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Shape construction problem by combining polygons based on adjacency information and its heuristic algorithm

Given a set of polygons with adjacency information, we consider the problem of constructing a shape that is similar to the input polygon (target shape) by grouping multiple adjacent polygons. An example of such a set is a set of prefectures in Japan. There are many attempts to create a mascot for a certain prefecture by focusing on the similarity of shapes, or to create a learning material of prefectures by finding an animal or a vehicle that looks like a given prefecture. On the other hand, we consider grouping multiple prefectures into one that resembles an input shape by mathematical optimization, and propose a heuristic solution method. The effectiveness of the proposed method is confirmed through numerical experiment to form animal shapes using prefectural data. Our approach has various interesting applications, such as creating learning materials for children to study prefectures, and making geographical puzzles.