In this paper, we present the first constant-approximation algorithm for {\em budgeted sweep coverage problem} (BSC). The BSC involves designing routes for a number of mobile sensors (a.k.a. robots) to periodically collect information as much as possible from points of interest (PoIs). To approach this problem, we propose to first examine the {\em multi-orienteering problem} (MOP). The MOP aims to find a set of $m$ vertex-disjoint paths that cover as many vertices as possible while adhering to a budget constraint $B$. We develop a constant-approximation algorithm for MOP and utilize it to achieve a constant-approximation for BSC. Our findings open new possibilities for optimizing mobile sensor deployments and related combinatorial optimization tasks.

翻译：本文针对预算约束下的扫描覆盖问题提出了首个常数近似算法。该问题旨在为若干移动传感器设计巡检路径，使其在满足预算约束的前提下最大化周期性信息采集量。为解决该问题，我们首先研究多路径定向问题，该问题要求在给定预算约束下寻找m条顶点互不相交的路径以覆盖尽可能多的顶点。我们为此问题设计了常数近似算法，并将其应用于扫描覆盖问题以获得常数近似解。本研究为移动传感器部署优化及相关组合优化任务开辟了新的可能性。