Abdol Hossein Esfahanian

Unicast-based multicast communication in wormhole-routed networks

Multicast communication, in which the same message is delivered from a source node to an arbitrary number of destination nodes, is being increasingly demanded in parallel computing. System supported multicast services can potentially offer improved performance, increased functionality, and simplified programming, and may in turn be used to support various higher-level operations for data movement and global process control. This paper presents efficient algorithms to implement multicast communication in wormhole-routed direct networks, in the absence of hardware multicast support, by exploiting the properties of the switching technology. Minimum-time multicast algorithms are presented for n-dimensional meshes and hypercubes that use deterministic, dimension-ordered routing of unicast messages. Both algorithms can deliver a multicast message to m-1 destinations in [log/sub 2/ m] message passing steps, while avoiding contention among the constituent unicast messages. Performance results of implementations on a 64-node nCUBE-2 hypercube and a 168-node Symult 2010 2-D mesh are given. >

Generalized measures of fault tolerance with application to N-cube networks

In developing deterministic measures of system-level fault tolerance for multiple-processor systems, it has generally been assumed that any subset of system components (processors or links) can potentially fail at the same time. In the present work, the author generalizes these measures by restricting the potentially faulty sets to some subsets of the system components. Using this model, he presents a fault-tolerance analysis for the n-cube networks that shows that such networks can tolerate up to 2n-3 processor failures and remain connected provided that for each processor p in the network, all the processors which are directly connected to p do not fail at the same time. He also shows that in this situation the diameter of the network may increase only by a constant value. The author presents an O((kn)/sup 2/) time algorithm for determining if the network is disconnected when a set of k faulty processors, k >

On computing a conditional edge-connectivity of a graph

Abstract The conditional edge-connectivity λ ( G : P ) of a graph G ( V , E ) has been defined by Harary as the minimum cardinality | S | of a set S of edges such that G – S is disconnected and every component of G – S has the given graph property P . I n this article we present lower and upper bounds for λ( G : P ) when P is defined as follows: A graph H satisfies property P if it contains more than one vertex. We then present a polynomial-time algorithm for the computation of λ( G : P ). A new generalization of the notion of connectivity is also given.

The twisted N-cube with application to multiprocessing

It is shown that by exchanging any two independent edges in any shortest cycle of the n-cube (n>or=3), its diameter decreases by one unit. This leads to the definition of a new class of n-regular graphs, denoted TQ/sub n/, with 2/sup n/ vertices and diameter n-1, which has the (n-1)-cube as subgraph. Other properties of TQ/sub n/ such as connectivity and the lengths of the disjoints paths are also investigated. Moreover, it is shown that the complete binary tree on 2/sup n/-1 vertices, which is not a subgraph of the n-cube, is a subgraph of TQ/sub n/. How these results can be used to enhance hypercube multiprocessors is discussed. >

Multicast in hypercube multiprocessors

Abstract An efficient interprocessor communication mechanism is essential to the performance of hypercube multiprocessors. All existing hypercube multiprocessors basically support one-to-one interprocessor communication only. However, multicast (one-to-many) communication is highly demanded in executing many data parallel algorithms. A multicast algorithm should attempt to inform each destination in a minimum number of time steps while generating a least amount of traffic. In this paper, we first propose a graph theoretical model, the Optimal Multicast Tree (OMT), for interprocessor communication in distributed-memory multiprocessors. The problem of finding an OMT is conjectured to be NP-hard even for hypercube multiprocessors. A heuristic Greedy multicast algorithm which guarantees a minimized message delivery time is proposed. Simulation results show that the performance of the Greedy algorithm is very close to the optimal solution. Routing of multicast messages is done in a distributed manner. The hardware design of a VLSI router which supports all types of communications is briefly discussed.

Node roles and community structure in networks

A node role is a subjective characterization of the part it plays in a network structure. Knowing the role of a node is important for many link mining applications. For example, in Web search, nodes that are deemed to be authorities on a given topic are often found to be most relevant to the users queries. There are a number of metrics that can be used to assign roles to individual nodes in a network, including degree, closeness, and betweenness. None of these metrics, however, take into account the community structure that underlies the network. In this paper we define community-based roles that the nodes can assume (ambassadors, big fish, loners, and bridges) and show how existing link mining techniques can be improved by knowledge of such roles. A new community-based metric is introduced for estimating the number of communities linked to a node. Using this metric and a modification of degree, we show how to assign community-based roles to the nodes. We also illustrate the benefits of knowing the community-based node roles in the context of link-based classification and influence maximization.

Prioritized overlay multicast in mobile ad hoc environments

Many proposed routing protocols for manets require nodes to maintain and update complicated route information, which incurs significant overhead when groups have different priorities. To address this problem, some researchers have begun focusing on application-layer, or overlay, multicast in which an overlay network forms a virtual network consisting of only member nodes atop the physical infrastructure. We propose a prototype of prioritized overlay multicast for manets in which participating nodes can carry out multiple functions and thus be associated with more than one overlay tree.

Exploration of Link Structure and Community-Based Node Roles in Network Analysis

Communities are nodes in a network that are grouped together based on a common set of properties. While the communities and link structures are often thought to be in alignment, it may not be the case when the communities are defined using other external criterion. In this paper we provide a new way to measure the alignment. We also provide a new metric that can be used to estimate the number of communities to which a node is attached. This metric, along with degree, is used to assign a community-based role to nodes. We demonstrate the usefulness of the community-based node roles by applying them to the influence maximization problem.

On computing the connectivities of graphs and digraphs

In this paper methods are described that will compute the edge-connectivity of a graph or a digraph at least twice as fast as the known methods. A study of the computation of the vertex-connectivity is presented which leads to new algorithms for this purpose or for the purpose of determining if the vertex-connectivity is at least k. These algorithms compare favorably with Kleitmans, Evens, Even and Tarjans, and Galils algorithms.

Lower-bounds on the connectivities of a graph

This article presents a study of the connectivities of a graph as a function of other graph parameters such as the number of vertices, the maximum degree, and the diameter. As a result, lower-bounds on the connectivities of a graph as a function of these parameters are computed. These bounds could serve as sufficient conditions for a graph to be h-edge-connected or k-connected. Consequently, the connectivity characteristics of many of the densest known graphs are determined.