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In this paper we define the notion of a block algebra, which is based upon a spatial application of Allen's interval algebra. In the Ô-dimensional Euclidean space, where Ô ½, we consider only blocks whose sides are parallel to the axes of some orthogonal basis. The block algebra consists of a set of relations (the block relations) together with the fundamental operations of composition, converse and intersection. The ½¿ Ô basic relations of this algebra constitute the exhaustive list of the relations possibly holding between two blocks. We are interested in the problem of testing the consistency of a set of spatial constraints between blocks, i.e. a block network. The consistency question for block networks is NP-complete. We first extend the notions of convexity and preconvexity to the block algebra. Similarly to the interval algebra case, convexity leads to a tractable set whereas, contrary to the interval algebra case, preconvexity leads to an intractable set. Nevertheless we characterize a tractable subset of the preconvex relations: the strongly preconvex relations. Moreover we show that strong preconvexity and ORD-Horn representability are the same.

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We improve the state-of-the-art method for checking the consistency of large qualitative spatial networks that appear in the Web of Data by exploiting the scale-free-like structure observed in their constraint graphs. We propose an implementation scheme that triangulates the constraint graphs of the input networks and uses a hash table based adjacency list to efficiently represent and reason with them. We generate random scale-free-like qualitative spatial networks using the Barabási-Albert (BA) model with a preferential attachment mechanism. We test our approach on the already existing random datasets that have been extensively used in the literature for evaluating the performance of qualitative spatial reasoners, our own generated random scale-free-like spatial networks, and real spatial datasets that have been made available as Linked Data. The analysis and experimental evaluation of our method presents significant improvements over the state-of-the-art approach, and establishes our implementation as the only possible solution to date to reason with large scale-free-like qualitative spatial networks efficiently.