An Efficient Algorithm for the Least Areas Path Problem

The goal of the least areas path problem (LAPP) is to find a path traversing through a given region covered by a set of areas with any arbitrary shape, between a given pair of points and with the property that each point on the path is covered by the least areas. Different the weighted region optimal path problem, the LAPP asks for the cost of each step in path is as low as possible. Based on the relationship between boundaries of sub-regions and the least areas path, we can transform this continuous-domain problem to a discrete one by calculating the coverage of curves of sub-regionspsila boundaries. Depending on binary-search and breadth-first-search, an efficient and fast algorithm was devised for solving the LAPP.