Critical path method

Abstract: Systems design involves the determination of interdependent variables. Thus the precedence ordering for the tasks of determining these variables involves circuits. Circuits require planning decisions about how to iterate and where to use estimates. Conventional planning techniques, such as critical path, do not deal with these problems. Techniques are shown which acknowledge these circuits in the design of systems. These techniques can be used to develop an effective engineering plan, showing where estimates are to be used, how design iterations and reviews are handled, and how information flows during the design work. This information flow can be used to determine the consequences of a change in any variable on the rest of the variables in the system, and thus which engineers must be informed and which documents must be changed. From this, a critical path schedule can be developed for implementing the change. This method is ideally suited to an automated design office where data, computer input and output, and communications are all handled through the use of computer terminals and data bases. However, these same techniques can also be effectively used in classical engineering environments.

Abstract: The fifth release of the multithreaded language Cilk uses a provably good "work-stealing" scheduling algorithm similar to the first system, but the language has been completely redesigned and the runtime system completely reengineered. The efficiency of the new implementation was aided by a clear strategy that arose from a theoretical analysis of the scheduling algorithm: concentrate on minimizing overheads that contribute to the work, even at the expense of overheads that contribute to the critical path. Although it may seem counterintuitive to move overheads onto the critical path, this "work-first" principle has led to a portable Cilk-5 implementation in which the typical cost of spawning a parallel thread is only between 2 and 6 times the cost of a C function call on a variety of contemporary machines. Many Cilk programs run on one processor with virtually no degradation compared to equivalent C programs. This paper describes how the work-first principle was exploited in the design of Cilk-5's compiler and its runtime system. In particular, we present Cilk-5's novel "two-clone" compilation strategy and its Dijkstra-like mutual-exclusion protocol for implementing the ready deque in the work-stealing scheduler.

Abstract: A fast and easily implementable approximation algorithm for the problem of finding a minimum makespan in a job shop is presented. The algorithm is based on a taboo search technique with a specific neighborhood definition which employs a critical path and blocks of operations notions. Computational experiments up to 2,000 operations show that the algorithm not only finds shorter makespans than the best approximation approaches but also runs in shorter time. It solves the well-known 10 × 10 hard benchmark problem within 30 seconds on a personal computer.

Abstract: This paper is concerned with establishing the mathematical basis of the Critical-Path Method---a new tool for planning, scheduling, and coordinating complex engineering-type projects. The essential ingredient of the technique is a mathematical model that incorporates sequence information, durations, and costs for each component of the project. It is a special parametric linear program that, via the primal-dual algorithm, may be solved efficiently by network flow methods. Analysis of the solutions of the model enables operating personnel to answer questions concerning labor needs, budget requirements, procurement and design limitations, the effects of delays, and communication difficulties.

Abstract: In this paper, we propose a static scheduling algorithm for allocating task graphs to fully connected multiprocessors. We discuss six recently reported scheduling algorithms and show that they possess one drawback or the other which can lead to poor performance. The proposed algorithm, which is called the Dynamic Critical-Path (DCP) scheduling algorithm, is different from the previously proposed algorithms in a number of ways. First, it determines the critical path of the task graph and selects the next node to be scheduled in a dynamic fashion. Second, it rearranges the schedule on each processor dynamically in the sense that the positions of the nodes in the partial schedules are not fixed until all nodes have been considered. Third, it selects a suitable processor for a node by looking ahead the potential start times of the remaining nodes on that processor, and schedules relatively less important nodes to the processors already in use. A global as well as a pair-wise comparison is carried out for all seven algorithms under various scheduling conditions. The DCP algorithm outperforms the previous algorithms by a considerable margin. Despite having a number of new features, the DCP algorithm has admissible time complexity, is economical in terms of the number of processors used and is suitable for a wide range of graph structures.