Abstract. Analysis of global geographic phenomena requires non-planar models. In the past, models for topological relations have focused either on a twodimensional or a three-dimensional space. When applied to the surface of a sphere, however, neither of the two models suffices. For the two-dimensional planar case, the eight binary topological relations between spatial regions are well known from the 9-intersection model. This paper systematically develops the binary topological relations that can be realized on the surface of a sphere. Between two regions on the sphere there are three binary relations that cannot be realized in the plane. These relations complete the conceptual neighborhood graph of the eight planar topological relations in a regular fashion, providing evidence for a regularity of the underlying mathematical model. The analysis of the algebraic compositions of spherical topological relations indicates that spherical topological reasoning often provides fewer ambiguities than planar topological reasoning. Finally, a comparison with the relations that can be realized for one-dimensional, ordered cycles draws parallels to the spherical topological relations. 1

In this paper, we present some preliminary results about the connections existing between qualitative and discrete constraint networks. We present a natural encoding of any qualitative network N into a discrete one P such that the constraints of N become the variables of P and the constraints of P are defined by the weak composition table of the used qualitative algebra. We then introduce some properties about the (global) consistency of networks, circumscribing conditions under which the two models are equivalent. We also relate some domain filtering consistencies (such as generalized arc consistency) of discrete networks encoding qualitative ones with ◦-consistency, where ◦ denotes the weak composition of the qualitative calculus.

In the real world, lots of objects with changing position can be found. Some of them repeat the same movement several times, called periodic movements. Examples include airplanes, trains, planets, and marine turtles. This paper describes a model for representing the periodic movements to be stored in a database system, exploiting the information about the repetitions. The model is generic enough to represent any kind of movement, not being restricted to objects with repetitions in their movement. We present algorithms to detect the repetitions and to convert to the periodic representation as well as the implementation of some operations on such representation. We claim that the data volume can be drastically reduced when repetitions in movements occur. Moreover, some operations can take advantage on the data representation and therefore have their performance improved. We show, in an experimental evaluation against the so-called flat representation, that the approach presented in this paper significantly improves the performance of query processing in a database system when dealing with objects with some periodic movement. We also show that, for the worst case where the objects do not follow any periodic movement at all, our approach still performs acceptably. 1.

Abstract. This paper develops a formal model of topological relations between a directed line segment (DLine) and a region in a two-dimensional space. Such model forms a foundation for characterizing movement patterns of an agent with respect to a region. The DLine-region relations are captured by the 9intersection for line-region relations with further distinction of the line’s boundary into two subparts (starting and ending points). This 9 +-intersection distinguishes 26 topological DLine-region relations. The relations ’ conceptual neighborhood graph takes the shape of a V-shaped tube, whose upper and lower halves are isomorphic to the conceptual neighborhood graph of 19 topological line-region relations. The conceptual neighborhood graph of the 26 DLineregion relations is applied to the iconic representation of movement patterns that satisfy a qualitative condition. By manipulating such iconic representations, the movement patterns that satisfy complex conditions are easily deduced. 1.

In this paper, we propose to study the interest of relaxing qualitative constraints networks by using the formalism of discrete Constraint Satisfaction Problem (CSP). This allows us to avoid the introduction of new definitions and properties in the domain of qualitative reasoning. We first propose a general (but incomplete) approach to show the unsatisfiability of qualitative networks, by using a relaxation on any set of relations. Interestingly enough, for some qualitative calculi, the proposed scheme can be extended to determine the satisfiability of any qualitative network, leading to an original, simple and complete method. However, as the efficiency of our approach depends on the chosen relaxation, total relations should be preferred due to their connections with the hardness of constraint networks. We then present some preliminary experimental results, with respect to unsatisfiability, which show some promising improvements on some classes of random qualitative networks.