3 research outputs found
Approximation Algorithm for Unrooted Prize-Collecting Forest with Multiple Components and Its Application on Prize-Collecting Sweep Coverage
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