59 research outputs found

    A multipath analysis of biswapped networks.

    Get PDF
    Biswapped networks of the form Bsw(G)Bsw(G) have recently been proposed as interconnection networks to be implemented as optical transpose interconnection systems. We provide a systematic construction of κ+1\kappa+1 vertex-disjoint paths joining any two distinct vertices in Bsw(G)Bsw(G), where κ1\kappa\geq 1 is the connectivity of GG. In doing so, we obtain an upper bound of max{2Δ(G)+5,Δκ(G)+Δ(G)+2}\max\{2\Delta(G)+5,\Delta_\kappa(G)+\Delta(G)+2\} on the (κ+1)(\kappa+1)-diameter of Bsw(G)Bsw(G), where Δ(G)\Delta(G) is the diameter of GG and Δκ(G)\Delta_\kappa(G) the κ\kappa-diameter. Suppose that we have a deterministic multipath source routing algorithm in an interconnection network GG that finds κ\kappa mutually vertex-disjoint paths in GG joining any 22 distinct vertices and does this in time polynomial in Δκ(G)\Delta_\kappa(G), Δ(G)\Delta(G) and κ\kappa (and independently of the number of vertices of GG). Our constructions yield an analogous deterministic multipath source routing algorithm in the interconnection network Bsw(G)Bsw(G) that finds κ+1\kappa+1 mutually vertex-disjoint paths joining any 22 distinct vertices in Bsw(G)Bsw(G) so that these paths all have length bounded as above. Moreover, our algorithm has time complexity polynomial in Δκ(G)\Delta_\kappa(G), Δ(G)\Delta(G) and κ\kappa. We also show that if GG is Hamiltonian then Bsw(G)Bsw(G) is Hamiltonian, and that if GG is a Cayley graph then Bsw(G)Bsw(G) is a Cayley graph

    Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes

    Full text link
    The nn-dimensional hypercube network QnQ_n is one of the most popular interconnection networks since it has simple structure and is easy to implement. The nn-dimensional locally twisted cube, denoted by LTQnLTQ_n, an important variation of the hypercube, has the same number of nodes and the same number of connections per node as QnQ_n. One advantage of LTQnLTQ_n is that the diameter is only about half of the diameter of QnQ_n. Recently, some interesting properties of LTQnLTQ_n were investigated. In this paper, we construct two edge-disjoint Hamiltonian cycles in the locally twisted cube LTQnLTQ_n, for any integer n4n\geqslant 4. The presence of two edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the locally twisted cube.Comment: 7 pages, 4 figure

    Properties and Algorithms of the KCube Interconnection Networks

    Get PDF
    The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes

    Fault-tolerant Designs in Lattice Networks on the Klein Bottle

    Full text link
    In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and find subgraphs with the property that for any jj vertices there exists a longest path (cycle) avoiding all of them. This completes work previously done in other lattices
    corecore