Two-machine flowshop scheduling problems with no-wait jobs

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is not available during a specified time interval. We consider three scenarios of handing the operation affected by the nonavailability interval. Its processing may (i) start from scratch after the interval, or (ii) be resumed from the point of interruption, or (iii) be partially restarted after the interval. The objective is to minimize the makespan. We present an approximation algorithm that for all these scenarios delivers a worst-case ratio of 3/2. For the second scenario, we offer a 4/3-approximation algorithm.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Three parallel programming paradigms: Comparisons on an archetypal PDE computation

Three paradigms for distributed-memory parallel computation that free the application programmer from the details of message passing are compared for an archetypal structured scientific computation -- a nonlinear, structured-grid partial differential equation boundary value problem -- using the same algorithm on the same hardware. All of the paradigms -- parallel languages represented by the Portland Group's HPF, (semi-)automated serial-to-parallel source-to-source translation represented by CAP-Tools from the University of Greenwich, and parallel libraries represented by Argonne's PETSc -- are found to be easy to use for this problem class, and all are reasonably effective in exploiting concurrency after a short learning curve. The level of involvement required by the application programmer under any paradigm includes specification of the data partitioning, corresponding to a geometrically simple decomposition of the domain of the PDE. Programming in SPMD style for the PETSc library requires writing only the routines that discretize the PDE and its Jacobian, managing subdomain-to-processor mappings (affine global-to-local index mappings), and interfacing to library solver routines. Programming for HPF requires a complete sequential implementation of the same algorithm as a starting point, introduction of concurrency through subdomain blocking (a task similar to the index mapping), and modest experimentation with rewriting loops to elucidate to the compiler the latent concurrency. Programming with CAPTools involves feeding the same sequential implementation to the CAPTools interactive parallelization system, and guiding the source-to-source code transformation by responding to various queries about quantities knowable only at runtime. Results representative of "the state of the practice" for a scaled sequence of structured grid problems are given on three of the most important contemporary high-performance platforms: the IBM SP, the SGI Origin 2000, and the CRAYY T3E.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution