Efficient optimization of monotonic functions on trees

  • Yehoshua Perl
  • Yossi Shiloach
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 112)


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.


Weighting Function Rooted Tree General Graph Internal Vertex Span Tree Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [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

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Yehoshua Perl
    • 1
  • Yossi Shiloach
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceBar-Ilan UniversityRamat-GanIsrael
  2. 2.IBM Israel Scientific Center Technion CityHaifaIsrael

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