Representing Space: A Hybrid Genetic Algorithm for Aesthetic Graph Layout

This paper describes a hybrid Genetic Algorithm (GA) that is used to improve the layout of a graph according to a number of aesthetic criteria. The GA incorporates spatial and topological information by operating directly with a graph based representation. Initial results show this to be a promising technique for positioning graph nodes on a surface and may form the basis of a more general approach for problems involving multi-criteria spatial optimisation

Expected Crossing Numbers

The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case where the edge-weights are independent random variables that are uniformly distributed on [0,1].Comment: 14 page

Crossing Numbers of Graphs, Lower Bound Techniques and Algorithms: A Survey

We give a survey of recent techniques for deriving lower bounds and algorithms for constructing upper bounds for several variations of the crossing number problem. Our aim is to emphasize the more general results or those results which have an algorithmic flavor, including the recent results of the outhors