The Weighted Maximum-Mean Subtree and Other Bicriterion Subtree Problems

  • Josiah Carlson
  • David Eppstein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


We consider problems where we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When the objective is the sum of linear function weights of a parameter, we show how to list all optima for all parameter values in O(nlogn) time. This can be used to solve many bicriterion optimizations problems in which each node has two values x i and y i associated with it, and the objective function is a bivariate function f(∑x i ,∑y i ) of the sums of these two values. When f is the ratio of the two sums, we have the Weighted Maximum-Mean Subtree Problem, or equivalently the Fractional Prize-Collecting Steiner Tree Problem on Trees; we provide a linear time algorithm when all values are positive, improving a previous O(nlogn) solution, and prove NP-completeness when certain negative values are allowed.


Rooted Tree Binary Search Piecewise Linear Function Tree Node Linear Time Algorithm 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Josiah Carlson
    • 1
  • David Eppstein
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaIrvineUSA

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