Elementary Approximation Algorithms for Prize Collecting Steiner Tree Problems

This paper deals with approximation algorithms for the prize collecting generalized Steiner forest problem, defined as follows. The input is an undirected graph G = (V, E), a collection T = {T1, . . . , Tk}, each a subset of V of size at least 2, a weight function w : E R+ , and a penalty function p : T R+ . The goal is to find a forest F that minimizes the cost of the edges of F plus the penalties paid for subsets Ti whose vertices are not all connected by F. Our main result is a combinatorial (3- 4 n )-approximation for the prize collecting generalized Steiner forest problem, where n 2 is the number of vertices in the graph. This obviously implies the same approximation for the special case called the prize collecting Steiner forest problem (all subsets Ti are of size 2). The approximation ratio we achieve is better than that of the best known combinatorial algorithm for this problem, which is the 3-approximation of Sharma, Swamy, and Williamson [13]. Furthermore, our algorithm is...

• Type: Conference
• Year: 2008
• Where: COCOA
• Authors: Shai Gutner
• Keywords: Algorithm, COCOA 2008, Discrete Geometry, Steiner Forest Problem, Subsets Ti