ABSTRACT
This chapter presents the algorithm by M. Goemans and D. P. Williamson for the Prize-Collecting Steiner Tree, which is a basic building block for all the other algorithms. It analyzes N. Garg’s technique showing a 5-approximation for both the k-MST and k-TSP and shows how to extend it to the Quota TSP. The chapter describes an algorithm for the general Prize-Collecting Traveling Salesman Problem (PCTSP) that builds over the algorithms for Quota TSP and Penalty TSP. It provides some applications of these algorithms to the minimum latency problem and graph searching. The chapter discusses some more research developments concerning the PCTSP and related problems. In the general form given, the PCTSP was first formulated by E. Balas, who gave structural properties of the PCTS polytope as well as heuristics. Heuristics were given by S. Y. Cheung and A. Kumar, who studied the problem in the context of communication networks.
