Interval routing schemes allow broadcasting with linear message-complexity

The purpose of compact routing is to provide a labeling of the nodes of a network and a way to encode the routing tables, so that routing can be performed efficiently (e.g., on shortest paths) whilst keeping the memory-space required to store the routing tables as small as possible. In this paper, we answer a long-standing conjecture by showing that compact routing may also assist in the performance of distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows broadcasting with a message-complexity of O(n), where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suffice to solve leader-election for any graph labeled by a shortest path interval routing scheme, improving the previous known bound of O(m + n). A general consequence of our result is that a shortest path interval routing scheme contains ample structural information to avoid developing ad-hoc or network-specific solutions for basic problems that distributed systems must handle repeatedly.