Lower bound on the number of processors and time for scheduling precedence graphs with communication costs

Abstract

This paper proposes a new bound on the number of processors and finish time for the problem of scheduling precedence graphs with communication costs. An algorithm (ETF) has been proposed by Hwang [1] for scheduling precedence graphs in systems with inter-processor communication times. In this paper the notion of the earliest starting time of a task is formulated for the context of lower bounds. A lower bound on the completion time of a schedule is defined. Each task can then be scheduled within a time interval without affecting the lower bound performance on the finish time. This leads to definition of a new lower bound performance on the finish time. This leads to definition of a new lower bound on the number of processors required to process the task graph. A derivation of the minimum time increase over the earliest completion time is also proposed for the case of smaller number of processors. Finally the paper proposes a lower bound on the minimum number if inter-processor communication links required to achieve optimum performance. Evaluation has been carried out by using a set of 360 small graphs. The bound on the finish time deviates at most by 5 % from the optimum solution in 96 % of the cases and performs well with respect to the minimum number of processors and communication links.

Energy reduction techniques for multimedia applications with tolerance to deadline misses

“…They include Fast Fourier Transform of two different implementations (FFT1 and FFT2); Laplace transform (Laplace); a quadrature mirror filter bank (qmf4); the Karplus-Strong music synthesis algorithm with 10 voices (karp10); a measurement application (meas); an upside down binary tree representing the sum of products computation (sum1); and others reported in early literatures [1,13,20,21].…”

“…Table 1 gives the number of vertices in each benchmark [1,13,20,21] and reports the results from three proposed energy minimization techniques. The deadlines are set to be around three times of the sum of BCET.…”

Program Repartitioning on Varying Communication Cost Parallel Architectures

“…(6). Let Ͱ be the cost increase for edge (1,2), ͱ the cost increase for edge (1,3), Ͳ the increase for edge (1,5), ͳ the increase for edge (2,8), the increase for edge (3,7), the increase for edge (4,6), and the increase for edge (6,7). Here, we consider the cost increases for only those edges whose source and destination nodes are allocated to different processors.…”

“…The computation costs t(v i ) of all the nodes v i are the same in both graphs. Also, assume that ᭙i, j, c 2 …”

“…There are several processor scheduling schemes described in the literature [1][2][3][4]. Recent surveys and a classification of different scheduling methods are given in [5,6].…”