We present RINGS, a technique for visualizing large trees. We introduce a new ringed circular layout of nodes to make more efficient use of limited display space. RINGS provides the user with the means to specify areas of primary and secondary focus, and is able to show multiple foci without compromising understanding of the graph. The strength of RINGS is its ability to show more area in focus and more contextual information than existing techniques. We demonstrate the effectiveness of RINGS by applying it to the visualization of a Unix file directory.

We study balanced circle packings and circle-contact representations for planar graphs, where the ratio of the largest circle’s diameter to the smallest circle’s diameter is polynomial in the number of circles. We provide a number of positive and negative results for the existence of such balanced configurations.