ABSTRACT

Given a grid of cells, each having a value indicating its cost per unit area, a variant of the least-cost path problem is to find a corridor of a specified width connecting two termini such that its cost-weighted area is minimized. A computationally efficient method exists for finding such corridors, but as is the case with conventional raster-based least-cost paths, their incremental orientations are limited to a fixed number of (typically eight orthogonal and diagonal) directions, and therefore, regardless of the grid resolution, they tend to deviate from those conceivable on the Euclidean plane. In this paper, we propose a method for solving the raster-based least-cost corridor problem with reduced distortion by adapting a distortion reduction technique originally designed for least-cost paths and applying it to an efficient but distortion-prone least-cost corridor algorithm. The proposed method is, in theory, guaranteed to generate no less accurate solutions than the existing one in polynomial time and, in practice, expected to generate more accurate solutions, as demonstrated experimentally using synthetic and real-world data.

摘要

给定一个单元格网格，每个单元格都有一个表示其单位面积成本的值，最小成本路径问题的一个变体是找到连接两个终端的指定宽度的走廊，使其成本加权区域最小化。存在一种计算效率高的方法来查找此类走廊，但与传统的基于栅格的最低成本路径的情况一样，它们的增量方向仅限于固定数量的（通常为 8 个正交和对角线）方向，因此，无论网格分辨率，它们往往偏离欧几里得平面上可以想象的那些。在本文中，我们提出了一种解决基于栅格的最小成本走廊问题的方法，该方法通过采用最初为最低成本路径设计的失真减少技术并将其应用于有效但容易失真的最低成本走廊算法。理论上，所提出的方法可以保证在多项式时间内生成不比现有方法差的解决方案，并且在实践中，预计会生成更准确的解决方案，如使用合成和真实世界数据进行的实验所证明的那样。