  N-ary relationships, which relate N entities where N is not necessarily two,
can be visually represented as polygons whose vertices are the entities of the
relationships. Manually generating a high-quality layout using this
representation is labor-intensive. In this paper, we provide an automatic
polygon layout generation algorithm for the visualization of N-ary
relationships. At the core of our algorithm is a set of objective functions
motivated by a number of design principles that we have identified. These
objective functions are then used in an optimization framework that we develop
to achieve high-quality layouts. Recognizing the duality between entities and
relationships in the data, we provide a second visualization in which the roles
of entities and relationships in the original data are reversed. This can lead
to additional insight about the data. Furthermore, we enhance our framework for
a joint optimization on the primal layout (original data) and the dual layout
(where the roles of entities and relationships are reversed). This allows users
to inspect their data using two complementary views. We apply our visualization
approach to a number of datasets that include co-authorship data and social
contact pattern data.
