An efficient method for single-facility location and path-connecting problems in a cell map

This article presents an efficient method for simultaneously finding both the Weber cell and optimal connective paths in a grid. As numerous barriers of arbitrary shape and weighted regions are distributed in the cell map of this research, the problem scenario is similar to working out a real-life facility location selection and path-routing problems in a geographical map. In this study, the Weber problem of finding a single-facility location from an accumulation cost table is generated by a grid wave propagation method (higher-geometry maze router). After finding the Weber point (cell), optimal connective paths with minimum total weighted cost are backtracked between the Weber location cell and the demand cells. This new computation algorithm with linear time and space complexity can be integrated as a spatial analytical function within GIS.