Multi-users scheduling in parallel systems

We are interested in this paper to study scheduling prob-lems in systems where many users compete to perform their respective jobs on shared parallel resources. Each user has specific needs or wishes for computing his/her jobs ex-pressed as a function to optimize (among maximum com-pletion time, sum of completion times and sum of weighted completion times). Such problems have been mainly studied through Game Theory. In this work, we focus on solving the problem by optimizing simultaneously each user’s objective function independently using classical combinatorial opti-mization techniques. Some results have already been pro-posed for two users on a single computing resource. How-ever, no generic combinatorial method is known for many objectives. The analysis proposed in this paper concerns an arbi-trarily fixed number of users and is not restricted to a single resource. We first derive inapproximability bounds; then we analyze several greedy heuristics whose approximation ratios are close to these bounds. However, they remain high since they are linear in the number of users. We pro-vide a deeper analysis which shows that a slightly modified version of the algorithm is a constant approximation of a Pareto-optimal solution