Scheduling for parallel dedicated machines with a single server

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is NP-hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst-case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two-machine flow shop and the open shop problems with a single server are also shown to be NP-hard in the strong sense. However, we reduce the two-machine flow shop no-wait problem with a single server to the Gilmore-Gomory traveling salesman problem and solve it in polynomial time. (c) 2000 John Wiley & Sons, Inc.

CAPLib - A 'thin layer' message passing library to support computational mechanics codes on distributed memory parallel systems

The Computer Aided Parallelisation Tools (CAPTools) [Ierotheou, C, Johnson SP, Cross M, Leggett PF, Computer aided parallelisation tools (CAPTools)-conceptual overview and performance on the parallelisation of structured mesh codes, Parallel Computing, 1996;22:163±195] is a set of interactive tools aimed to provide automatic parallelisation of serial FORTRAN Computational Mechanics (CM) programs. CAPTools analyses the user's serial code and then through stages of array partitioning, mask and communication calculation, generates parallel SPMD (Single Program Multiple Data) messages passing FORTRAN. The parallel code generated by CAPTools contains calls to a collection of routines that form the CAPTools communications Library (CAPLib). The library provides a portable layer and user friendly abstraction over the underlying parallel environment. CAPLib contains optimised message passing routines for data exchange between parallel processes and other utility routines for parallel execution control, initialisation and debugging. By compiling and linking with different implementations of the library, the user is able to run on many different parallel environments. Even with today's parallel systems the concept of a single version of a parallel application code is more of an aspiration than a reality. However for CM codes the data partitioning SPMD paradigm requires a relatively small set of message-passing communication calls. This set can be implemented as an intermediate `thin layer' library of message-passing calls that enables the parallel code (especially that generated automatically by a parallelisation tool such as CAPTools) to be as generic as possible. CAPLib is just such a `thin layer' message passing library that supports parallel CM codes, by mapping generic calls onto machine specific libraries (such as CRAY SHMEM) and portable general purpose libraries (such as PVM an MPI). This paper describe CAPLib together with its three perceived advantages over other routes: - as a high level abstraction, it is both easy to understand (especially when generated automatically by tools) and to implement by hand, for the CM community (who are not generally parallel computing specialists); - the one parallel version of the application code is truly generic and portable; - the parallel application can readily utilise whatever message passing libraries on a given machine yield optimum performance.

Scheduling batches with sequential job processing for two-machine flow and open shops

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches. A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.

Parallel mesh partitioning on distributed memory systems

The problem of deriving parallel mesh partitioning algorithms for mapping unstructured meshes to parallel computers is discussed in this chapter. In itself this raises a paradox - we seek to find a high quality partition of the mesh, but to compute it in parallel we require a partition of the mesh. In fact, we overcome this difficulty by deriving an optimisation strategy which can find a high quality partition even if the quality of the initial partition is very poor and then use a crude distribution scheme for the initial partition. The basis of this strategy is to use a multilevel approach combined with local refinement algorithms. Three such refinement algorithms are outlined and some example results presented which show that they can produce very high global quality partitions, very rapidly. The results are also compared with a similar multilevel serial partitioner and shown to be almost identical in quality. Finally we consider the impact of the initial partition on the results and demonstrate that the final partition quality is, modulo a certain amount of noise, independent of the initial partition.

The development of parallel implementation for a CFD based fire field model utilising conventional office based PCs

Parallel processing techniques have been used in the past to provide high performance computing resources for activities such as fire-field modelling. This has traditionally been achieved using specialized hardware and software, the expense of which would be difficult to justify for many fire engineering practices. In this article we demonstrate how typical office-based PCs attached to a Local Area Network has the potential to offer the benefits of parallel processing with minimal costs associated with the purchase of additional hardware or software. It was found that good speedups could be achieved on homogeneous networks of PCs, for example a problem composed of ~100,000 cells would run 9.3 times faster on a network of 12 800MHz PCs than on a single 800MHz PC. It was also found that a network of eight 3.2GHz Pentium 4 PCs would run 7.04 times faster than a single 3.2GHz Pentium computer. A dynamic load balancing scheme was also devised to allow the effective use of the software on heterogeneous PC networks. This scheme also ensured that the impact between the parallel processing task and other computer users on the network was minimized.

Matching search in fractal video compression and its parallel implementation in distributed computing environments

Fractal video compression is a relatively new video compression method. Its attraction is due to the high compression ratio and the simple decompression algorithm. But its computational complexity is high and as a result parallel algorithms on high performance machines become one way out. In this study we partition the matching search, which occupies the majority of the work in a fractal video compression process, into small tasks and implement them in two distributed computing environments, one using DCOM and the other using .NET Remoting technology, based on a local area network consists of loosely coupled PCs. Experimental results show that the parallel algorithm is able to achieve a high speedup in these distributed environments.

Parallel CFD fire modelling on office PCs with dynamic load balancing

Parallel processing techniques have been used in the past to provide high performance computing resources for activities such as Computational Fluid Dynamics. This is normally achieved using specialized hardware and software, the expense of which would be difficult to justify for many fire engineering practices. In this paper, we demonstrate how typical office-based PCs attached to a local area network have the potential to offer the benefits of parallel processing with minimal costs associated with the purchase of additional hardware or software. A dynamic load balancing scheme was devised to allow the effective use of the software on heterogeneous PC networks. This scheme ensured that the impact between the parallel processing task and other computer users on the network was minimized thus allowing practical parallel processing within a conventional office environment. Copyright © 2006 John Wiley & Sons, Ltd.

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.