Apostolos Gerasoulis

DSC: scheduling parallel tasks on an unbounded number of processors

We present a low-complexity heuristic, named the dominant sequence clustering algorithm (DSC), for scheduling parallel tasks on an unbounded number of completely connected processors. The performance of DSC is on average, comparable to, or even better than, other higher-complexity algorithms. We assume no task duplication and nonzero communication overhead between processors. Finding the optimum solution for arbitrary directed acyclic task graphs (DAGs) is NP-complete. DSC finds optimal schedules for special classes of DAGs, such as fork, join, coarse-grain trees, and some fine-grain trees. It guarantees a performance within a factor of 2 of the optimum for general coarse-grain DAGs. We compare DSC with three higher-complexity general scheduling algorithms: the ETF by J.J. Hwang, Y.C. Chow, F.D. Anger, and C.Y. Lee (1989); V. Sarkars (1989) clustering algorithm; and the MD by M.Y. Wu and D. Gajski (1990). We also give a sample of important practical applications where DSC has been found useful. >

On the granularity and clustering of directed acyclic task graphs

The authors consider the impact of the granularity on scheduling task graphs. Scheduling consists of two parts, the processors assignment of tasks, also called clustering, and the ordering of tasks for execution in each processor. The authors introduce two types of clusterings: nonlinear and linear clusterings. A clustering is nonlinear if two parallel tasks are mapped in the same cluster otherwise it is linear. Linear clustering fully exploits the natural parallelism of a given directed acyclic task graph (DAG) while nonlinear clustering sequentializes independent tasks to reduce parallelism. The authors also introduce a new quantification of the granularity of a DAG and define a coarse grain DAG as the one whose granularity is greater than one. It is proved that every nonlinear clustering of a coarse grain DAG can be transformed into a linear clustering that has less or equal parallel time than the nonlinear one. This result is used to prove the optimality of some important linear clusterings used in parallel numerical computing. >

List scheduling with and without communication delays

Abstract Empirical results have shown that the classical critical path (CP) list scheduling heuristic for task graphs is a fast and practical heuristic when communication cost is zero. In the first part of this paper we study the theoretical properties of the CP heuristic that lead to its near optimum performance in practice. In the second part we extend the CP analysis to the problem of ordering the task execution when the processor assignment is given and communication cost is nonzero. We propose two new list scheduling heuristics, the RCP and RCP∗ that use critical path information and ready list priority scheduling. We show that the performance properties for RCP and RCP∗, when communication is nonzero, are similar to CP when communication is zero. Finally, we present an extensive experimental study and optimality analysis of the heuristics which verifies our theoretical results.

The use of piecewise quadratic polynomials for the solution of singular integral equations of Cauchy type

Abstract A method for the numerical solution of singular integral equations of Cauchy type is developed. The unknown function is expressed as a product of a weight function and a continuous function φ( t ). The continuous function φ( t ) is approximated by piecewise quadratic polynomials, and the singular integral equation is reduced to a linear algebraic system. Numerical examples are given, and comparisons are made with the widely used Gauss-type methods.

A fast static scheduling algorithm for DAGs on an unbounded number of processors

No abstract available

Clustering task graphs for message passing architectures

Clustering is a mapping of the nodes of a task graph onto labeled clusters. We present a unified framework for clustering of directed acyclic graphs (DAGs). Several clustering algorithms from the literature are compared using this framework. For coarse grain DAGs two interesting properties are presented. For every nonlinear clustering there exists a linear clustering whose parallel time is less than the nonlinear one. Furthermore, the parallel time of any linear clustering is within a factor of two of the optimal. Two clustering algorithms are presented with near linear time complexity for coarse grain DAGs. The conclusion is that linear clustering is an efficient and accurate operation.

Piecewise-polynomial quadratures for Cauchy singular integrals

In this paper, we propose piecewise-polynomial methods for the approximation of Cauchy principal value integrals and develop a simple, efficient and numerically stable algorithm for the evaluation of the weights of the resulting piecewise-polynomial quadratures. We present two examples to illustrate the advantages of these quadratures versus the Gauss–Jacobi quadratures.

On the existence of approximate solutions for singular integral equations of Cauchy type discretized by Gauss-Chebyshev quadrature formulae

It is shown that the direct Gauss-Chebyshev method used for the numerical solution of singular integral equations of Cauchy-type possesses a unique solution for sufficiently largen.

Singular integral equations — The convergence of the Nyström interpolant of the Gauss-Chebyshev method

Nyströms interpolation formula is applied to the numerical solution of singular integral equations. For the Gauss-Chebyshev method, it is shown that this approximation converges uniformly, provided that the kernel and the input functions possess a continuous derivative. Moreover, the error of the Nyström interpolant is bounded from above by the Gaussian quadrature errors and thus convergence is fast, especially for smooth functions. ForC∞ input functions, a sharp upper bound for the error is obtained. Finally numerical examples are considered. It is found that the actual computational error agrees well with the theoretical derived bounds.

A scheduling approach to parallel harmonic balance simulation

Rather than approach the parallelization of the harmonic balance simulation method numerically, a novel scheduling-oriented approach is described. The technique leverages circuit substructure to expose potential parallelism in the form of a directed, acyclic graph (dag) of computations. This dag is then allocated and scheduled using various linear clustering techniques. The result is a highly scalable and efficient approach to harmonic balance simulation. Two large examples, one from the integrated circuit regime and another from the communication regime, executed on three different parallel computers are used to demonstrate the efficacy of the approach. Published in 2000 by John Wiley & Sons, Ltd.