The Fractional Prize-Collecting Steiner Tree Problem on Trees: Extended 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 c 0 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.