Prize-Collecting Steiner Tree: A 1.79 Approximation

Prize-Collecting Steiner Tree (PCST) is a generalization of the Steiner Tree problem, a fundamental problem in computer science. In the classic Steiner Tree problem, we aim to connect a set of vertices known as terminals using the minimum-weight tree in a given weighted graph. In this generalized version, each vertex has a penalty, and there is flexibility to decide whether to connect each vertex or pay its associated penalty, making the problem more realistic and practical.