New Divisible Load Distribution Methods on Tree and Pyramid Networks

A divisible load (job, task) can be arbitrarily divided into independent small load fractions which are assigned to processors in a parallel or distributed computing system for simultaneous processing. Given an arbitrarily divisible load without precedence constraint and a parallel/distributed computing system with communication delays, the problem of divisible load distribution is to find the proportions in which the load is partitioned and distributed among the processors such that the entire load is processed in the shortest possible time [11]. The theory and techniques of divisible load distribution have applications in a wide range of areas such as computer vision [12], large scale data file processing [29], data intensive applications [30], query processing in database systems [31], scientific computing [32], video and multimedia applications [38], numerical computing [47], biomedicine and bioinformatics [51]. Divisible load distribution has applications in filtering for radio communications, encryption for secure communications, and coding for digital communications [27]. Aerospace applications include satellite signal and image processing [13], radar and infrared tracking [25], and data reporting and aggregation and processing in wireless sensor networks [41]. Other applications include finite-element and engineering computations, grid computing, metacomputing, distance learning, real-time computing such as target identification and searching, data collection, and processing in distributed intelligent sensor networks in military surveillance systems [11]. Divisible load distribution, scheduling, sharing, and processing has been a very active and fruitful research field in the last twenty years since the problem was first proposed in 1988 [2, 19]. Extensive investigation has been conducted by numerous researchers for bus systems [6, 45], linear arrays [40, 43], tree networks [4, 6, 20], 2-dimensional meshes [15], 2-dimensional toroidal meshes [17], 3-dimensional meshes [21], k-dimensional meshes and tori [35, 36], hypercubes [14], partitionable networks [33, 34], arbitrary networks [52, 53], clusters [22, 48], grids [50], and networks of workstations [5, 39]. Other studies can be found in [7—9, 16, 18, 19, 23, 26, 28, 29, 42, 46, 49]. The reader is also referred to the web site [1] for more references in this field and Robertazzi’s recent article [44] on divisible load theory. When a divisible load is processed on a multicomputer system with a static interconnection network, there is communication overhead for distributing the load among the processors in the system. The network topology determines the speed at which a divisible load is distributed over a network and has strong impact on performance, i.e., parallel