Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

Collaborative grid infrastructure for molecular simulations: The eMinerals minigrid as a prototype integrated computer and data grid

This paper describes a prototype grid infrastructure, called the eMinerals minigrid, for molecular simulation scientists. which is based on an integration of shared compute and data resources. We describe the key components, namely the use of Condor pools, Linux/Unix clusters with PBS and IBM's LoadLeveller job handling tools, the use of Globus for security handling, the use of Condor-G tools for wrapping globus job submit commands, Condor's DAGman tool for handling workflow, the Storage Resource Broker for handling data, and the CCLRC dataportal and associated tools for both archiving data with metadata and making data available to other workers.

Modeling the effects of node heterogeneity on the performance of grid applications

The performance benefit when using grid systems comes from different strategies, among which partitioning the applications into parallel tasks is the most important. However, in most cases the enhancement coming from partitioning is smoothed by the effects of synchronization overheads, mainly due to the high variability in the execution times of the different tasks, which, in turn, is accentuated by the large heterogeneity of grid nodes. In this paper we design hierarchical, queuing network performance models able to accurately analyze grid architectures and applications. Thanks to the model results, we introduce a new allocation policy based on a combination between task partitioning and task replication. The models are used to study two real applications and to evaluate the performance benefits obtained with allocation policies based on task replication.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

The collaborative P-GRADE grid portal

Grid portals are increasingly used to provide uniform access to the grid infrastructure. This paper describes how the P-GRADE Grid Portal could be used in a collaborative manner to facilitate group work and support the notion of Virtual Organisations. We describe the development issues involved in the construction of a collaborative portal, including ensuring a consistent view between participants of a collaborative workflow and management of proxy credentials to allow separate nodes of the workflow to be submitted to different grids.

Maximizing revenue in Grid markets using an economically enhanced resource manager

Traditional resource management has had as its main objective the optimization of throughput, based on parameters such as CPU, memory, and network bandwidth. With the appearance of Grid markets, new variables that determine economic expenditure, benefit and opportunity must be taken into account. The Self-organizing ICT Resource Management (SORMA) project aims at allowing resource owners and consumers to exploit market mechanisms to sell and buy resources across the Grid. SORMA's motivation is to achieve efficient resource utilization by maximizing revenue for resource providers and minimizing the cost of resource consumption within a market environment. An overriding factor in Grid markets is the need to ensure that the desired quality of service levels meet the expectations of market participants. This paper explains the proposed use of an economically enhanced resource manager (EERM) for resource provisioning based on economic models. In particular, this paper describes techniques used by the EERM to support revenue maximization across multiple service level agreements and provides an application scenario to demonstrate its usefulness and effectiveness. Copyright © 2008 John Wiley & Sons, Ltd.

A grouped P2P network for scalable grid information services

Information services play a crucial role in grid environments in that the state information can be used to facilitate the discovery of resources and the services available to meet user requirements, and also to help tune the performance of a grid system. However, the large size and dynamic nature of the grid brings forth a number of challenges for information services. This paper presents PIndex, a grouped peer-to-peer network that can be used for scalable grid information services. PIndex builds on Globus MDS4, but introduces peer groups to dynamically split the large grid information search space into many small sections to enhance its scalability and resilience. PIndex is subsequently modeled with Colored Petri Nets for performance evaluation. The simulation results show that PIndex is scalable and resilient in dealing with a large number of peer nodes.

On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

An oblivious shortest-path routing algorithm for fully connected cubic networks

Fully connected cubic networks (FCCNs) are a class of newly proposed hierarchical interconnection networks for multicomputer systems, which enjoy the strengths of constant node degree and good expandability. The shortest path routing in FCCNs is an open problem. In this paper, we present an oblivious routing algorithm for n-level FCCN with N = 8(n) nodes, and prove that this algorithm creates a shortest path from the source to the destination. At the costs of both an O(N)-parallel-step off-line preprocessing phase and a list of size N stored at each node, the proposed algorithm is carried out at each related node in O(n) time. In some cases the proposed algorithm is superior to the one proposed by Chang and Wang in terms of the length of the routing path. This justifies the utility of our routing strategy. (C) 2006 Elsevier Inc. All rights reserved.

Largest connected component of a star graph with faulty vertices

In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n >= 3) with up to 2n-4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.