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arXiv · 2504.15445

Prize-Collecting Forest with Submodular Penalties: Improved Approximation

Ali Ahmadi·Iman Gholami·MohammadTaghi Hajiaghayi·Peyman Jabbarzade·Mohammad Mahdavi
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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.

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Ali Ahmadi, Iman Gholami, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, Mohammad Mahdavi. 2025-04-21. Prize-Collecting Forest with Submodular Penalties: Improved Approximation. https://arxiv.org/abs/2504.15445

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