Generalized Edge-Rankings of Trees

概要

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In this paper we newly define a generalized edge-ranking of a graph G as follows:for a positive integer c, a c-edge-ranking of G is a labeling (ranking) of the edges of G with integers such that, for any label I, deletion of all edges with labels >I leaves connected components, each having at most c edges with label I. The problem of finding an optimal c-edge-ranking of G, that is, a c-edge-ranking using the minimum number of ranks, has applications in scheduling the manufacture of complex multipart products;it is equivalent to finding a c-edge-separator tree of G having the minimum height. We present an algorithm to find an optimal c-edge-ranking of a given tree T for any positive integer c in time O(n^2logΔ), where n is the number of vertices in T and Δ is the maximum vertex-degree of T. Our algorithm is faster than the best algorithm known for the case c=1.
社団法人電子情報通信学会の論文
1998-02-25