Michael T Gastner | PubMed Health

PubMed2006

Optimal design of spatial distribution networks.

We consider the problem of constructing facilities such as hospitals, airports, or malls in a country with a nonuniform population density, such that the average distance from a person's home to the nearest facility is minimized. We review some previous approximate treatments of this problem that indicate that the optimal distribution of facilities should have a density that increases with population density, but does so slower than linearly, as the two-thirds power. We confirm this result numerically for the particular case of the United States with recent population data using two independent methods, one a straightforward regression analysis, the other based on density-dependent map projections. We also consider strategies for linking the facilities to form a spatial network, such as a network of flights between airports, so that the combined cost of maintenance of and travel on the network is minimized. We show specific examples of such optimal networks for the case of the United States.

Journal Article↗

PubMed2004

From The Cover: Diffusion-based method for producing density-equalizing maps.

Map makers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. Our method is conceptually simple and produces useful, elegant, and easily readable maps. We illustrate the method with applications to the results of the 2000 U.S. presidential election, lung cancer cases in the State of New York, and the geographical distribution of stories appearing in the news.

Data Interpretation, Statistical↗