6533b7d2fe1ef96bd125de4e

RESEARCH PRODUCT

Minimum-cost distances in spatial analysis

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An axiomatic approach to distance is developed which focuses on thosebehavioral concepts of distance related to movement in space. In particular,spatial movement by behaving units is postulated to involve a choice fromamong some set of abstract trips in space, and implicitly, to involve theminimization of some relevant notion of trip costs. In this context, therelevant behavioral notion of distance in space is taken to be theminimum-cost distance generated by this choice process. These trip-costconcepts extend the classical notions of paths, path lengths, and shortestpaths in metric spaces. Hence many of the analytical results of the paperinvolve extensions of classical shortest-path distance properties tominimum-cost distances. In addition to these extensions, a characterizationtheorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.