Efficient optimization of monotonic functions on trees
The problem of optimizing weighting functions over all the k-subtrees (subtrees with k vertices) of a given tree, is considered. A general algorithm is presented, that finds an optimal k-subtree of a given tree whenever the weighting function is what we call ‘monotonic’. Monotonicity is a very natural property, satisfied by most of the functions that one can think of.
The problem is solved for both cases of rooted and undirected trees. On the ohter hand, even simple extensions of it to general graphs are NP-hard.
KeywordsWeighting Function Rooted Tree General Graph Internal Vertex Span Tree Problem
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- [GJ]Garey, M.R. and Johnson, D.S., COMPUTERS AND INTRACTABILITY; A GUIDE TO THE THEORY OF NP-COMPLETENESS, W.H. Freeman and Co., San Francisco, 1979.Google Scholar