Abstract
ABSTRACT Many algorithms for calculating graph theoretic quantities on trees rely implicitly on an inductive procedure for calculating a certain function defined on the vertices of the tree, after which the function is used to determine the quantity. Examples of such quantities are the diameter, 1-centre, core and cutting centre. Each of the latter can be calculated in linear time, but in the last three cases this is far from obvious, and they have been the subjects of research papers in recent years. We present a unified treatment of a class of algorithms, containing amongst them algorithms for the above problems, which proceed in a sense by a method analagous to that of difference equations on an n-dimensional integer lattice. An analysis of the time complexity is given, and applications are made to the calculations of the above quantities, as well as to the calculation of the vertex v such that if the tree is rooted at v, then the number of maximal antichains is maximal (or minimal).
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