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Two subsets of vertices in a graph are called homometric if the multisets of distances determined by them are the same. Let h(n) denote the largest number h such that any connected graph of n vertices contains two disjoint homometric subsets of size h. It ...
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying th ...
Institute of Electrical and Electronics Engineers2011
We analyse the results of our experimental laboratory approximation of motorways networks with slime mould Physarum polycephalum. Motorway networks of fourteen geographical areas are considered: Australia, Africa, Belgium, Brazil, Canada, China, Germany, I ...
Clustering on graphs has been studied extensively for years due to its numerous applications. However, in contrast to the classic problems, clustering in mobile and online social networks brings new challenges. In these scenarios, it is common that observa ...
Implementing machine learning algorithms for large data, such as the Web graph and social networks, is challenging. Even though much research has focused on making sequential algorithms more scalable, their running times continue to be prohibitively long. ...
The obstacle number of a graph G is the smallest number of polygonal obstacles in the plane with the property that the vertices of G can be represented by distinct points such that two of them see each other if and only if the corresponding vertices are jo ...
In this paper we deal with the critical node problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the (weighted or unweighted) number of connections between pairs of nodes in the residual graph. ...
The obstacle number of a graph G is the smallest number of polygonal obstacles in the plane with the property that the vertices of G can be represented by distinct points such that two of them see each other if and only if the corresponding vertices are jo ...
We introduce a family of reductions for removing proper and homogeneous pairs of cliques from a graph G. This family generalizes some routines presented in the literature, mostly in the context of claw-free graphs. These reductions can be embedded in a sim ...
Artificial neural networks, electronic circuits, and gene networks are some examples of systems that can be modeled as networks, that is, as collections of interconnected nodes. In this paper we introduce the concept of terminal graph (t-graph for short), w ...