A scheduling algorithm aims to minimize the overall execution time of the program by properly allocating and arranging the execution order of the tasks on the core processors such that the precedence constraints among the tasks are preserved. In this paper, we present a new scheduling algorithm by using geometry analysis of the Task Precedence Graph (TPG) based on A* search technique and uses a computationally efficient cost function for guiding the search with reduced complexity and pruning techniques to produce an optimal solution for the allocation/scheduling problem of a parallel application to parallel and multiprocessor architecture. The main goal of this work is to significantly reduce the search space and achieve the optimality or near optimal solution. We implemented the algorithm on general task graph problems that are processed on most of related search work and obtain the optimal scheduling with a small number of states. The proposed algorithm reduced the exhaustive search by at least 50% of search space. The viability and potential of the proposed algorithm is demonstrated by an illustrative example.

We consider the problem of placing resources in a distributed computing system so that certain performance requirements may be met while minimizing the number of resource copies needed. Resources include special I/O processors, expensive peripheral devices, or such software modules as compilers, library routines, and data files. Due to the delay in accessing each of these resources, system performance degrades as the distance between each processor and its nearest resource copy increases. Thus, every processor must be within a given distance k1 of at least one resource copy, which is called the k-bounded placement problem. The structure of a distributed computing system is represented by a graph. The k-bounded placement problem is first transformed into the problem of finding smallest k-dominating sets in a graph. Searching for smallest k-dominating sets is formulated as a state-space search problem. We derive heuristic information to speed up the search, which is then used to solve the problem with the well-known A* algorithm. An illustrative example and some experimental results are presented to demonstrate the effectiveness of the heuristic search.