Online routing in quasi-planar and quasi-polyhedral graphs

We address the problem of online route discovery for a class of graphs that can be embedded either in two or in three dimensional spaces. In two dimensions, we propose the class of quasi-planar graphs and in three dimensions the class of quasi-polyhedral graphs. In both cases, we provide a routing algorithm that guarantees delivery. Our algorithms need only "remember" the source and destination nodes and one (respectively, two) reference nodes. Moreover, we show that the quasi-planar routing algorithm is inherently flexible in its path-finding, and as an application demonstrate computational results for a network load problem.