Net and Prune: A Linear Time Algorithm for Euclidean Distance Problems

We provide a general framework for getting expected linear time constant factor approximations (and in many cases FPTAS's) to several well known problems in Computational Geometry, such as $k$-center clustering and farthest nearest neighbor. The new approach is robust to variations in the input problem, and yet it is simple, elegant and practical. In particular, many of these well studied problems which fit easily into our framework, either previously had no linear time approximation algorithm, or required rather involved algorithms and analysis. A short list of the problems we consider include farthest nearest neighbor, $k$-center clustering, smallest disk enclosing $k$ points, $k$th largest distance, $k$th smallest $m$-nearest neighbor distance, $k$th heaviest edge in the MST and other spanning forest type problems, problems involving upward closed set systems, and more. Finally, we show how to extend our framework such that the linear running time bound holds with high probability

Mobile Computing in Physics Analysis - An Indicator for eScience

This paper presents the design and implementation of a Grid-enabled physics analysis environment for handheld and other resource-limited computing devices as one example of the use of mobile devices in eScience. Handheld devices offer great potential because they provide ubiquitous access to data and round-the-clock connectivity over wireless links. Our solution aims to provide users of handheld devices the capability to launch heavy computational tasks on computational and data Grids, monitor the jobs status during execution, and retrieve results after job completion. Users carry their jobs on their handheld devices in the form of executables (and associated libraries). Users can transparently view the status of their jobs and get back their outputs without having to know where they are being executed. In this way, our system is able to act as a high-throughput computing environment where devices ranging from powerful desktop machines to small handhelds can employ the power of the Grid. The results shown in this paper are readily applicable to the wider eScience community.Comment: 8 pages, 7 figures. Presented at the 3rd Int Conf on Mobile Computing & Ubiquitous Networking (ICMU06. London October 200

Numerical non-LTE 3D radiative transfer using a multigrid method

3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as $\mathcal{O}(n^2)$, with $n$ the number of grid points. When the grid gets finer, the computational cost increases quadratically. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative-MHD simulations as input atmospheres. With multigrid, we obtain a factor 3.3-4.5 speedup compared to MALI. With full-multigrid the speed-up increases to a factor 6. The speedup is expected to increase for input atmospheres with more grid points and finer grid spacing. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial speed-up.Comment: Accepted for publication by A&

Job Monitoring in an Interactive Grid Analysis Environment

The grid is emerging as a great computational resource but its dynamic behavior makes the Grid environment unpredictable. Systems and networks can fail, and the introduction of more users can result in resource starvation. Once a job has been submitted for execution on the grid, monitoring becomes essential for a user to see that the job is completed in an efficient way, and to detect any problems that occur while the job is running. In current environments once a user submits a job he loses direct control over the job and the system behaves like a batch system: the user submits the job and later gets a result back. The only information a user can obtain about a job is whether it is scheduled, running, cancelled or finished. Today users are becoming increasingly interested in such analysis grid environments in which they can check the progress of the job, obtain intermediate results, terminate the job based on the progress of job or intermediate results, steer the job to other nodes to achieve better performance and check the resources consumed by the job. In order to fulfill their requirements of interactivity a mechanism is needed that can provide the user with real time access to information about different attributes of a job. In this paper we present the design of a Job Monitoring Service, a web service that will provide interactive remote job monitoring by allowing users to access different attributes of a job once it has been submitted to the interactive Grid Analysis Environment

The impact of global communication latency at extreme scales on Krylov methods

Krylov Subspace Methods (KSMs) are popular numerical tools for solving large linear systems of equations. We consider their role in solving sparse systems on future massively parallel distributed memory machines, by estimating future performance of their constituent operations. To this end we construct a model that is simple, but which takes topology and network acceleration into account as they are important considerations. We show that, as the number of nodes of a parallel machine increases to very large numbers, the increasing latency cost of reductions may well become a problematic bottleneck for traditional formulations of these methods. Finally, we discuss how pipelined KSMs can be used to tackle the potential problem, and appropriate pipeline depths