David P. Bunde

Processor allocation on Cplant: achieving general processor locality using one-dimensional allocation strategies

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.

Communication-Aware Processor Allocation for Supercomputers: Finding Point Sets of Small Average Distance

Abstract 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 ℜd, find a size-k subset with minimum average pairwise L1 distance. We present a natural approximation algorithm and show that it is a

Power-aware scheduling for makespan and flow

\frac{7}{4}

Communication patterns and allocation strategies

-approximation for two-dimensional grids; in d dimensions, the approximation guarantee is

Average rate speed scaling

2-\frac{1}{2d}

Communication-aware processor allocation for supercomputers

, which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d, and we report on experimental results.

Scheduling Restartable Jobs with Short Test Runs

We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work.For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by Pruhs et al. to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor.

Backfilling with guarantees made as jobs arrive

Summary form only given. 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.

Optimal strong parity edge-coloring of complete graphs

Speed scaling is a power management technique that involves dynamically changing the speed of a processor. This gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. Yao, Demers, and Shenker [8] considered the problem where the QoS constraint is deadline feasibility and the objective is to minimize the energy used. They proposed an online speed scaling algorithm Average Rate (AVR) that runs each job at a constant speed between its release and its deadline. They showed that the competitive ratio of AVR is at most (2α)α/2 if a processor running at speed s uses power sα. We show the competitive ratio of AVR is at least ((2-δ)α)α/2, where δ is a function of α that approaches zero as α approaches infinity. This shows that the competitive analysis of AVR by Yao, Demers, and Shenker is essentially tight, at least for large α. We also give an alternative proof that the competitive ratio of AVR is at most (2α)α/2 using a potential function argument. We believe that this analysis is significantly simpler and more elementary than the original analysis of AVR in [8].

Comparing Global Link Arrangements for Dragonfly Networks

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