How local constraints influence network diameter and applications to LCL generalizations

TL;DR

This paper explores how local constraints at nodes affect network diameter, providing new insights into the structure of unbounded degree graphs and implications for locally checkable labelings.

Contribution

It establishes new results on network diameter influenced by local rules, extending understanding to unbounded degree graphs in the context of LCL problems.

Findings

Network diameter bounds depend on local constraints.

Unbounded degree graphs exhibit different LCL behaviors than bounded ones.

Results impact the design and analysis of distributed algorithms.

Abstract

In this paper, we investigate how local rules enforced at every node can influence the topology of a network. More precisely, we establish several results on the diameter of trees as a function of the number of nodes, as listed below. These results have important consequences on the landscape of locally checkable labelings (LCL) on \emph{unbounded} degree graphs, a case in which our lack of knowledge is in striking contrast with that of \emph{bounded degree graphs}, that has been intensively studied recently. [See paper for full abstract.]