A Greedy Algorithm for Jobs Allocation in a Multiprocessor System

We present a greedy 0.5-approximation algorithm for allocation indivisible jobs in a multiprocessor system. The algorithm uses an ordering of processors according to the non-decreasing of size, and two orderings of items: in nonincreasing utility order and in nonincreasing order of the utility/ size ratio. These orderings create two lexicographic orderings on the set $ I\times J$ (here I is the set of jobs and J is the set of processors). Based on these lexicographic orderings, the algorithm creates an admissible allocation by looking through the pairs $(i,\ j) \in I\times J$ in the corresponding order and allocating the job i to processor j if this job is not allocated yet and can be allocated to processor j. The algorithm chooses the best of the two obtained solutions. This algorithm is 0.5-approximate and has running time $O(mn)$ (without sorting), where m and n are the sizes of the sets I and J correspondingly.