## Parallel Job Scheduling Policies to Improve Fairness: A Case Study

Journal of Scheduling

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Journal of Scheduling

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Proceedings - International Parallel and Distributed Processing Symposium, IPDPS 2004 (Abstracts and CD-ROM)

Motivated by observations about job runtimes on the CPlant system, we use a trace-driven microsimulator to begin characterizing the performance of different classes of allocation algorithms on jobs with different communication patterns in space-shared parallel systems with mesh topology. We show that relative performance varies considerably with communication pattern. The Paging strategy using the Hilbert space-filling curve and the Best Fit heuristic performed best across several communication patterns.

We give processor-allocation algorithms for grid architectures, where the objective is to select processors from a set of available processors to minimize the average number of communication hops. The associated clustering problem is as follows: Given n points in R{sup d}, find a size-k subset with minimum average pairwise L{sub 1} distance.We present a natural approximation algorithm and show that it is a 7/4-approximation for 2D grids. In d dimensions, the approximation guarantee is 2 - 1/2d, which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d and report on experimental results.

The Computational Plant or Cplant is a commodity-based distributed-memory supercomputer under development at Sandia National Laboratories. Distributed-memory supercomputers run many parallel programs simultaneously. Users submit their programs to a job queue. When a job is scheduled to run, it is assigned to a set of available processors. Job runtime depends not only on the number of processors but also on the particular set of processors assigned to it. Jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs. This report introduces new allocation strategies and performance metrics based on space-filling curves and one dimensional allocation strategies. These algorithms are general and simple. Preliminary simulations and Cplant experiments indicate that both space-filling curves and one-dimensional packing improve processor locality compared to the sorted free list strategy previously used on Cplant. These new allocation strategies are implemented in Release 2.0 of the Cplant System Software that was phased into the Cplant systems at Sandia by May 2002. Experimental results then demonstrated that the average number of communication hops between the processors allocated to a job strongly correlates with the job's completion time. This report also gives processor-allocation algorithms for minimizing the average number of communication hops between the assigned processors for grid architectures. The associated clustering problem is as follows: Given n points in {Re}d, find k points that minimize their average pairwise L{sub 1} distance. Exact and approximate algorithms are given for these optimization problems. One of these algorithms has been implemented on Cplant and will be included in Cplant System Software, Version 2.1, to be released. In more preliminary work, we suggest improvements to the scheduler separate from the allocator.

Abstract not provided.

Proceedings - IEEE International Conference on Cluster Computing, ICCC

The Computational Plant or Cplant is a commodity-based supercomputer under development at Sandia National Laboratories. This paper describes resource-allocation strategies to achieve processor locality for parallel jobs in Cplant and other supercomputers. Users of Cplant and other Sandia supercomputers submit parallel jobs to a job queue. When a job is scheduled to run, it is assigned to a set of processors. To obtain maximum throughput, jobs should be allocated to localized clusters of processors to minimize communication costs and to avoid bandwidth contention caused by overlapping jobs. This paper introduces new allocation strategies and performance metrics based on space-filling curves and one dimensional allocation strategies. These algorithms are general and simple. Preliminary simulations and Cplant experiments indicate that both space-filling curves and one-dimensional packing improve processor locality compared to the sorted free list strategy previously used on Cplant. These new allocation strategies are implemented in the new release of the Cplant System Software, Version 2.0, phased into the Cplant systems at Sandia by May 2002.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

This paper investigates the questions of what statistical information about a memory request sequence is useful to have in making page replacement decisions. Our starting point is the Markov Request Model for page request sequences. Although the utility of modeling page request sequences by the Markov model has been recently put into doubt ([13]), we find that two previously suggested algorithms (Maximum Hitting Time [11] and Dominating Distribution [14]) which are based on the Markov model work well on the trace data used in this study. Interestingly, both of these algorithms perform equally well despite the fact that the theoretical results for these two algorithms differ dramatically. We then develop succinct characteristics of memory access patterns in an attempt to approximate the simpler of the two algorithms. Finally, we investigate how to collect these characteristics in an online manner in order to have a purely online algorithm.

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.

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