Parallel Machine Model Research Articles

Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Machine

Based on the screw theory, the force analysis of the 3-RPS parallel machine is illuminated. Been equivalent to a 6-chain parallel machine, the deformation harmony equation of the parallel machine under the outside generalized force is interpreted. The instantaneous stiffness model of the parallel machine, which includes the change of the force Jacobian matrix, is established. Considering the deviation of the position and orientation of the moving platform, which is resulted from the distortion of the PRS chains of the parallel machine, the influence of the change of the Jacobian matrix to the instantaneous stiffness model of the 3-RPS parallel machine is analyzed, and furthermore, it is verified with an instance.

Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Machine

Based on the screw theory, the force analysis of the 3-RPS parallel machine is illuminated. Been equivalent to a 6-chain parallel machine, the deformation harmony equation of the parallel machine under the outside generalized force is interpreted. The instantaneous stiffness model of the parallel machine, which includes the change of the force Jacobian matrix, is established. Considering the deviation of the position and orientation of the moving platform, which is resulted from the distortion of the PRS chains of the parallel machine, the influence of the change of the Jacobian matrix to the instantaneous stiffness model of the 3-RPS parallel machine is analyzed, and furthermore, it is verified with an instance.

Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms

The concept of parallel machines has been widely used in manufacturing. This article proposes a genetic algorithm (GA) approach to minimize total tardiness of a set of tasks for identical parallel machines and worker assignment to machines. A spreadsheet-based GA approach is presented to solve the problem. A domain-independent general purpose GA is used, which is an add-in to the spreadsheet software. The paper demonstrates an adaptation of the proprietary GA software to the problem of minimizing total tardiness for the worker assignment scheduling problem for identical parallel machine models. Two 100 I/P/n/m/W problems taken from Hu (Int J Adv Manuf Technol 23:383–388, 2004, Int J Adv Manuf Technol 29:165–169, 2006) for a similar study are simulated. The performance of GA is superior to SES-A/LMC approach used by Hu and very close to the Exhaustive search procedure. It is shown that the spreadsheet GA implementation makes it very easy to adapt the problem for any set of objective measures without changing the actual model. Empirical analysis has been carried out to study the effect of GA parameters, namely, crossover rate, mutation rate, and the population size.

Efficient algorithms for parallelizing Monte Carlo simulations for 2D Ising spin models

In this paper, we design and implement a variety of parallel algorithms for both sweep spin selection and random spin selection. We analyze our parallel algorithms on LogP, a portable and general parallel machine model. We then obtain rigorous theoretical runtime results on LogP for all the parallel algorithms. Moreover, a guiding equation is derived for choosing data layouts (blocked vs. stripped) for sweep spin selection. In regard to random spin selection, we are able to develop parallel algorithms with efficient communication schemes. We introduce two novel schemes, namely the FML scheme and the ?-scheme. We analyze randomness of our schemes using statistical methods and provide comparisons between the different schemes.

An unrelated parallel machines model for an industrial production resetting problem

Efficient production resettings are necessary to achieve production flexibility. For this reason, most modern companies are trying to reduce the setup time required to switch the production from one product type to another. One way to minimise these times is to schedule correctly the various tasks involved during a production resetting: changing tools, modifying each machine setting, etc. In this paper, we present how this problem can be identified to an unrelated parallel machines problem with release dates and delivery times where the resources are operators. We show that the data structure allows simplifying the problem into an assignment problem, even when we take into consideration the availability constraints of the operators. A branch-and-bound method is presented which has been tested on industrial and generated instances. [Received 6 February 2007; Revised 22 August 2007; Accepted 11 November 2007]

1103 オンライン・スケジューリングにおけるハイブリッド・タイミング方策 : 並列機械モデルへの適用(OS1-1 生産スケジューリング)

1103 オンライン・スケジューリングにおけるハイブリッド・タイミング方策 : 並列機械モデルへの適用(OS1-1 生産スケジューリング)

Further study of minimizing total tardiness for the worker assignment scheduling problem in the identical parallel-machine models

Minimizing total tardiness in the model of an identical parallel-machine with nonpreemptive jobs of the worker assignment scheduling problem is further studied in this paper. More complicated simulation processes are established for this purpose. The specific worker assignment scheduling problem is solved in two parts of job scheduling and worker assignment. The S_PT, E_DD, S_lack (SES) heuristic is used for the job scheduling part while the largest marginal contribution (LMC) procedure is used to for the worker assignment part and then minimizes the total tardiness. From the new simulations conducted, the heuristics developed have again shown very convincing results quite efficiently.

