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 space. 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. 1