Finding hypergraph transversals is a major algorithmic issue which was shown having many connections with the data mining area. In this paper, by defining a new Galois connection, we show that this problem is closely related to the mining of the so-called condensed representations of frequent patterns. This data mining formalization enables us to benefit… (More)
On one hand the graph isomorphism problem (GI) has received considerable attention due to its unresolved complexity status and its many practical applications. On the other hand a notion of compatible topologies on graphs has emerged from digital topology (see [5, 7, 17, 9, 14, 16]). In this article we study GI from the topological point of view. Firstly we… (More)
In this article we give a polynomial algorithm to recognize if any partial sub-hypergraph of a hypergraph has the Helly property.
In the framework of structural representations for applications in image understanding, we establish links between similarities, hypergraph theory and mathematical morphology. We propose new similarity measures and pseudo-metrics on lattices of hypergraphs based on morphological operators. New forms of these operators on hypergraphs are introduced as well.… (More)
Hypergraphs are a very powerful tool and can represent many problems. In this paper we define a new image representation based on hypergraphs. This representation conducts to a new lossless compression algorithm for images called HLC. We present the algorithm and give some experimental results proving its efficiency. Finally we show that this algorithm can… (More)