In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate path is at most $ (1 +\varepsilon) $ times larger than the length of the actual shortest path. The algorithm is based on the discretization of the space by placing points on the boundary of the disks. Using such a discretization we can use Dijkstra's algorithm for computing a shortest path in the geometric graph obtained in (pseudo-)polynomial time.

翻译：本文提出了一种近似算法，用于求解平面上$ n $个非重叠加权圆盘环境下的加权区域问题。对于给定参数$ \varepsilon \in (0,1] $，近似路径的长度至多为实际最短路径长度的$ (1 +\varepsilon) $倍。该算法通过在圆盘边界上布点实现空间离散化，利用此离散化方法可在（伪）多项式时间内构建几何图，进而运用Dijkstra算法计算最短路径。