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Abstract.We report an experience on a practical system for drawing hypergraphs in the subset standard. The Patate system is based on the application of a classical force directed method to a dynamic graph, which is deduced, at a given iteration time, from the hypergraph structure and particular vertex locations. Different strategies to define the dynamic underlying graph are presented. We illustrate in particular the method when the graph is obtained by computing an Euclidean Steiner tree.

Abstract. We show that every integer between 1290741 and 3.375 × 10 12 is a sum of 5 nonnegative cubes, from which we deduce that every integer which is a cubic residue modulo 9 and an invertible cubic residue modulo 37 is a sum of 7 nonnegative cubes.

We present a new algorithm, called Nuage, for drawing graphs with both adjacency and inclusion relationships between nodes, that is, compound graphs. Compound graphs are more general than classical graph models or clustered graphs. Nuage can be applied to both directed and undirected compound graphs. It can be parameterized by classical graph drawing algorithms. Nuage can be viewed as a method for unifying several classical algorithms within the same drawing by using the structure of the compound graph. Additionally, we present a refinement technique that can be used in conjunction with Nuage to reduce the number of edge crossings.

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