Improved Compact Routing Tables for Planar Networks via Orderly Spanning Trees

• Authors: Hsueh-I Lu
• Venue: COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
• Year: 2002

We address the problem of designing compact routing tables for an unlabeled connected n-node planar network G. For each node r of G, the designer is given a routing spanning tree Tr of G rooted at r, which specifies the routes for sending packets from r to the rest of G. Each node r of G is equipped with ports 1, 2, . . . , dr, where dr is the degree of r in Tr. Each port of r is supposed to be assigned to a neighbor of r in Tr in a one-to-one manner. For each node v of G with v 驴 r, let portr(v) be the port to which r should forward packets with destination v. Under the assumption that the designer has the freedom to determine the label and the port assignment of each node in G, the routing table design problem is to design a compact routing table Rr for r such that portr(v) can be determined only from Rr and the label of v.Compact routing tables for various network topologies have been extensively studied in the literature. Planar networks are particularly important for routing with geometric metrics. Based upon four-page decompositions of G, Gavoille and Hanusse gave the best previously known result for this problem: Each portr(v) is computable in O(log2+驴 n) bit operations for any positive constant 驴; and the number of bits required to encode their Rr is at most 8n + o(n). We give a new design that improves the code length of Rr to at most 7.181n + o(n) bits without increasing the time required to compute portr(v).