29 research outputs found
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On shortest disjoint paths and Hamiltonian cycles in some interconnection networks
Parallel processors are classified into two classes: shared-memory multiprocessors and distributed- memory multiprocessors. In the shared-memory system, processors communicate through a common memory unit. However, in the distributed multiprocessor system, each processor has its own memory unit and the communications among the processors are performed through an interconnection network. Thus, the interconnection topology plays an important role in the performance of these parallel systems. Recently, some new classes of interconnection networks, referred as Gaussian and Eisenstein- Jacobi networks, have been introduced. In this dissertation, we study the problem of finding the shortest node disjoint paths in the Gaussian and the Eisenstein-Jacobi networks. Moreover, we also describe how to generate edge disjoint Hamiltonian cycles in Eisenstein- Jacobi and Generalized Hypercube networks. Node disjoint paths are paths between any given source and destination nodes such that the paths have no common nodes except the endpoints. Similarly, edge disjoint Hamiltonian cycles are cycles in a given graph where each node is visited once and returns to the starting node and every edge is in at most one cycle.Keywords: Hamiltonian cycles, Disjoint paths, Parallel computing, Interconnection networ
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Some communication algorithms for Gaussian and Eisenstein-Jacobi networks
Interconnection networks play important roles in designing high performance computers. Recently two new classes of interconnection networks based on the concept of Gaussian and Eisenstein-Jacobi integers were introduced. In this research, efficient routing and broadcasting algorithms for these networks are developed. Furthermore, constructing edge disjoint Hamiltonian cycles in Gaussian networks are also investigated. Some resource placement methods for Eisenstein-Jacobi networks are also studied
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Interconnection Networks Based on Gaussian and Eisenstein-Jacobi Integers
Quotient rings of Gaussian and Eisenstein-Jacobi(EJ) integers can be deployed to construct interconnection networks with good topological properties. In this thesis, we propose deadlock-free deterministic and partially adaptive routing algorithms for hexagonal networks, one special class of EJ networks. Then we discuss higher dimensional Gaussian networks as an alternative to classical multidimensional toroidal networks. For this topology, we explore many properties including distance distribution and the decomposition of higher dimensional Gaussian net works into Hamiltonian cycles. In addition, we propose some efficient communication algorithms for higher dimensional Gaussian networks including one-to-all broadcasting and shortest path routing. Simulation results show that the routing algorithm proposed for higher dimensional Gaussian networks outperforms the routing algorithm of the corresponding torus networks with approximately the same number of nodes. These simulation results are expected since higher dimensional Gaussian networks have a smaller diameter and a smaller average message latency as compared with toroidal networks.
Finally, we introduce a degree-three interconnection network obtained from pruning a Gaussian network. This network shows possible performance improvement over other degree-three networks since it has a smaller diameter compared to other degree-three networks. Many topological properties of degree-three pruned Gaussian network are explored. In addition, an optimal shortest path routing algorithm and a one-to-all broadcasting algorithm are given
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
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic
Fuzzy EOQ Model with Trapezoidal and Triangular Functions Using Partial Backorder
EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR ̃C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the company's problems in estimating the costs for the next term