The Performance on Slope Number of Hypercube, Normal Representation of Butterfly and Benes Networks

Abstract

Many quality measures have been defined for graph drawings. In order to optimize these measures, slope number is considered to minimize the distinct edge slopes. The edges of the graphs are designed here as straight line segments. A number of distinct slopes required to draw the graph is called slope number. In this paper the slopenumber is discussed for known parallel architectures like hypercube, butterfly and benes networks. In addition to that the characterization of these networks is investigated and the results are observed for the defined problem.