Algorithm for constructing an optimally connected rectangular floor plan

In most applications, such as urbanism and architecture, randomly utilizing given spaces is certainly not favorable. This study proposes an explicit algorithm for utilizing the given spaces inside a rectangle with satisfactory results. In the literature, connectivity is not considered as a criterion for floor plan design, but it is deemed essential in architecture. For example, dining rooms are preferably connected to kitchens, toilets should be connected to many rooms, and each bedroom should be separated from the other rooms. This paper describes adjacency among spaces and proves that the obtained rectangular floor plan is one of the best ones in terms of connectivity. An architectural and mathematical object called extra spaces is introduced by the proposed algorithm and is subsequently examined in this work.