Two-Layered Genetic Network Drawings with Minimum Edge Crossings

Abstract

Inference of genetic networks from expression profile data is one of the challenging works in the field of the array informatics. A good visualization tool for the inferred networks would help us to deepen our understandings of the interactions among the genes. Here, we focus on the time series data of expression profiles, and discuss the method to draw a two-layered graph representing the causality among the genes. Consider that the causality among the genes is given. The two layers in the graph correspond to time steps t and t+ 1, respectively. Each vertex in a layer corresponds to a gene. The causality between a pair of genes is expressed as an edge from a vertex in the layer for time t to a vertex in the layer for time t+ 1. There is a restriction for drawing a two-layered graph for a genetic network that the same gene should occupy the same positions in the two layers. In drawing a visually understandable graph on a plane, readability, i.e., aesthetic criteria, is indispensable. Minimizing the edge crossings is the most popular aesthetic criterion [1] and we employ it to obtain a drawing to read easily. In general, the problem to minimize the edge crossings of a graph is called the minimum crossing number problem. There have been many studies on the problem, especially for a two-layered graph [2, 4, 5]. We have dealed with a the problem to find a drawing under the restriction with the minimum number of edge crossing and have presented a heuristics for the problem for the first time [6]. However, since the heuristics needs large resources, it is hard to use for huge graph like genetic networks. Now we present another algorithm that runs at higher speed. Furthermore, we show that the algorithm can output better solutions than the previous one.