41331971
An optimal routing policy for mesh-connected topologies
We present a new routing policy, called maximum shortest paths (MP) routing policy, within the class of shortest-path routing policies for mesh-connected topologies which include popular 2-D and 3-D meshes, 2-D and 3-D tori, and n-dimensional hypercubes (n-cubes). In this policy, the routing message is always forwarded to a neighbor from which there exists a maximum number of shortest paths to the destination. An optimal routing defined in this paper is the one that maximizes the probability of reaching the destination from a given source without delays at intermediate nodes. We show that the MP routing policy is equivalent to the e-cube routing in n-cubes which is optimal, and it is also equivalent to the Badr and Podar's zig-zag (Z/sup 2/) routing policy in 2-D meshes which is also optimal. We prove that the Z/sup 2/ routing policy is not optimal in any N/spl times/N torus, where N is an even number larger than four. A routing algorithm is proposed to implement the MP routing policy in 2-D tori and if is proved to be at least suboptimal (optimal for some cases). Our approach is the first attempt to address optimal routing in the torus network which is still an open problem.
2254959
Local-Safety-Information-Based Broadcasting in Hypercube Multicomputers with Node and Link Faults
This paper presents a method to cope with fault-tolerant broadcasting in hypercube multicomputers with both node and link faults. The local safety concept is extended to faulty hypercubes with both node and link faults. The local-safety-based algorithm is used in a fully unsafe hypercube, where there is no safe node. A fully unsafe hypercube can be split into a set of maximal safe subcubes. We show that if these maximal safe subcubes meet certain requirements given in the paper, broadcasting can still be carried out successfully and in some case optimal broadcast is still possible. The method is extended to fault-tolerant routing and multicasting when the system contains both node and link faults.
17371165
QoS Routing in Hypercube Multicomputers
In this paper, we present a coding method to capture QoS information in hypercube multicomputers. The coding method is based on a localized algorithm where each node interacts with its neighbors to gather QoS information. Specifically, each node maintains a QoS vector where the k-th element represents the guaranteed QoS performance to a destination that is k hops away. The localized algorithm exhibits desirable properties of self-stabilizing, self-optimizing, and self-healing. Simulation results show that this coding method provides a good approximation of the minimum QoS value to a k-hop destination and, at the same time, uses a relatively small number of packets to propagate a change in link state (QoS value) compared with the classical distributed Bellman-Ford method.
7582647
On self-similarity and hamiltonicity of dual-cubes
The dual-cube is a newly proposed topology for interconnection networks, which uses low dimensional hypercubes as building blocks. The primary advantages of the dual-cube over the hypercube are that, with the same node degree n, the dual-cube contains 2/sup n-1/ times more nodes than the hypercube and, with the same amount of nodes, the dual-cube has approximately 50% less links than the hypercube. This paper was focused on the investigations of the structural self-similarity and the Hamiltonian property of the dual-cube. It was shown that a dual-cube can be recursively constructed from lower dimensional dual-cubes and, conversely, a dual-cube can be recursively decomposed into lower dimensional dual-cubes. It was also proved that all dual-cubes are Hamiltonian. There exist multiple Hamiltonian cycles on a dual-cube, among which, [(n-1)/2] cycles are edge-disjoint. It was illustrated that rings and linear arrays can be effectively emulated on dual-cubes. Some strategies for track sharing in efficient VLSI layout design were also discussed.
27746153
Broadcasting in Faulty Cube-Connected-Cycles with Minimum Recovery Time
We propose a broadcasting algorithm for a faulty Cube-Connected-Cycles multiprocessor. The broadcasting algorithm delivers a message to all the nodes non-redundantly using a binomial tree. The traffic generated because of the recovery is guaranteed to be minimum.
16257632
XYZ: a scalable, partially centralized lookup service for large-scale peer-to-peer systems
Peer-to-peer (P2P) systems are characterized by direct access between peer computers, rather than through a centralized server. File sharing is the dominant P2P application on the Internet, allowing users to easily contribute, search and obtain content. P2P systems can be categorized by the degrees of centralization. For fully centralized systems, the lookup service will not be available when the central directory server is down. For purely decentralized and unstructured systems, since there is no information about which nodes are likely to have the relevant files, searching essentially amounts to random search. This makes the lookup service unscalable and unpredictable. The objective of this paper is to design a partially centralized, scalable and self-organizing lookup service (XYZ) for wide area P2P systems. A clustering method is used to create the system backbone by connecting the cluster heads together and a color clustering method is adopted to create color overlays and minimize the searching space. Simulations and analysis are also provided. Extensions are proposed to achieve better performance
6186942
The number of removable edges in a 4-connected graph
Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G - e; second, for all the vertices x of degree 3 in G - e, delete x from G - e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G ⊖ e. If G ⊖ e is still 4-connected, then e is called a removable edge of G. In this paper we prove that every 4-connected graph of order at least six (excluding the 2-cyclic graph of order six) has at least (4|G|+16)/7 removable edges. We also give the structural characterization of 4-connected graphs for which the lower bound is sharp.
42869793
Edge-coloring critical graphs with high degree
It is proved here that any edge-coloring critical graph of order n and maximum degree Δ ≥ 8 has the size at least 3(n + Δ - 8). It generalizes a result of Hugh Hind and Yue Zhao.
17000130
Removable Edges in Longest Cycles of 4-Connected Graphs
Abstract.Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G−e; second, for all vertices x of degree 3 in G−e, delete x from G−e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G⊖e. If G⊖e is 4-connected, then e is called a removable edge of G. In this paper we obtain some results on removable edges in a longest cycle of a 4-connected graph G. We also show that for a 4-connected graph G of minimum degree at least 5 or girth at least 4, any edge of G is removable or contractible.
3144023
Tiling slideshow
This paper presents a new medium, called tiling slideshow, to display photos in a tile-like manner, coordinating with the pace of background music. In contrast to the conventional photo slideshow, multiple photos that have similar characteristics are well arranged and displayed at the same layout. Motivated by the concepts of technical writing, each displaying layout is composed of a larger topic photo and several small-size supportive photos. Based on this idea, the proposed tiling slideshow system consists of three major components: image clustering, music analyzer, and layout organizer. Given the limited displaying space, we consider the context and relationship between photos and model the layout organization as a constrainted optimization problem. Experiments on real consumer photograph collections show that the novel displaying method gives users more pleasant browsing experience than the methods that focus only on single photograph display.
2785443
An upper bound on the number of edges of edge-coloring critical graphs with high maximum degree
In this paper, we prove that any edge-coloring critical graph G with maximum degree @D>=([email protected])/2, where @e= =8 and |V(G)|>[email protected]@d-4-(@D+6)/(@d-6), where @d is the minimum degree of G. It generalizes a result of Sanders and Zhao.