Crossing Minimization in k-layer graphs

Abstract

The crossing minimization problem in graphs has been extensively studied for the case when graphs are to be embedded on two layers. There are many well known heuristics for the 2-layer crossing minimization problem, like, for example, the barycenter and the median heuristic. The problem has not been studied much for k-layer graphs. The k-layer graph crossing minimization problem has specific application in aesthetic design of hierarchical structures, in VLSI circuit design to reduce the total wire length and crosstalk, and in various organization charts, flow diagrams and large graphs that arise in activity-based management.

In our thesis work, we have extended the 2-layer graph heuristics to the crossing minimization problem for k-layer graphs. We have proposed twenty six heuristics for the k-layer graph problem. We have tested all the proposed heuristics on various classes of graphs instances including the structures that arise in activity-based management. The proposed heuristics have significantly outperformed the traditional sweep based heuristics. Additional experiments performed on the best performing heuristics have helped us to propose new enhancements on those heuristics, which have improved the performance of the heuristics further.