2 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
Efficient algorithms for flexible sweep coverage in crowdsensing
Sweep coverage is an important covering technique in mobile crowdsensing, in which users or participants are employed to periodically monitor a set of points of interest (POIs) each with a weight indicating the value of its information to be collected. Traditionally, each user proposes a route along which there is a set of POIs to be monitored. The task is to select a set of participants such that the total weight of the monitored POIs is maximized. However, in real applications, users should have the flexibility to offer several preferred routes. This arises our studied maximum sweep assignment problem with flexibility, where each participant proposes several routes, and the new task is to strategically assign each participant a route among their choices in which the way maximizes the total weight of the monitored POIs. In this paper, we first prove that the problem is NP -complete and then devise two novel approximation algorithms with ratios 0.5 and 0.632. Experiments are also conducted to evaluate algorithms’ practical performance. The results demonstrate that the proposed approximate methods are significantly faster (with up to two orders of magnitude runtime reduction) than the exact integer linear programming solution. In addition, we theoretically study another flexible sweep coverage model in which it costs to hire each user, and the goal is to cover all POIs multiple times (for more complete and accurate information) while minimizing the total hiring cost