Approximation Algorithm for Unrooted Prize-Collecting Forest with Multiple Components and Its Application on Prize-Collecting Sweep Coverage
Abstract
In this paper, we introduce a polynomial-time 2-approximation algorithm for the Unrooted Prize-Collecting Forest with Components (URPCF) problem. URPCF aims to find a forest with exactly connected components while minimizing both the forest's weight and the penalties incurred by unspanned vertices. Unlike the rooted version RPCF, where a 2-approximation algorithm exists, solving the unrooted version by guessing roots leads to exponential time complexity for non-constant . To address this challenge, we propose a rootless growing and rootless pruning algorithm. We also apply this algorithm to improve the approximation ratio for the Prize-Collecting Min-Sensor Sweep Cover problem (PCMinSSC) from 8 to 5. Keywords: approximation algorithm, prize-collecting Steiner forest, sweep cover.
Keywords
Cite
@article{arxiv.2306.13996,
title = {Approximation Algorithm for Unrooted Prize-Collecting Forest with Multiple Components and Its Application on Prize-Collecting Sweep Coverage},
author = {Wei Liang and Shaojie Tang and Zhao Zhang},
journal= {arXiv preprint arXiv:2306.13996},
year = {2023}
}