Abstract
In this paper we deal with the problem of finding an optimal query execution plan in database systems. We improve the analysis of a polynomial-time approximation algorithm due to Makino et al. for designing query execution plans with almost optimal number of parallel steps. This algorithm is based on the concept of edge ranking of graphs. We use a new upper bound for the edge ranking number of a tree to derive a better worst-case performance guarantee for this algorithm. We also present some experimental results obtained during the tests of the algorithm on random graphs in order to compare the quality of both approximation ratios on average. Both theoretical analysis and experimental results indicate the superiority of our approach.