Building functionality assignment in dense and compact blocks using graph theory and game theory

In prospect of sustainable urban densification, a tool aiming to assess and to
assist the design of compact housing blocks with a target population density was
created and tested in the scope of the CoMod Project (Compactness under
mathematics Modeling). The concept of spatial compactness is here applied, at
the architectural scale, on the built environment, the non-built environment and
both combined. This approach encourages typo-morhologies which save land and
material resources while achieving high energy efficiency. Potential misuse of the
concept is prevented by numerous objective criteria notably relative to green
areas, projected shadows as well as minimal distances and surfaces to consider.
However, targeting urban compactness faces a difficult conciliation between
various quantitative and qualitative parameters.
Among these parameters, there is the need for the population to have easy
access to various facilities (schools, convenience stores, etc.). The question at the
center of this paper is the following : 'given a set of locations, what is the best
locations for different facilities?' To answer to this question, we use notions from
graph theory and game theory.