On the complexity of intersecting multiple circles for graphical display

Abstract

Many experiments in the biomedical field generate vast amounts of data. This is especially true for microarray experiments which measure the expression levels of thousands of genes simultaneously. In this context the display of functional information attributed to the individual gene is important to obtain an overview of the major processes involved. This set data can be displayed as Euler/Venn diagrams in which the circle size corresponds to the cardinality of the set. Efficient algorithms for the calculation of intersections of circles and their resulting boundary have not been published so far. We present two algorithms (one optimal) for intersecting these different sized circles to display set relationships.