Algorithm for embedding a class of non-even routing problems in even routing problems

In this paper we present part of a complete solution of a two-terminal net routing problem for certain non-convex grids without holes that we call channel graphs. We present an algorithm for embedding a non-even channel graph routing problem in an even channel graph routing problem. We refer to the algorithm as EMBED. EMBED runs in time O(b), where b is the number of vertices on the boundary, and is similar to an algorithm described by Becker and Mehlhorn for planar graphs. Due to the restrictions we place on the shape of channel graph routing problems, however, we are able to obtain a lower complexity for our algorithm than that of the Becker and Mehlhorn algorithm. Their algorithm has complexity O(bn), where n is the number of vertices in the graph.