On bounded load routings for modeling k-regular connection topologies

Abstract

The paper deals with the problem of modeling a k-regular topology over an existing network architecture by establishing virtual point-to-point communication paths, referred to as k-routing. We consider the question of the existence and minimisation of edge spread of k-routings with bounded edge load in undirected networks. Efficient algorithms are presented for determining minimal k-routings with edge load 1 and for certain cases with edge load 2. On the negative side, the problems of finding a 6-routing with load 2 and of minimising a 2-routing with load 2 are proven to be NP-haid (though the latter is approximable within 7/6). The results imply the AfP-hardness of the well known allto-all routing problem for bounded edge load. © Springer-Verlag Berlin Heidelberg 2005.