Further study of minimizing total flowtime for the worker assignment scheduling problem in the identical parallel-machine models

Previously, minimizing total flow time in the model of an identical, parallel machines with nonpreemptive jobs has been investigated. Because the specific problem has been shown as NP-complete, heuristics have been developed for solving it. A shortest processing time for Ai part (SPT-A) heuristic is used for the job scheduling subproblem. In addition, the largest marginal contribution (LMC) procedure is used for the worker assignment subproblem and then minimizes the total flow time. Different values of W (number of workers) are used for further study of the performance of these heuristics developed. In conclusion, for the simplified processing time function, values of W have no significant influence when the heuristics are applied. In other words, no matter what value of W was used when SPT rule was applied, the heuristics generate the same, excellent results.

Parallel recognition algorithms for chordal_planar graphs and planar [formula omitted]-trees

This paper presents parallel algorithms for recognizing chordal_planar graphs and planar k -trees. Both the algorithms run in O ( log 2 n ) time using O ( n + m ) processors on a concurrent-read and concurrent-write (CRCW), parallel random access machine (PRAM) model, where n and m are, respectively, the number of nodes and edges in the graph.The novelty of our chordal_planar graph recognition algorithm lies in that it is based on an elegant structural characterization of chordal_planar graphs proposed in this paper. Moreover, it is simpler than separately testing chordality and planarity. Our planar k-trees recognition algorithm is based on a new characterization of k-trees presented in this paper.

Efficient parallel factorization and solution of structured and unstructured linear systems

This paper gives improved parallel methods for several exact factorizations of some classes of symmetric positive definite (SPD) matrices. Our factorizations also provide us similarly efficient algorithms for exact computation of the solution of the corresponding linear systems (which need not be SPD), and for finding rank and determinant magnitude. We assume the input matrices have entries that are rational numbers expressed as a ratio of integers with at most a polynomial number of bits β . We assume a parallel random access machine (PRAM) model of parallel computation, with unit cost arithmetic operations, including division, over a finite field Z p , where p is a prime number whose binary representation is linear in the size of the input matrix and is randomly chosen by the algorithm. We require only bit precision O ( n ( β + log n ) ) , which is the asymptotically optimal bit precision for β ⩾ log n . Our algorithms are randomized, giving the outputs with high likelihood ⩾ 1 - 1 / n Ω ( 1 ) . We compute LU and QR factorizations for dense matrices, and LU factorizations of sparse matrices which are s ( n ) -separable, reducing the known parallel time bounds for these factorizations from Ω ( log 3 n ) to O ( log 2 n ) , without an increase in processors (matching the best known work bounds of known parallel algorithms with polylog time bounds). Using the same parallel algorithm specialized to structured matrices, we compute LU factorizations for Toeplitz matrices and matrices of bounded displacement rank in time O ( log 2 n ) with n log log n processors, reducing by a nearly linear factor the best previous processor bounds for polylog times (however, these prior works did not generally require unit cost division over a finite field). We use this result to solve in the same bounds: polynomial resultant; and Padé approximants of rational functions; and in a factor O ( log n ) more time: polynomial greatest common divisors (GCD) and extended GCD; again reducing the best processor bounds by a nearly linear factor.

Minimizing total flow time for the worker assignment scheduling problem in the identical parallel-machine models

The worker assignment scheduling problem consists of two basic questions of job scheduling and worker assignment. In this study, only the performance measure of total flow time is investigated in the model of identical parallel-machine with nonpreemptive jobs. Because the worker assignment scheduling problem in this specific model can be shown as NP-complete, heuristics have been developed for minimizing the total flow time. This selected worker assignment scheduling problem is solved in two stages of job scheduling and worker assignment. The shortest processing time for Ai part (SPT-A) heuristic is used for the stage of job scheduling. For the stage of worker assignment, the largest marginal contribution (LMC) procedure is used to minimize the total flow time. Two 100 I/P/n/m/W problems were simulated; results obtained by the heuristics are either optimal or near optimal. In conclusion, the heuristics developed have shown very impressive results quite efficiently.

SCHEDULING TO MINIMIZE MAX FLOW TIME: OFF-LINE AND ON-LINE ALGORITHMS

We investigate the max flow time scheduling problem in the off-line and on-line setting. We prove positive and negative theoretical results. In the off-line setting, we address the unrelated parallel machines model and present the first known fully polynomial time approximation scheme, when the number of machines is fixed. In the on-line setting and when the machines are identical, we analyze the First In First Out (FIFO) heuristic when preemption is allowed. We show that FIFO is an on-line algorithm with a (3-2/m)-competitive ratio. Finally, we present two lower bounds on the competitive ratio of deterministic on-line algorithms.

Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models

The worker assignment scheduling problem involves both the decisions of job scheduling and worker assignment. In this research, only the performance measure of total tardiness is investigated in the model of identical parallel machines with nonpreemptive jobs. Since the worker assignment scheduling problem in the selected model can be shown to be NP-complete, heuristics have been developed for minimising the total tardiness. The worker assignment scheduling problem is solved in two phases of job scheduling and worker assignment. The SES (SPT, EDD, SLACK) heuristic is used for the phase of job scheduling. For the phase of worker assignment, the largest marginal contribution (LMC) procedure is used to minimise the total tardiness. From the simulation conducted, 88 out of 100 simulated problems yielded optimal solutions while the others also obtained very good results. In conclusion, the heuristics developed have shown very impressive results in both effectiveness and efficiency aspects.

