Elsevier

Journal of Algorithms

Volume 10, Issue 3, September 1989, Pages 381-402
Journal of Algorithms

Solving parametric problems on trees

https://doi.org/10.1016/0196-6774(89)90035-7Get rights and content

Abstract

We consider optimization problems on weighted trees, including weighted versions of the minimum vertex cover and the minimum dominating set problems, where vertex and edge weights vary as linear functions of time. For each of the problems studied here, we derive bounds on the number of breakpoints of the piecewise linear functions describing the cost of the optimum solution and we present efficient methods for constructing these functions. We also consider the problem of determining optimum steady-state solutions and finding the time t at which the steady state is reached.

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