The fractional prize-collecting steiner tree problem on trees

Abstract

We consider the fractional prize-collecting Steiner tree problem on trees. This problem asks for a subtree T containing the root of a given tree G = (V, E) maximizing the ratio of the vertex profits ∑v∈V(T)P(v) and the edge costs ∑e∈E(T) c(e) plus a fixed cost c0 and arises in energy supply management. We experimentally compare three algorithms based on parametric search: the binary search method, Newton's method, and a new algorithm based on Megiddo's parametric search method. We show improved bounds on the running time for the latter two algorithms. The best theoretical worst case running' time, namely O(|V|log|V|), is achieved by our new algorithm. A surprising result of our experiments is the fact that the simple Newton method is the clear winner of the tested algorithms. © Springer-Verlag 2003.