Visualization of Bipartite Graphs in Limited Window Size

Abstract

Bipartite graphs are commonly used to visualize objects and their features. An object may possess several features and several objects may share a common feature. The standard visualization of bipartite graphs, with objects and features on two (say horizontal) parallel lines at integer coordinates and edges drawn as line segments, can often be difficult to work with. A common task in visualization of such graphs is to consider one object and all its features. This naturally defines a drawing window, defined as the smallest interval that contains the x-coordinates of the object and all its features. We show that if both objects and features can be reordered, minimizing the average window size is NP-hard. However, if the features are fixed, then we provide an efficient polynomial time algorithm for arranging the objects, so as to minimize the average window size. Finally, we introduce a different way of visualizing the bipartite graph, by placing the nodes of the two parts on two concentric circles. For this setting we also show NP-hardness for the general case and a polynomial time algorithm when the features are fixed.