Determination of the Topology of a Directed Network

TL;DR

This paper presents an efficient protocol for determining the topology of strongly-connected directed networks of identical finite-state processors, achieving near-optimal time complexity for large networks.

Contribution

It extends existing algorithms to solve the global topology determination problem with an asymptotically optimal protocol in terms of time complexity.

Findings

Protocol solves the topology determination problem in O(ND) time.

The problem has a lower bound of Omega(N log N) time.

The proposed protocol is asymptotically time-optimal for large networks.

Abstract

We consider strongly-connected directed networks of identical synchronous, finite-state processors with in- and out-degree uniformly bounded by a network constant. Via a straightforward extension of Ostrovsky and Wilkerson's Backwards Communication Algorithm in [OW], we exhibit a protocol which solves the Global Topology Determination Problem, the problem of having the root processor map the global topology of a network of unknown size and topology, with running time O(ND) where N represents the number of processors and D represents the diameter of the network. A simple counting argument suffices to show that the Global Topology Determination Problem has time-complexity Omega(N logN) which makes the protocol presented asymptotically time-optimal for many large networks.