What if we can relocate convenience stores in accordance with fairness.

Convenience stores in Japan become more and more important not only in a normal time but also in a time of disaster. Therefore, locating convenience stores in accordance with fairness becomes very important to enhance safety of a region.

In this article, we try to relocate convenience stores in Ueno, Tokyo as a trial experiment. There are 215 convenience stores in Ueno. Usually, we draw voronoi diagrams when estimating “sphere” of certain facility (convenience store), but note that we have to consider not “Euclidean distance” but “Network distance”. When we focus on one sphere and calculate min-sum point of this sphere, the location of convenience store is not correspond to this min-sum point in many cases. If we relocate the convenience store to min-sum point, the geometry of sphere changes at the same time. But repeating following steps again and again, it’s location converge at one point.

  1. Calculate “Sphere” of convenience stores
  2. Calculate min-sum point of this sphere
  3. Move convenience stores to min-sum point of each sphere
  4. Repeat step1 to step2 till the location of convenience converge at min-sum point

In case of Ueno, we can find each location in 10 steps.