1. ¹200 Bexell Hall, College of Business, Oregon State University Corvallis, OR, U.S.A.
2. ²School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, U.S.A.

Correspondence: René Reitsma, 200 Bexell Hall, College of Business, Oregon State University, Corvallis, OR 97331, U.S.A. Tel: +1 541 737 6162; Fax: +1 541 737 6023; E-mail: reitsmar@bus.oregonstate.edu

Received 1 March 2006; Revised 26 July 2006; Accepted 14 August 2006; Published online 17 May 2007.

Abstract

In this paper, we present and evaluate a Voronoi method for partitioning continuous information spaces. We define the formal characteristics of the problem and discuss several well-known partitioning methods and approaches. We submit that although they all partially solve the problem, they all have shortcomings. As an alternative, we offer an approach based on an adaptive version of the multiplicatively weighted Voronoi diagram. The diagram is 'adaptive' because it is computed backwards; that is, the generators' weights are treated as dependent rather than independent variables. We successfully test this adaptive solution using both ideal-typical (artificial) and empirical data. Since the resultant visualizations are meant to be used by human subjects, we then discuss the results of a usability experiment, positioning the adaptive solution against a commonly used rectangular solution and the classic nonweighted Voronoi solution. The results indicate that in terms of usability, both the rectangular and the adaptive Voronoi solution outperform the standard Voronoi solution. In addition, although subjects are better able to gage rectangular area relationships, only the adaptive Voronoi solution satisfies all geometric constraints of weight-proportional partitioning.