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100
Evolution of networks
 Adv. Phys
, 2002
"... We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence rece ..."
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Cited by 268 (2 self)
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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scalefree and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks selforganize into scalefree structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems
Deterministic manytomany hot potato routing
 IEEE Transactions on Parallel and Distributed Systems
, 1997
"... We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurrin ..."
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Cited by 31 (0 self)
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We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurring networks such as the hypercube, meshes and tori of various dimensions and sizes, trees and hypercubic networks such as the butterfly. All these algorithms are analyzed using a charging scheme that may be applicable to other algorithms as well. Moreover, all bounds hold in a dynamic setting in which packets can be injected at arbitrary times.
Potential Function Analysis of Greedy HotPotato Routing (Extended Abstract)
 Theory of Computing Systems
, 1994
"... Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpo ..."
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Cited by 30 (2 self)
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Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpotato or deflection routing algorithms. The important characteristic of these algorithms is that they use no buffer space for storing delayed packets. Each packet, unless already arrived to its destination, must leave the processor at the step following its arrival. The main advantage in hotpotato routing is that there is no need to store delayed packets in the processors, and therefore, the processors can be much simpler, and contain less hardware. This work is concerned with greedy routing, in which a packet is bound to use an outgoing link in the direction of its destination, whenever such a link is available. In this way, greediness guarantees that, unless some global congestion forbids...
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
A Case for Bufferless Routing in OnChip Networks
 ISCA'09
, 2009
"... Buffers in onchip networks consume significant energy, occupy chip area, and increase design complexity. In this paper, we make a case for a new approach to designing onchip interconnection networks that eliminates the need for buffers for routing or flow control. We describe new algorithms for ro ..."
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Cited by 29 (10 self)
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Buffers in onchip networks consume significant energy, occupy chip area, and increase design complexity. In this paper, we make a case for a new approach to designing onchip interconnection networks that eliminates the need for buffers for routing or flow control. We describe new algorithms for routing without using buffers in router input/output ports. We analyze the advantages and disadvantages of bufferless routing and discuss how router latency can be reduced by taking advantage of the fact that input/output buffers do not exist. Our evaluations show that routing without buffers significantly reduces the energy consumption of the onchip cache/processortocache network, while providing similar performance to that of existing buffered routing algorithms at low network utilization (i.e., on most real applications). We conclude that bufferless routing can be an attractive and energyefficient design option for onchip cache/processortocache networks where network utilization is low.
Analysis of HotPotato Optical Networks with Wavelength Conversion
 IEEE JOURNAL OF LIGHTWAVE TECHNOLOGY
, 1999
"... Wavelength conversion has been shown to reduce the probability of blocking in both circuitswitching and packetswitching wavelength routed optical networks (WRONs). The effectiveness of the blocking reduction depends on the topology, and is known to be best for meshed topologies, where the average ..."
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Cited by 20 (1 self)
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Wavelength conversion has been shown to reduce the probability of blocking in both circuitswitching and packetswitching wavelength routed optical networks (WRONs). The effectiveness of the blocking reduction depends on the topology, and is known to be best for meshed topologies, where the average number of hops per path is large. This paper shows that by exploiting wavelength conversion, routing without buffers, known as hotpotato, becomes an interesting option for packet switching WRONs with meshed topologies, such as Manhattan Street (MS) Network and ShuffleNet (SN). The results show that, by using more than 4 wavelengths, a 64 node MS or SN network can work at full load with a hop delay within one hop from its lowest achievable value. We also show that using delayline routing buffers at the node is a much more effective way of reducing blocking than using wavelength conversion.
HardPotato Routing
, 2000
"... We present the rst hotpotato routing algorithm for the n × n mesh whose running time on any "hard" (i.e., n)) "manytoone" batch routing problem is, with high probability, within a polylogarithmic factor of optimal. For any instance I of a batch routing problem, there exists a wellknown low ..."
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Cited by 20 (11 self)
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We present the rst hotpotato routing algorithm for the n × n mesh whose running time on any "hard" (i.e., n)) "manytoone" batch routing problem is, with high probability, within a polylogarithmic factor of optimal. For any instance I of a batch routing problem, there exists a wellknown lower bound LBI based on maximum path length and maximum congestion. If LBI is n), our algorithm solves I with high probability in time O(LBI log 3 n). The algorithm is distributed and greedy, and it makes use of a new routing technique based on multibend paths, a departure from paths using a constant number of bends used in prior hotpotato algorithms.
On hierarchical traffic grooming in WDM networks
 IEEE/ACM Transactions on Networking
, 2008
"... Abstract—The traffic grooming problem is of high practical importance in emerging widearea wavelength division multiplexing (WDM) optical networks, yet it is intractable for any but trivial network topologies. In this work, we present an effective and efficient hierarchical traffic grooming framewo ..."
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Cited by 17 (9 self)
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Abstract—The traffic grooming problem is of high practical importance in emerging widearea wavelength division multiplexing (WDM) optical networks, yet it is intractable for any but trivial network topologies. In this work, we present an effective and efficient hierarchical traffic grooming framework for WDM networks of general topology, with the objective of minimizing the total number of electronic ports. At the first level of hierarchy, we decompose the network into clusters and designate one node in each cluster as the hub for grooming traffic. At the second level, the hubs form another cluster for grooming intercluster traffic. We view each (firstor secondlevel) cluster as a virtual star, and we present an efficient nearoptimal algorithm for determining the logical topology of lightpaths to carry the traffic within each cluster. Routing and wavelength assignment is then performed directly on the underlying physical topology. We demonstrate the effectiveness of our approach by applying it to two networks of realistic size, a 32node, 53link topology and a 47node, 96link network. Comparisons to lower bounds indicate that hierarchical grooming is efficient in its use of the network resources of interest, namely, electronic ports and wavelengths. In addition to scaling to large network sizes, our hierarchical approach also facilitates the control and management of multigranular networks. Index Terms—Hierarchical traffic grooming, Kcenter, optical networks, wavelength division multiplexing (WDM).
Optimal Bounds for Matching Routing on Trees
 In Proceedings of the 8th Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
"... The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 2 n + O(log n) steps. This answers an open problem of Alon, ..."
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Cited by 16 (1 self)
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The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 2 n + O(log n) steps. This answers an open problem of Alon, Chung and Graham. Key words. matching routing, offline algorithms, trees AMS subject classifications. 05C, 68M, 68R 1 Introduction Routing problems on networks arise in different fields such as communications, parallel architectures and VLSI theory, and have been extensively studied in recent years (see [9, 10] for a comprehensive survey). In this paper, we study permutation routing under the matching model, which was proposed by Alon, Chung and Graham[2]. The routing of this type is described as follows. Given a graph G = (V; E) with vertex set V and edge set E. Initially, each vertex v of G is occupied by a "packet" p. To each packet p is associated a destination ß(v) 2 V , so that di...