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In this paper, we envision a solution to the problem of capturing an intruder in a product network. This solution is derived based on the assumed existing algorithms for basic member graphs of a graph product. In this problem, a team of cleaner agents are responsible for capturing a hostile intruder in the network. While the agents can move in the network one hop at a time, the intruder is assumed to be arbitrarily fast in a way that it can traverse any number of nodes contiguously as far as no agents reside in those nodes. Here, we consider a version of the problem where each agent can replicate new agents. Hence, the algorithm start with a single agent and new agents are created on demand.... 

In this paper, we propose a solution to the problem of capturing an intruder in a product network. This solution is derived based on the assumption of existing algorithms for basic member graphs of a graph product. In this problem, a team of cleaner agents are responsible for capturing a hostile intruder in the network. While the agents can move in the network one hop at a time, the intruder is assumed to be arbitrarily fast in a way that it can traverse any number of nodes contiguously as far as no agents reside in those nodes. Here, we consider a version of the problem where each agent can replicate new agents. Thus, the algorithm starts with a single agent and new agents are created on... 

The utilization of the limited resources of a multiprocessor or multicomputer system is a primary performance issue crucial for the design of many scheduling algorithms. While many of the existing parallel machines benefit from a regular product network topology, almost none of the previous resource placement techniques have come to recognize and exploit this Inherent regularity. This paper introduces some novel algorithms for deriving resource placement schemes in product networks based on the assumed perfect resource placement in their underling basic graphs. © 2007 IEEE  

In this paper, we propose the first comprehensive mathematical performance model for product networks where fully adaptive routing is applied. Besides the generality of this model which makes it suitable to be used for any product graph, our analysis shows that the proposed model exhibits high accuracy. Simulation results show the validity and accuracy of the model even in heavy traffic and saturation region, where other models have severe problems for prediction. © 2007 IEEE  

This paper presents a comprehensive performance model for fully adaptive routing in wormhole-switched Cartesian product networks. Besides the generality of the model which makes it suitable to be used for any product graph, experimental (simulation) results show that the proposed model exhibits high accuracy even in heavy traffic and saturation region, where other models have severe problems to predict the performance of the network. Most popular interconnection network can be defined as a Cartesian product of two or more networks including the mesh, hypercube, and torus networks. Torus and mesh networks are the most popular topologies used in recent supercomputing parallel machines. They... 

The utilization of the limited resources of a multiprocessor or multicomputer system is a primary performance issue which is crucial for the design of many scheduling algorithms. While many of the existing parallel machines benefit from a regular product network topology, almost none of the previous resource placement techniques have come to recognize and exploit this inherent regularity. This paper introduces several novel algorithms for deriving resource placement schemes in product networks based on the assumption of perfect resource placement in their underling basic graphs. Our techniques use known schemes for the basic networks as their building blocks for deploying the resource... 

This paper presents a comprehensive performance model for fully adaptive routing in wormhole-switched Cartesian product networks. Besides the generality of the model which makes it suitable to be used for any product graph, experimental (simulation) results show that the proposed model exhibits high accuracy even in heavy traffic and saturation region, where other models have severe problems to predict the performance of the network. Most popular interconnection network can be defined as a Cartesian product of two or more networks including the mesh, hypercube, and torus networks. Torus and mesh networks are the most popular topologies used in recent supercomputing parallel machines. They... 

The utilization of the limited resources of a multiprocessor or multicomputer system is a primary performance issue which is crucial for the design of many scheduling algorithms. While many of the existing parallel machines benefit from a regular product network topology, almost none of the previous resource placement techniques have come to recognize and exploit this inherent regularity. This paper introduces several novel algorithms for deriving resource placement schemes in product networks based on the assumption of perfect resource placement in their underling basic graphs. Our techniques use known schemes for the basic networks as their building blocks for deploying the resource... 

In a large system, it is neither economical nor efficient to equip each node with a copy of the resource, and it is desirable to distribute the copies of the resource so that certain performance measure is obtained. In this paper we consider the problem of distributing resources in the edge product of networks. The algorithms presented in this paper make use of the known placements for the basic graphs composing the product graph. Therefore, in these placements we avoid the additional costs needed for deploying and rescaling the network. © 2008 IEEE  

So far, many analytical models have been proposed in the literature to evaluate the performance of networks with different topologies such as hypercube, torus, mesh, hypermesh, Cartesian product networks, star graph, and k-ary n-cube; however, to the best of our knowledge, no mathematical model has been presented for irregular networks. Therefore, as an effort to fill this gap, this paper presents a comprehensive mathematical model for fully adaptive routing in wormhole-switched irregular networks. Moreover, since our approach holds no assumption for the network topology, the proposed analytical model covers all the aforementioned models (i.e. it covers both regular and irregular...