A lower bound for interval routing in general networks

Interval routing is a space-efficient routing method for point-to-point communication networks. Themethod has drawn considerable attention in recent years because of its being incorporated into the design of a commercially available routing chip. Themethod is based on proper labeling of edges of the graphwith intervals. An optimal labelingwould result in routing of messages through the shortest paths. Optimal labelings have existed for regular aswell as some of the common topologies, but not for arbitrarygraphs. In fact, it has already been shown that it is impossible to find optimal labelings for arbitrary graphs. In this paper, we prove a 7D=4 1 lower bound for interval routing in arbitrary graphs, where D is the diameter—i.e., the best any interval labeling scheme could do is to produce a longest path having a length of at least 7D=4 1.