Evaluating Cartogram Effectiveness

Cartograms are maps in which areas of geographic regions (countries, states) appear in proportion to some variable of interest (population, income). Cartograms are popular visualizations for geo-referenced data that have been used for over a century and that make it possible to gain insight into patterns and trends in the world around us. Despite the popularity of cartograms and the large number of cartogram types, there are few studies evaluating the effectiveness of cartograms in conveying information. Based on a recent task taxonomy for cartograms, we evaluate four major different types of cartograms: contiguous, non-contiguous, rectangular, and Dorling cartograms. Specifically, we evaluate the effectiveness of these cartograms by quantitative performance analysis, as well as by subjective preferences. We analyze the results of our study in the context of some prevailing assumptions in the literature of cartography and cognitive science. Finally, we make recommendations for the use of different types of cartograms for different tasks and settings

Computing homotopic shortest paths efficiently

AbstractWe give deterministic and randomized algorithms to find shortest paths homotopic to a given collection Π of disjoint paths that wind amongst n point obstacles in the plane. Our deterministic algorithm runs in time O(kout+kinlogn+nn), and the randomized algorithm runs in expected time O(kout+kinlogn+n(logn)1+ε). Here kin is the number of edges in all the paths of Π, and kout is the number of edges in the output paths