Topological Inference

Michelangelo Grigni and Dimitris Papadiasy and Christos Papadimitriouz Computer Science and Engineering University of California, San Diego 9500 Gilman Drive La Jolla, CA 92093{0114 Abstract Geographical database systems deal with certain basic topological relations such as \A overlaps B" and \B contains C" between simply connected regions in the plane. It is of great interest to make sound inferences from elementary statements of this form. This problem has been identi ed extensively in the recent literature, but very limited progress has been made towards addressing the considerable technical di culties involved. In this paper we study the computational problems involved in developing such an inference system. We point out that the problem has two distinct components that interact in rather complex ways: relational consistency, and planarity. We develop polynomial-time algorithms for several important special cases, and prove almost all the others to be NP-hard.