## Section: New Results

### Graph Drawing

Participants : David Auber, Romain Bourqui, Antoine Lambert, Arnaud Sallaberry, Paolo Simonetto.

#### Edge Bundling

Visualizing graphs containing many nodes and edges efﬁciently is quite challenging. Drawings of such graphs generally suffer from visual clutter induced by the large amount of edges and their crossings. Consequently, it is difﬁcult to read the relationships between nodes and the high-level edge patterns that may exist in standard node- link diagram representations. Edge bundling techniques have been proposed to help solve this issue, which rely on high quality edge rerouting. We introduce in [16] an intuitive edge bundling technique which efﬁciently reduces edge clutter in graphs drawings. Our method is based on the use of a grid built using the original graph to compute the edge rerouting. In comparison with previously proposed edge bundling methods, our technique improves both the level of clutter reduction and the computation performance. The second contribution of this paper is a GPU-based rendering method which helps users perceive bundles densities while preserving edge color.

In [24] , we present a generalization of [16] to reduce the clutter in a 3D representation by routing edges into bundles as well as a GPU-based rendering method to emphasize bundles densities while preserving edge color. To visualize geographical networks in the context of the globe, we also provide a new technique allowing to bundle edges around and not across it.

#### Pattern visualization

Data mining techniques allow users to discover novelty in huge amounts of data. Frequent pattern methods have proved to be efficient, but the extracted patterns are often too numerous and thus difficult to analyze by end-users. In [26] , we focus on sequential pattern mining and propose a new visualization system, which aims at helping end-users to analyze extracted knowledge and to highlight the novelty according to referenced biological document databases. Our system is based on two visualization techniques: Clouds and solar systems. We show that these techniques are very helpful for identifying associations and hierarchical relationships between patterns among related documents. Sequential patterns extracted from gene data using our system were successfully evaluated by two biology laboratories working on Alzheimer disease and cancer.

#### Hypergraph

A path-based support of a hypergraph H is a graph with the same vertex set as H in which each hyperedge induces a Hamiltonian subgraph. While it is NP-complete to compute a path-based support with the minimum number of edges or to decide whether there is a planar path-based support, we show in [20] that a path-based tree support can be computed in polynomial time if it exists.

In [19] , we show how to test in polynomial time whether a given hypergraph has a cactus support, i.e. a support that is a tree of edges and cycles. While it is NP-complete to decide whether a hypergraph has a 2-outerplanar support, we show how to test in polynomial time whether a hypergraph that is closed under intersections and differences has an outerplanar or a planar support. In all cases our algorithms yield a construction of the required support if it exists. The algorithms are based on a new definition of biconnected components in hypergraphs.