Let G be a group given by a presentation. We study the decomposition of the elements of G as quotients of “positive” elements (the elements of G that can be expressed without using the inverses of the generators) in the special case when the presentation satisfies some syntactical condition. This approach works in particular for Artin’s braid groups, and results in a very simple quadratic algor...

We show that for any infinite cardinal κ , every complete lattice where each element has at most one complement can be regularly embedded into a uniquely complemented κ-complete lattice. This regular embedding preserves all joins and meets, in particular it preserves the bounds of the original lattice. As a corollary, we obtain that every lattice where each element has at most one complement ca...

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

For a graph search algorithm, the end vertex problem is concerned with which vertices of can be last visited by this algorithm. We characterize all maximum cardinality searches on chordal graphs and derive from characterization polynomial-time algorithm for graphs. It complemented proof NP-completeness same weakly also show linear-time algorithms deciding breadth-first interval lexicographic de...

While multi-agent systems have been successfully applied to combinatorial optimization, very few works concern their applicability to continuous optimization problems. In this article we propose a framework for modeling a continuous optimization problems as multi-agent system, which we call NDMO, by representing the problem as an agent graph, and complemented with optimization solving behaviors...