Motion planning is the problem of computing valid paths through an environment. However, because computing exact solutions is intractable, sampling-based algorithms, such as Probabilistic RoadMaps (PRMs), have gained popularity. PRMs compute an approximate mapping of the planning space by sacrificing completeness in favor of efficiency. However, these algorithms have certain bottlenecks that hi...

In recent works, a new notion of component-graph has been introduced to extend the data structure of component-tree –and the induced antiextensive filtering methodologies– from grey-level images to multivalued ones. In this article, we briefly recall the main structural key-points of component-graphs, and we present the first algorithmic results that open the way to the actual development of co...

Using the modified linear quadtree proposed in [1,9], this paper presents an O(n·N) algorithm for labeling connected components of a region consisting of N BLACK nodes in a 2n by 2n binary image. As a direct application of the algorithm, a method for computing the perimeter of a region is also described.

Studies on the real-time detection of connected components in graph streams have been carried out. The existing component method cannot process incrementally, and performance deteriorates due to frequent data transmission when GPU is used. In this paper, we propose a new incremental processing solve problems found methods for detecting GPUs. proposed minimizes amount be sent by determining subg...

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...