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Optimal node ranking of trees. (English) Zbl 0661.68063
We discuss the problem of ranking nodes of a tree, which is a restriction of the general node coloring problem. A tree is said to have rank number k if its vertices can be ranked using the integers 1,2,...,k such that if two nodes have the same rank i, then there is a node with rank greater than i on the path between the two nodes. The optimal rank number of a tree gives the minimum height of its node separator tree. We present an O(n log n) algorithm for optimal node ranking of trees.

MSC:
68P10 Searching and sorting
68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
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