Khaled Day

Fault diameter of k-ary n-cube networks

We obtain the fault diameter of k-ary n-cube interconnection networks (also known as n-dimensional k-torus networks). We start by constructing a complete set of node-disjoint paths (i.e., as many paths as the degree) between any two nodes of a k-ary n-cube. Each of the obtained paths is of length zero, two, or four plus the minimum length except for one path in a special case (when the Hamming distance between the two nodes is one) where the increase over the minimum length may attain eight. These results improve those obtained by B. Bose et al. (1995) where the length of some of the paths has a variable increase (which can be arbitrarily large) over the minimum length. These results are then used to derive the fault diameter of the k-ary n-cube, which is shown to be /spl Delta/+1 where /spl Delta/ is the fault free diameter.

Topological properties of OTIS-networks

We conduct a general study of the topological properties of optical transpose interconnection systems (OTIS). We first obtain their basic topological metrics of size, degree, shortest distance and diameter, and then we obtain results related to the recursive structure and efficient embedding of meshes, cubes, spanning trees and cycles. We also present minimal one-to-one routing and optimal broadcasting algorithms, and we show how to construct node-disjoint paths between any two nodes of an OTIS network. Recent studies have addressed only particular members of the general class of OTIS networks. In this paper, we present unified tools for obtaining the topological properties of an arbitrary OTIS network based on the properties of the corresponding factor network.

The cross product of interconnection networks

We study the cross product as a method for generating and analyzing interconnection network topologies for multiprocessor systems. Consider two interconnection graphs G/sub 1/ and G/sub 2/ each with some established properties such as symmetry, low degree and diameter, scalability, simple optimal routing, recursive structure (partitionability), fault tolerance, existence of node-disjoint paths, low cost embedding, and efficient broadcasting. We investigate and evaluate the corresponding properties for the cross product of G/sub 1/ and G/sub 2/ based on the properties of G/sub 1/ and those of G/sub 2/. We also give a mathematical characterization of product families of graphs which are closed under the cross product operation. This investigation is useful in two ways. On one hand, it gives a new tool for further studying some of the known interconnection topologies, such as the hypercube and the mesh, which can be defined using the cross product operation. On the other hand, it can be used in defining and evaluating new interconnection graphs using the cross product operation on known topologies.

THE CONDITIONAL NODE CONNECTIVITY OF THE k-ARY n-CUBE

This paper derives the conditional node connectivity of the k-ary n-cube interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). It is shown that under this condition and for k≥4 and n≥2, the k-ary n-cube, whose connectivity is 2n, can tolerate up to 4n-3 faulty nodes without becoming disconnected. The conditional node connectivity in this case is therefore 4n-2. For k=3 and n≥2 the established conditional node connectivity is 4n-3. The result for the remaining smaller values of k and n are also obtained.

Minimal fault diameter for highly resilient product networks

We present a number of results related to the fault tolerance of Cartesian product networks. We start by presenting a method for building containers (i.e., sets of node-disjoint paths) between any two nodes of a product network based on given containers for the factor networks. Then, we show that the best achievable fault diameter (i.e., diameter under maximum fault conditions), under reasonable network regularity and connectivity conditions, is equal to the fault-free diameter plus one. The concept of high fault resilience is then defined. We then prove that if each factor network is highly resilient, then their Cartesian product has minimal fault diameter. We derive from these results that Cartesian products of several popular networks are highly resilient and have minimal fault diameter equal to diameter plus one. These results spare future efforts that would be needed to individually determine the fault diameter of such networks as has been the practice with previously studied networks.

