Information about the geographic distribution of economic activity, health statistics, and similar matters of human interest has long been of great value to governments, commercial concerns, and political entities and organizations. Much effort and many resources are expended on the collection and analysis of information pertaining to product sales, consumer preferences, crime statistics, incomes, occurrence of disease, voting patterns, and many other types of data; the results are used in a variety of ways, ranging from targeted marketing to identifying causes of disease to drawing boundaries for election districts. Applications are both inductive and abductive. The use of a map and pins, and the application of local knowledge and domain expertise for making inferences are the simplest manifestations of geospatial abduction. Computational aids to reasoning have been used in various domains. This monograph is an attempt to formalize abductive reasoning based on geospatial information. It includes conceptual definitions, algorithms for exact and approximate solutions, descriptions of heuristics, and examples of applying geospatial abduction to real-world problems.

At the technical core of this book are the three chapters on point, region, and adaptive geospatial abduction. The chapter on point-based abduction introduces a formalization and complexity analysis of geospatial abduction problems, accompanied by exact algorithms and heuristics. The next chapter extends the point problem to regions, with the intention of reducing the nondeterminism of point algorithms. Included here are a formalization of geospatial abduction in terms of regions as compared to points (in brief, representation of the problem in the domain of real numbers as compared to the integer domain of the previous chapter), and reductions to set-cover and k-set-cover problems. The next chapter addresses the general dynamic problem by modeling it in terms of adversarial two-player games with adaptive strategies. These three chapters also include notes on implementation and experimental results. A final chapter discusses the application of computational geospatial abduction to detecting improvised explosive device (IED) caches and high-value targets. The systems are, given the availability of data and domain knowledge, also applicable other domains such as animal habitat conservation.

The exposition is comparable to senior undergraduate or graduate-level texts in algorithms and computability theory. Diagrams and screen captures accompany the text, and though the latter could have been improved with the use of color plates or better resolution, their essential points are generally made. The intended audience consists of academics and graduate students in computer science (especially computability theory and algorithm analysis) and geography, and those in the natural and social sciences who are interested in the spatial distribution and relationships of data within their fields. Application developers should also find much to interest them. Professionals working in application domains involving geospatial information, ranging from military intelligence to environmental conservation, would find the first chapter (introductory material) and the final chapter (describing applications in the real world) informative, though much of the intervening material will be too technical for those without educational backgrounds in computer science, geography, or mathematics. This monograph will be a useful addition to the shelves of academics, students, and developers working with geospatial knowledge in a variety of domains.