The weightable quasi-pseudo-metric spaces have been introduced by Matthews as part of the study of the denotational semantics of dataflow networks (e.g. [Mat92] and [Mat92a]). The study of these spaces has been continued in the context of Nonsymmetric Topology by Kunzi and Vajner ([KV93] and [Kün93]). We introduce and motivate the class of upper weightable quasi-pseudo-metric spaces. The relati...

TREE is an optimized RETE-like pattern-matching algorithm. It has been designed for a production system whose restricted data formalism leads to a highly combinatorial join step like in SOAR. TREE aims at reducing the join search spaces without using hashing techniques. Its join strategy uses constraint propagation to define the solution space of a join, then a constraint relaxation to determin...

Similarity join is an interesting complement of the wellestablished similarity range and nearest neighbors search primitives in metric spaces. However, the quadratic computational complexity of similarity join prevents from applications on large data collections. We present MCAN, an extension of MCAN (a Content-Addressable Network for metric objects) to support similarity self join queries. The...

This paper presents a series of important results from the theory n-hypergroups. Connections with binary relations and lattices are presented. Special attention is paid to fundamental relation commutative relation. In particular, join n-spaces analyzed.

The terminology of addition and of multiplication may be readily extended to apply to homogeneous linear systems or to their geometrical interpretations, linear projective spaces. The product ab of two linear spaces a and b, denotes the intersection or greatest linear space common to the two given spaces. I t is thus the logical product of the spaces. The sum a+b denotes the join or least linea...

Given two sets S1, S2 of moving objects, a future timestamp tq, and a distance threshold d, a spatio-temporal join retrieves all pairs of objects that are within distance d at tq. The selectivity of a join equals the number of retrieved pairs divided by the cardinality of the Cartesian product S1 S2. This paper develops a model for spatio-temporal join selectivity estimation based on rigorous p...

Baer [1] observed that modular lattices of finite length (for example subgroup lattices of abelian groups) can be conceived as subspace lattices of a projective geometry structure on an ordered point set; the set of join irreducibles which in this case are the cyclic subgroups of prime power order. That modular lattices of finite length can be recaptured from the order on the points and, in add...

In two previous papers we introduced the notion of an Affine Klingenberg space A and presented a geometric description of its free subspaces. Presently, we consider the operations of join, intersection and parallelism on the free subspaces of A. As in the case of ordinary affine spaces, we obtain the Parallel Postulate. The situation with join and intersection is not that straightforward. In pa...