Lorentz gas cellular automata on graphs

Lorentz Gas Cellular Automata (LGCA) are models of parallel many-tape Turing machines generated by the motion of localized (point) objects (particles, signals, wave trains, etc.) on a graph. In each vertex v of the graph we store a symbol. A read/write head of the Turing machine is represented as an object that hops from one vertex of the graph to another according to a rule (symbol) stored in the vertex. Thus, the symbols stored in the vertices represent scattering rules (or simply scatterers) of the lattice gas. It is assumed that initially the scatterers are randomly distributed among the vertices of the graph. The random environment formed by the scatterers may either be fixed or evolve due to collisions with the moving object. The collisions simulate storing of a new symbol in the vertex of the graph. We investigate these models with fixed environment in general types of graphs and the models with evolving environments on trees. Remarkably, it occurred that all models with fixed environments and many models with evolving environment behave like a depth-first search on the underlying graph. Observe that such behavior occurs for any initial random distribution of scatterers rather than for some “specially prepared” initial configurations of scatterers. We also give estimates of periods of orbits on finite graphs.

Pipelined Decomposable BSP Computers

The class of weak parallel machines is interesting, because it contains some realistic parallel machine models, especially suitable for pipelined computations. We prove that a modification of the bulk synchronous parallel (BSP) machine model, called decomposable BSP (dBSP), belongs to the class of weak parallel machines if restricted properly. We will also correct some earlier results about pipelined parallel Turing machines.

PARALLEL GIVENS SEQUENCES FOR SOLVING THE GENERAL LINEAR MODEL ON A EREW PRAM*

Parallel Givens sequences for solving the General Linear Model (GLM) are developed and analyzed. The block updating GLM estimation problem is also considered. The solution of the GLM employs as a main computational device the Generalized QR Decomposition, where one of the two matrices is initially upper triangular. The proposed Givens sequences efficiently exploit the initial triangular structure of the matrix and special properties of the solution method. The complexity analysis of the sequences is based on a Exclusive Read-Exclusive Write (EREW) Parallel Random Access Machine (PRAM) model with limited parallelism. Furthermore, the number of operations performed by a Givens rotation is determined by the size of the vectors used in the rotation. With these assumptions one conclusion drawn is that a sequence which applies the smallest number of compound disjoint Givens rotations to solve the GLM estimation problem does not necessarily have the lowest computational complexity. The various Givens sequences and their computational complexity analyses will be useful when addressing the solution of other similar factorization problems.

SORTING AND SELECTION ON A LINEAR ARRAY WITH OPTICAL BUS SYSTEM

In this paper we present randomized algorithms for selection and sorting on linear arrays with optical bus communication systems. We show that sorting n given numbers can be performed in O( log n) time with high probability on a linear array, of n processors, with a reconfigurable optical bus system (Linear-AROB). We also show that selection can be performed in O(1) time with high probability on the same parallel machine model.

Language and library support for practical PRAM programming

We investigate the well-known Parallel Random Access Machine (PRAM) model of parallel computation as a practical parallel programming model. The two components of this project are a general-purpose PRAM programming language, called Fork95, and a library, called PAD, of fundamental, efficiently implemented parallel algorithms and data structures. We outline the main features of Fork95 as they apply to the implementation of PAD, and describe the implementation of library procedures for prefix-sums and sorting. The Fork95 compiler generates code for the SB-PRAM, a hardware emulation of the PRAM, which is currently being completed at the University of Saarbrücken. Both language and library can immediately be used with this machine. The project is, however, of independent interest. The programming environment can help the algorithm designer to evaluate the practicality of new parallel algorithms, and can furthermore be used as a tool for teaching and communication of parallel algorithms.

An Efficient General In-Place Parallel Sorting Scheme

We present a simple and general parallel sorting scheme, ZZ-sort, which can be used to derive a class of efficient in-place sorting algorithms on realistic parallel machine models. We prove a tight bound for the worst case performance of ZZ-sort. We also demonstrate the average performance of ZZ-sort by experimental results obtained on a MasPar parallel computer. Our experiments indicate that ZZ-sort can be incorporated into a distributed memory parallel computer system as a standard routine, and this routine is useful for space critical situations. Finally, we show that ZZ-sort can be used to convert a non-adaptive parallel sorting algorithm into an in-place and adaptive one by considering the problem of sorting an arbitrarily large input on fixed-size reconfigurable meshes.

Minimizing average completion time in the presence of release dates

A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of schedulingn jobs that are released over time in order to minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when all jobs are available at time 0, all the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynomial time. We give the first constant-factor approximation algorithms for several variants of the single and parallel machine models. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of averageweighted completion time as well. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.