Extracting nonplanar connections in a terminal-vertex graph

This paper proposes a method for extracting a spanning planar subgraph from a given graph called a terminal-vertex graph, in which a path or a directed cycle represents how pins of a given element of electrical circuits are located, and a net performs the connection requirement among pins. It is based on transforming the graph without changing the connection requirement of each net. Experimental results are provided to show the capability of the proposed method. Finding a smallest possible set of nonplanar connections or extracting a largest planar spanning subgraph of this graph has application to the routing problem in layout design of printed wiring boards or of VLSI