Classification of Spatial Properties for Spatial Allocation Modeling TAKESHI SHIRABE Institute for Geoinformation, Technical University of Vienna, Gusshausstr 27Y29, 1040 Vienna, Austria E-mail: shirabe@geoinfo.tuwien.ac.at Received November 20, 2003; Revised February 8, 2005; Accepted March 8, 2005 Abstract Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations. Key Words: spatial properties, spatial allocation, mathematical programming 1. Introduction Efficient use of limited resources of space is a common interest for almost all who live on the earth. Farmers look for suitable sites for growing particular types of crops. Planners spend countless hours and meetings to design zoning plans for their jurisdictions. A politician may be interested in Bgerrymandering’’ [50], i.e., redrawing boundaries of voting districts in favor of herself or against her opponents. With the continuing growth of computer technology and information science, these problems are now more efficiently tackled than before. In order for digital devices such as geographic information systems (GIS) to handle the infinite continuous nature of spatial variation, however, space must be discretized into a manageable number of elements [24]. This representation of space enables us to generalize the problems described above to what we call Bspatial allocation:’’ the grouping of discrete spatial units into larger clusters according to specified criteria. Spatial units involved in spatial allocation may be socio- economic ones such as counties, Zip-code areas, census tracts, and land parcels [17], or results of systematic sampling such as pixels and grid cells [45]. There are different terms for clusters to which spatial units are allocated, such as Bzones’’ [45], Bregions’’ [6], Bdistricts’’ [28], Bterritories’’ [27], and Bturfs’’ [38] depending on context. They are herein referred to as Bobjects’’ for generality. Since such objects are not natural ones but products of human mental acts, they should be regarded as fiat in terms of Smith [42]. GeoInformatica 9:3, 269–287, 2005 # 2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.