A Quality and Cost Approach for Comparison of Small-World Networks

We propose an approach based on analysis of cost-quality tradeoffs for comparison of efficiency of various algorithms for small-world network construction. A number of both known in the literature and original algorithms for complex small-world networks construction are shortly reviewed and compared. The networks constructed on the basis of these algorithms have basic structure of 1D regular lattice with additional shortcuts providing the small-world properties. It is shown that networks proposed in this work have the best cost-quality ratio in the considered class.Comment: 27 pages, 16 figures, 1 tabl

I/O embedding and broadcasting in star interconnection networks

The issues of communication between a host or central controller and processors, in large interconnection networks are very important and have been studied in the past by several researchers. There is a plethora of problems that arise when processors are asked to exchange information on parallel computers on which processors are interconnected according to a specific topology. In robust networks, it is desirable at times to send (receive) data/control information to (from) all the processors in minimal time. This type of communication is commonly referred to as broadcasting. To speed up broadcasting in a given network without modifying its topology, certain processors called stations can be specified to act as relay agents. In this thesis, broadcasting issues in a star-based interconnection network are studied. The model adopted assumes all-port communication and wormhole switching mechanism. Initially, the problem treated is one of finding the minimum number of stations required to cover all the nodes in the star graph with i-adjacency. We consider 1-, 2-, and 3-adjacencies and determine the upper bound on the number of stations required to cover the nodes for each case. After deriving the number of stations, two algorithms are designed to broadcast the messages first from the host to stations, and then from stations to remaining nodes; In addition, a Binary-based Algorithm is designed to allow routing in the network by directly working on the binary labels assigned to the star graph. No look-up table is consulted during routing and minimum number of bits are used to represent a node label. At the end, the thesis sheds light on another algorithm for routing using parallel paths in the star network

The Effect Of Hot Spots On The Performance Of Mesh--Based Networks

Direct network performance is affected by different design parameters which include number of virtual channels, number of ports, routing algorithm, switching technique, deadlock handling technique, packet size, and buffer size. Another factor that affects network performance is the traffic pattern. In this thesis, we study the effect of hotspot traffic on system performance. Specifically, we study the effect of hotspot factor, hotspot number, and hot spot location on the performance of mesh-based networks. Simulations are run on two network topologies, both the mesh and torus. We pay more attention to meshes because they are widely used in commercial machines. Comparisons between oblivious wormhole switching and chaotic packet switching are reported. Overall packet switching proved to be more efficient in terms of throughput when compared to wormhole switching. In the case of uniform random traffic, it is shown that the differences between chaotic and oblivious routing are indistinguishable. Networks with low number of hotspots show better performance. As the number of hotspots increases network latency tends to increase. It is shown that when the hotspot factor increases, performance of packet switching is better than that of wormhole switching. It is also shown that the location of hotspots affects network performance particularly with the oblivious routers since their achieved latencies proved to be more vulnerable to changes in the hotspot location. It is also shown that the smaller the size of the network the earlier network saturation occurs. Further, it is shown that the chaos router’s adaptivity is useful in this case. Finally, for tori, performance is not greatly affected by hotspot presence. This is mostly due to the symmetric nature of tori

Recursive cubes of rings as models for interconnection networks

We study recursive cubes of rings as models for interconnection networks. We first redefine each of them as a Cayley graph on the semidirect product of an elementary abelian group by a cyclic group in order to facilitate the study of them by using algebraic tools. We give an algorithm for computing shortest paths and the distance between any two vertices in recursive cubes of rings, and obtain the exact value of their diameters. We obtain sharp bounds on the Wiener index, vertex-forwarding index, edge-forwarding index and bisection width of recursive cubes of rings. The cube-connected cycles and cube-of-rings are special recursive cubes of rings, and hence all results obtained in the paper apply to these well-known networks