Transformation models of directed cyclic graph onto acyclic graph and mapping for task assignment problem

Abstract

Task assignment is one of the most challenging problems in distributed computing environment. Several approaches and techniques of optimal task assignment have been proposed by various researchers, ranging from graph partitioning-based tools to heuristic graph matching. A good task assignment algorithm and mapping strategy ensure completion time minimization. Previous work put efforts on solving a directed acyclic task graph. However, if a cycle exists, it is difficult and sometimes impossible to complete the task according to the constraints. Thus, it is desirable to develop a method that can eliminate the cycle to obtain a directed acyclic graph for a task assignment problem. In this thesis, the techniques of transforming a directed cyclic graph formed by a plurality of nodes into a directed acyclic graph are studied. Three models have been developed, starting with graph matching which transforms unweighted directed graph with cycle into acyclic graph. The second model is an extension from the first model, but with weightage on the edges. The third model discussed edge reversing technique to solve the weighted directed cyclic graph. This technique comprises of three main stages which are cycle identification, decomposition and formation of acyclic graph, and task assignment. Preferably, the length of the edge is the computational time. The optimal solution gives the minimum time required to complete the proposed task. The proposed algorithms were coded and simulations are run for each model using respective program developed by JavaScript programming language with D3 library. Based on the results, the proposed models give better optimality index by 20.83% compared to previous works. This research provides fundamental solution and better understanding to avoid cycle on assignment problems thus helping organizations or companies to increase the efficiency in planning as well as reducing the routing cost. This will give a great impact and benefit the manufacturing industry as well as transportation business where model and algorithms can be adjusted in their software and applications.