On the consistency of cardinal direction constraints 
 
Authors:  Spiros Skiadopoulos Manolis Koubarakis 
 
Institution:  ^{a} Knowledge and Database Systems Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens, Zographou, 157 73 Athens, Greece ^{b} Intelligent Systems Laboratory, Department of Electronic and Computer Engineering, Technical University of Crete, Chania, 731 00 Crete, Greece 
 
Abstract:  We present a formal model for qualitative spatial reasoning with cardinal directions utilizing a coordinate system. Then, we study the problem of checking the consistency of a set of cardinal direction constraints. We introduce the first algorithm for this problem, prove its correctness and analyze its computational complexity. Utilizing the above algorithm, we prove that the consistency checking of a set of basic (i.e., nondisjunctive) cardinal direction constraints can be performed in O(n^{5}) time. We also show that the consistency checking of a set of unrestricted (i.e., disjunctive and nondisjunctive) cardinal direction constraints is NPcomplete. Finally, we briefly discuss an extension to the basic model and outline an algorithm for the consistency checking problem of this extension. 
 
Keywords:  Cardinal direction relations Spatial constraints Consistency checking Qualitative spatial reasoning 
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