Compact routing tables for graphs of bounded genus (extended abstract)

Abstract

For planar graphs on n nodes we show how to construct in linear time shortest path routing tables that require 8n + o(n) bits per node, and O(log2+ε n) bit-operations per node to extract the route, with constant ε > 0. We generalize the result for every graph of bounded crossing-edge number. We also extend our result to any graph of genus bounded by , by building shortest path routing tables of n log ( γ + 1)+ O(n) bits per node, and with O(log2+ε n) bit-operations per node to extract the route. This result is obtained by the use of dominating sets, compact coding of non-crossing partitions, and k-page representation of graphs. © Springer-Verlag Berlin Heidelberg 1999.