Task Splitting Research Articles

Parallel techniques for physically based simulation on multi-core processor architectures

As multi-core processor systems become more and more widespread, the demand for efficient parallel algorithms also propagates into the field of computer graphics. This is especially true for physically based simulation, which is notorious for expensive numerical methods. In this work, we explore possibilities for accelerating physically based simulation algorithms on multi-core architectures. Two components of physically based simulation represent a great potential for bottlenecks in parallelisation: implicit time integration and collision handling. From the parallelisation point of view these two components are substantially different. Implicit time integration can be treated efficiently using static problem decomposition. The linear system arising in this context is solved using a data-parallel preconditioned conjugate gradient algorithm. The collision handling stage, however, requires a different approach, due to its dynamic structure. This stage is handled using multi-threaded programming with fully dynamic task decomposition. In particular, we propose a new task splitting approach based on a reasonable estimation of work, which analyses previous simulation steps. Altogether, the combination of different parallelisation techniques leads to a concise and yet versatile framework for highly efficient physical simulation.

Improving unit-specific event based continuous-time approaches for batch processes: Integrality gap and task splitting

In this work, we address a challenging issue in the area of batch processing scheduling, namely the ability to reduce or even close the integrality gap for large-scale scheduling problems. Because of the multipurpose and multiproduct characteristics of batch plants, their resulting scheduling problems can be highly combinatorial in nature with many variables and constraints. In order to help reduce this complexity, a number of preprocessing steps are performed and new sets of rigorous constraints are incorporated within a novel and effective continuous-time formulation for the short-term scheduling of batch plants. Several example problems are solved to demonstrate the effectiveness of the proposed algorithmic techniques. In addition, a new rigorous mathematical model is proposed to help reduce the complexity experienced in unit-specific event based, continuous-time formulations. A challenging benchmark problem involving several complicating features is solved for several demand instances in order to further demonstrate the effectiveness of the proposed approach.

A tandem queueing system with task-splitting, feedback, and blocking

A novel two-station single-processing tandem queueing system with task splitting, feedback, and blocking is considered. Two cases are analysed: a finite buffer at each station, and only the intermediate buffer finite. After completing processing at each station, a task may leave the system, join the other station, go for split, go to the other station or return to its own station. The steady-state joint distribution of the queue lengths that will lead to the moments of the queue lengths, mean waiting time, probabilities of each station and the system being busy and being idle are obtained through algorithms. A numerical example is provided.

Relational Contracts and Job Design

This paper analyzes the problem of optimal job design when there is only one contractible and imperfect performance measure for all tasks whose contribution to firm value is non-veritable. I find that task splitting is optimal when relational contracts based on firm value are not feasible. By contrast, if an agent who performs a given set of tasks receives an implicit bonus, the principal always benefits from assigning an additional task to this agent.

A compact task graph representation for real-time scheduling

A new task graph representation, namely the compact task graph (CTG), is developed to aid in the scheduling of a set of communicating periodic real-time tasks. This representation explicitly expresses the potential for parallelism across tasks as well as the idle times that may be encountered within application tasks. A CTG based scheduler can generate schedules that are able to meet deadlines by interleaving the execution of tasks on a single processor and/or overlapping the execution of tasks on multiple processors. The construction of a CTG is based upon the busy-idle execution profiles for the tasks generated by the compiler. The profiles are computed assuming that sufficient resources are available for parallel execution of all tasks. Thus, they expose all opportunities for overlapped and interleaved execution. The compiler analyzes the profiles to identify useful opportunities for interleaving and expresses them in the CTG without unnecessary partitioning of the tasks. The CTG is powerful because it expresses schedules that are not expressed by existing approaches for constructing task graphs. Schedules can be generated efficiently since a CTG's construction minimizes the splitting of tasks. We briefly demonstrate the usefulness of CTGs in scheduling real-time tasks and scheduling monitoring tasks without affecting the timing of application tasks.

Minimizing the sum of weighted completion times with unrestricted weights

Given a set of tasks with associated processing times, deadlines and weights unrestricted in sign, we consider the problem of determining a task schedule on one machine by minimizing the sum of weighted completion times. The problem is NP-hard in the strong sense. We present a lower bound based on task splitting, an approximation algorithm, and two exact approaches, one based on branch-and-bound and one on dynamic programming. An overall exact algorithm is obtained by combining these two approaches. Extensive computational experiments show the effectiveness of the proposed algorithm.

An interactive approach to the design of noncontinuous plants

The design of noncontinuous plants has been an area of active research for the past 20 yr. Much of the past work has been focused on optimal equipment sizing using mathematical programming techniques, often with further restrictions on the types of equipment, intermediate storage, operating policies and so on. A more comprehensive view of the design should include equipment selection, task assignment and configuration synthesis as well as path sequencing and unit sizing, but such a design does not lend itself readily to the existing techniques. In this paper we report a novel approach to the design of noncontinuous plants. This approach is based on a design tool, BatchEx, which performs three basic functions. First, it maintains current plant configurations, production plans, path sequences and useful design indices such as equipment utilization. Second, it provides a set of design operators which are used to enter design decisions and to evaluate their consequences. Third, it provides a graphic interface for a user to access the knowledge base and the design operators. Implemented in ART, an expert system shell with schema representation and rule programming, BatchEx is applicable to both OPAT (One Product At A Time) and MPAT (Multiple Products At A Time) noncontinuous plants. It provides for task merging, task splitting and equipment reuse. It allows for nonidentical parallel units, in-phase, out-of-phase, mixed operating modes and intermediate storage. Full flexibility is available with regard to the selection and sequencing of production paths. In its present implementation a design is guided by total equipment cost minimization. Given a design BatchEx determines its feasibility and provides information which may be used to improve the design. BatchEx allows the user to enter an initial design for a given problem and information about the design is presented to the user upon request. The design is modified by the user based on his experience and analysis. Heuristics have been developed for design initialization and improvement. Examples are presented to illustrate these heuristics. A preliminary assessment of the efficacy of this approach is given.

Task splitting for three machine preemptive scheduling

Optimal preemptive schedules of jobs with unit completion times and given precedence constraints may require arbitrarily many short intervals of work on a single task.