem of deciding whether there exists a 2IRS for any network G is NPcomplete. This is the first hardness result for kIRS where k is constant and the graph underlying the network is unweighted. Moreover, the NPcompleteness holds also for linear and strict 2IRS.
A Lower Bound for Linear Interval Routing
 Networks
, 1996
"... Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such r ..."
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Cited by 8 (5 self)
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Linear Interval Routing is a spaceefficient routing method for pointtopoint communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such routing methods is in terms of the maximal length of a path a message traverses. For Interval Routing the upper bound and lower bound on this quantity are 2D and 1:75D \Gamma 1, respectively, where D is the diameter of the network. We prove a lower bound of \Omega\Gamma D 2 ) on the length of a path a message traverses under Linear Interval Routing. We further extend the result by showing a connection between the efficiency of Linear Interval Routing and the bi diameter of the network. 1 Introduction In a communication network, where communication between nodes is accomplished by sending and receiving messages, a routing algorithm is employed to ensure that every message will reach its des...
Network FaultTolerance with Interval Routing Devices
, 1993
"... Massively Parallel Computers are built out of millions of devices, making the overall system's dependability too low. Faulttolerant measures have thus to be included. In this paper we will address network faulttolerance. More specifically, a routing algorithm is developed which is able to isolate ..."
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Cited by 7 (2 self)
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Massively Parallel Computers are built out of millions of devices, making the overall system's dependability too low. Faulttolerant measures have thus to be included. In this paper we will address network faulttolerance. More specifically, a routing algorithm is developed which is able to isolate faulty units, entire nodes as well as single links, and to reroute messages to spares. The proposed method, based on multiinterval routing, is nearoptimal and requires only few extra intervals. In the second section of the paper we will describe the machine our algorithms are to be run on. We suppose the routing device to support multiinterval routing [3], [5]. We will briefly explain some necessary concepts of multiinterval routing and its limitations. A description of faultfree routing for this system will be given, since it forms the basis for the faulttolerance algorithms. Next we will consider the faults that may occur. We will then also state the general ideas about how to over...