English

A note on Johnson, Minkoff and Phillips' algorithm for the Prize-Collecting Steiner Tree Problem

Data Structures and Algorithms 2010-06-21 v2 Discrete Mathematics

Abstract

The primal-dual scheme has been used to provide approximation algorithms for many problems. Goemans and Williamson gave a (2-1/(n-1))-approximation for the Prize-Collecting Steiner Tree Problem that runs in O(n^3 log n) time. it applies the primal-dual scheme once for each of the n vertices of the graph. Johnson, Minkoff and Phillips proposed a faster implementation of Goemans and Williamson's algorithm. We give a proof that the approximation ratio of this implementation is exactly 2.

Keywords

Cite

@article{arxiv.1004.1437,
  title  = {A note on Johnson, Minkoff and Phillips' algorithm for the Prize-Collecting Steiner Tree Problem},
  author = {Paulo Feofiloff and Cristina G. Fernandes and Carlos E. Ferreira and Jose Coelho de Pina},
  journal= {arXiv preprint arXiv:1004.1437},
  year   = {2010}
}
R2 v1 2026-06-21T15:08:16.278Z