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 scale-free 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 self-organize into scale-free 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

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We consider algorithms for many-to-many 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 many-tomany 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.

Amir Ben-Dor 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 hot-potato 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 hot-potato 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 out-going link in the direction of its destination, whenever such a link is available. In this way, greediness guarantees that, unless some global congestion forbids...

We survey routing problems on fixed-connection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, k-relation 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.

Wavelength conversion has been shown to reduce the probability of blocking in both circuit-switching and packet-switching 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 hot-potato, 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 delay-line routing buffers at the node is a much more effective way of reducing blocking than using wavelength conversion.

We present the rst hot-potato routing algorithm for the n × n mesh whose running time on any "hard" (i.e., n)) "many-to-one" 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 well-known 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 multi-bend paths, a departure from paths using a constant number of bends used in prior hot-potato algorithms.

The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (so-called) caterpillar tree partition, we prove that any permutation on an n-node 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, off-line 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...

Buffers in on-chip networks consume significant energy, occupy chip area, and increase design complexity. In this paper, we make a case for a new approach to designing on-chip 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 on-chip cache/processor-to-cache 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 energy-efficient design option for onchip cache/processor-to-cache networks where network utilization is low.

We present a novel greedy hot-potato routing algorithm for the 2-dimensional n × n mesh or torus. This algorithm uses randomization to adjust packet priorities. For any permutation problem or random destination problem, it ensures that each packet reaches its destination in asymptotically optimal expected O(n) steps, and all packets reach their destinations in O(n ln n) steps with high probability, an improvement over the previously-known deterministic upper bound of O(n²) for greedy algorithms. For a general batch problem, with high probability all packets reach their destination nodes in at most O(m ln n) steps, where m = min(mr ; mc ), where mr and mc are respectively the maximum number of packets targeted to a single row or column.