Fast tree numeration in networks with synchronized time

TL;DR

This paper introduces a linear-time protocol for dense network numeration and spanning tree construction, enabling efficient bridge detection and network analysis in unknown topologies.

Contribution

It presents a novel linear-time protocol for building dense numeration and spanning trees in unknown networks, with applications in bridge detection.

Findings

Numeration building time is linear in network size.

Each node learns about all network bridges.

Protocol matches informational lower bounds.

Abstract

In this article we present a protocol for building dense numeration in network with unknown topology. Additionally to a unique number each node as result of the protocol will get information about a spanning tree. This spanning tree is constructed during BFS search from the leader node. This property of the numeration can be useful in other tasks, as example we present a protocol for searching bridges in network. The time of numeration building in our protocol is linear in network size, simple informational lower bounds also linear (it is required at least linear number of bits for code tree structure). In bridges searching problem our protocol also heats lower linear bound: in result each node knows about all bridges.