An algorithm for embedding a class of non-even routing problems in even routing problems

The authors present part of a complete solution of a two-terminal net routing problem for certain non-convex grids without holes that they call channel graphs. They present an algorithm for embedding a non-even channel graph routing problem in an even channel graph routing problem. They 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 M. Becker and K. Mehlhorn (1986) for planar graphs. Due to the restrictions the authors place on the shape of channel graph routing problems they are able to obtain a lower complexity for their 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