The Hyperstar Interconnection Network

In this paper, a multiprocessor interconnection topology, the hyperstar, based on the Cartesian product of star graphs is studied. The basic properties of the hyperstar are discussed and proved. This includes reduced degree and diameter, hierarchical structure, vertex symmetry, optimal routing, and shortest path characterization. The hyperstar is shown to be a member of the Cayley class of symmetric graphs. Embeddings of hypercubes, star graphs, and meshes are discussed. An optimal one-to-all broadcasting algorithm is obtained and analyzed. Some results on fault tolerance, parallel paths, Hamiltonian cycles, and VLSI layouts are obtained. Furthermore, a comparative study between the hyperstar and seven related networks is conducted. The comparison is based on scalability, broadcasting cost, link requirements, cost/performance ratio, and other static parameters such as degree, diameter, and average diameter.

Optical transpose k -ary n -cube networks

This paper derives a number of results related to the topological properties of OTIS k-ary n-cube interconnection networks. The basic topological metrics of size, degree, shortest distance, and diameter are obtained. Then results related to embedding in OTIS k-ary n-cubes of OTIS k-ary (n-1)-cubes, cycles, meshes, cubes, and spanning trees are derived. The OTIS k-ary n-cube is shown to be Hamiltonian. Minimal one-to-one routing and optimal broadcasting algorithms are proposed. The OTIS k-ary n-cube is shown to be maximally fault-tolerant. These results are derived based on known properties of k-ary n-cube networks and general properties of OTIS networks.

Bandwidth borrowing-based QoS approach for adaptive call admission control in multiclass traffic wireless cellular networks

SUMMARY This paper proposes a QoS approach for an adaptive call admission control (CAC) scheme for multiclass service wireless cellular networks. The QoS of the proposed CAC scheme is achieved through call bandwidth borrowing and call preemption techniques according to the priorities of the traffic classes, using complete sharing of the available bandwidth. The CAC scheme maintains QoS in each class to avoid performance deterioration through mechanisms for call bandwidth degradation, and call bandwidth upgrading based on min–max and max–min policies for fair resource deallocation and reallocation, respectively. The proposed adaptive CAC scheme utilizes a measurement-based online monitoring approach of the system performance, and a prediction model to determine the amount of bandwidth to be borrowed from calls, or the amount of bandwidth to be returned to calls. The simulation-based performance evaluation of the proposed adaptive CAC scheme shows the strength and effectiveness of our proposed scheme. Copyright

A multilevel partitioning approach for efficient tasks allocation in heterogeneous distributed systems

This work addresses the problem of allocating parallel application tasks to heterogeneous distributed computing resources, such as multiclusters or Grid environments. The proposed allocation scheme is based on a multilevel graph partitioning and mapping approach. The objective is to find an efficient allocation that minimizes the application completion time, subject to the specified constraints pertinent to the application and system environment. The allocation scheme consists of three phases; the clustering phase, the initial mapping phase and the refinement and remapping phase. The scheme introduces an efficient heuristic in the clustering phase for contracting (coarsening) large size application graphs to the number of processors, called the VHEM method. An initial mapping technique based on a tabu-search approach has been introduced as a basis for the process of refinement and remapping phase. The simulation study shows that the VHEM coarsening heuristic can achieve optimal or near-optimal communication, compared to the HEM method, when the ratio of the number of tasks to the number of processors exceeds a threshold value. The simulation study shows that those optimal or near-optimal VHEM-coarsened graphs have an effect of generating very efficient mappings, when they are compared to the HEM-coarsened graphs.

Probability-based Fault-tolerant Routing in Hypercubes

This paper describes a new fault-tolerant routing algorithm for the hypercube, using the concept of probability vectors. To compute these vectors, a node first determines its faulty set, which represents the set of all its neighbouring nodes that are faulty or unreachable due to faulty nodes or links. Each node then calculates a probability vector, where the kth element represents the probability that a destination node at distance k cannot be reached through a minimal path due to a faulty node or link. The probability vectors are used by all the nodes to achieve an efficient fault-tolerant routing in the network. A performance comparison with the recently-proposed safety-vectors algorithm, through extensive simulation, shows that the new algorithm exhibits superior performance in terms of routing distances and percentage of reachability. Received ; revised