A new algorithm for finding an upper bound of the genus of a graph

Abstract

In this paper we discuss the problem of finding an upper bound on the genus of a graph. This problem has applications to circuit layouts. An electronic circuit may be modelled by a graph. By punching holes into the circuit board, one may be able to lay out the circuit so that no two wires cross. The smallest number of holes that are required for a given graph ( that models such a circuit) is called the genus of tbe graph. The number of holes in the surface equals the genus of the surface. Thus, finding an algorithm which approximates the genus of the graph which models the circuit is important. We present a new algorithm for finding an upper bound on the genus of a graph, which uses a combinatorial data structure called the PQ-tree data structure. Four additional PQ-tree templates are used to extend the basic combinatorial reduction process of the PQ-trees to consider a genus approximation algorithm.