Using the A⋆ algorithm to find optimal sequences for area aggregation

Abstract

Given two land-cover maps of different scales, we wish to find a sequence of small incremental changes that gradually transforms one map into the other. We assume that the two input maps consist of polygons that constitute a planar subdivision and belong to different land-cover classes. Every polygon in the small-scale map is the union of a set of polygons in the large-scale map. In each step of the sequence that we compute, the smallest area in the current map is merged with one of its neighbors. We do not select that neighbor according to a prescribed rule but define the whole sequence of pairwise merges at once, based on global optimization. An important requirement for such a method is a formalization of the problem in terms of optimization objectives and constraints, which we present together with a solution that is based on the so-called A⋆ algorithm. This algorithm allows us to limit the exploration of the search space such that we can compute solutions of high quality in reasonable time. We tested the method with a dataset of the official German topographic database ATKIS and discuss our results.