Lower Bounds for Interval Routing on BoundedDegree

Interval Routing was introduced to reduce the size of the routing tables: a router nds the direction to forward a message by determining the interval that contains the destination address of the message, each interval being associated to one particular direction. In this paper, we give lower bounds for the minimum number of intervals per edge needed to achieve shortest path routing for the class of 3-regular networks. We prove a tight lower bound of (n) intervals for a 3-regular network of order at most n. Moreover, for the particular case of 3-regular planar networks, we establish a lower bound of (p n) intervals. This lower bound is also proved for 4-regular and 5-regular planar graphs, and bounded degree planar graphs whose all the faces are triangles.