Prize-Collecting Forest with Submodular Penalties: Improved Approximation
Abstract
Constrained forest problems form a class of graph problems where specific connectivity requirements for certain cuts within the graph must be satisfied by selecting the minimum-cost set of edges. The prize-collecting version of these problems introduces flexibility by allowing penalties to be paid to ignore some connectivity requirements. Goemans and Williamson introduced a general technique and developed a 2-approximation algorithm for constrained forest problems. Further, Sharma, Swamy, and Williamson extended this work by developing a 2.54-approximation algorithm for the prize-collecting version of these problems. Motivated by the generality of their framework, which includes problems such as Steiner trees, Steiner forests, and their variants, we pursued further exploration. We present a significant improvement by achieving a 2-approximation algorithm for this general model, matching the approximation factor of the constrained forest problems.
Keywords
Cite
@article{arxiv.2504.15445,
title = {Prize-Collecting Forest with Submodular Penalties: Improved Approximation},
author = {Ali Ahmadi and Iman Gholami and MohammadTaghi Hajiaghayi and Peyman Jabbarzade and Mohammad Mahdavi},
journal= {arXiv preprint arXiv:2504.15445},
year = {2025}
}