Geographic information systems (GIS) have become increasingly important in helping us understand complex social, economic, and natural dynamics where spatial components play a key role. The critical algorithms used in GIS, however, are notoriously difficult to both teach and understand, in part due to the lack of a coherent representation. GIS Algorithms attempts to address this problem by combining rigorous formal language with example case studies and student exercises. Using Python code throughout, Xiao breaks the subject down into three fundamental areas:  • Geometric Algorithms  • Spatial Indexing  • Spatial Analysis and Modelling With its comprehensive coverage of the many algorithms involved, GIS Algorithms is a key new textbook in this complex and critical area of geography.

Spatial Optimization

Spatial Optimization

Agent Smith: We’ll need a search running.

Agent Jones: It has already begun.

The Matrix (1999)

Many problems in the world demand solutions that are deemed to be the best or optimal, and we believe these optimal solutions can be found by searching through many alternative solutions to the problem. For any such problem, we have a way to evaluate how an alternative solution performs so that we can tell one solution is “better” than another. We use an objective function to tell how a solution can be evaluated and compared with others. Of course being better may be subjective, but when it comes to solving an optimization problem we will need a formal objective function so that all alternative solutions can be measured ...

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