Abstract
A k-edge ranking of an undirected graph is a labeling of the edges of the graph with integers 1, 2, …, k, with the property that all paths between two edges with the same label i contain an edge with label j[rang] i. The edge ranking problem is that of finding the smallest k for which a graph has a k-edge ranking. This problem is useful in the optimization of the number of parallel stages required to assemble a product from its components. The problem is also related to that of finding minimum height edge partition trees of graphs. The main result in the paper is an O( n log n) time approximation algorithm for edge ranking of trees, which has a worst case performance ratio of 2.
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