Abstract
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 multi-part 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 2 log δ), 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.
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© 1997 Springer-Verlag Berlin Heidelberg
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Zhou, X., Kashem, M.A., Nishizeki, T. (1997). Generalized edge-rankings of trees. In: d'Amore, F., Franciosa, P.G., Marchetti-Spaccamela, A. (eds) Graph-Theoretic Concepts in Computer Science. WG 1996. Lecture Notes in Computer Science, vol 1197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62559-3_31
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DOI: https://doi.org/10.1007/3-540-62559-3_31
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