Optimal algorithms for scheduling divisible workloads on heterogeneous systems

Abstract

In this paper, we discuss several algorithms for scheduling divisible loads on heterogeneous systems. Our main contributions are (i) new optimality results for single-round algorithms and (ii) the design of an asymptotically optimal multi-round algorithm. This multi-round algorithm automatically performs resource selection, a difficult task that was previously left to the user. Because it is periodic, it is simpler to implement, and more robust to changes in the speeds of the processors and/or communication links. On the theoretical side, to the best of our knowledge, this is the first published result assessing the absolute performance of a multi-round algorithm. On the practical side, extensive simulations reveal that our multi-round algorithm outperforms existing solution on a large variety of platforms, especially when the communication-to-computation ratio is not very high (the difficult case).

Load-balancing scatter operations for grid computing

“…The same mistake was also made in the same context by Bla_ zewicz and Drozdowski in [11]. Beaumont, Legrand, and Robert [7,8] proved, for the single-level tree networks with front-end processors, that in any optimal solution the processors are ordered by decreasing bandwidth, they all participate in the computation, and all finish their execution at the same time. Beaumont, Legrand, and Robert also proposed asymptotically optimal multi-round algorithms.…”

“…In their model, the master does not compute anything, and he cannot send and receive data simultaneously. A major drawback with their work is that they simply assume that the processors should be ordered by non-increasing order of their computational power (fastest processors first), while several authors have shown that in many cases, the sort criterion should be the network links bandwidths [24,5,7,17].…”

Simple Performance Bounds for Multicore and Parallel Channel Systems

“…The concept of equivalent networks [16] was developed for complex networks such as multilevel tree networks. Research has also considered scheduling policy with multi-installment [17], multi-round algorithms [18], parallel load distribution [19] [20], independent task scheduling [21], fixed communication charges [22], detailed parameterizations and solution reporting time optimization [23] and combinatorial optimization [24]. Though divisible load theory is fundamentally a deterministic theory, it has been shown that there is some mathematical equivalence to Markov chain models [25].…”

A Real Coded Genetic Algorithm for Data Partitioning and Scheduling in Networks with Arbitrary Processor Release Time

“…Optimal Sequence for Numerical Example. 1: The optimal sequence of load distribution (by root processor p 0 ) obtained using the above genetic algorithm is {p 7 …”

“…A study on computational complexity of divisible load scheduling problem is presented in [6]. The effect of communication latencies (start-up time delays in communication) are studied in [7][8][9][10][11] using single-round and multi-round load distribution strategies. The problem of scheduling divisible loads in presence of processor release times is considered in [12][13][14].…”