An Efficient Algorithm for Edge-Ranking Trees

Abs t rac t . An edge-ranking of an undirected graph G is a labeling of the edges of G with integers such that all paths between two edges with the same label i contain an edge with label j > i. The problem of finding an edge-ranking of G using a minimum number of ranks has applications in scheduling the manufacture of complex multi-part products; it is equivalent to finding the minimum height edge separator tree. Deogun and Peng and independently de la Torre et al. have given polynomialtime algorithms which find an edge-ranking of trees T using a minimum number of ranks in time O(n 3) and O(n 3 logn) respectively, where n is the number of nodes in T. This paper presents a more efficient and simple algorithm, which finds an edge-ranking of trees using a minimum number of ranks in O(n 2) time.