On Implementing Stabilizing Leader Election with Weak Assumptions on Network Dynamics

Abstract

We consider self-stabilization and its weakened form called pseudostabilization. We study conditions under which (pseudo-and self-) stabilizing leader election is solvable in networks subject to frequent topological changes. To model such an high dynamics, we use the dynamic graph (DG) paradigm and study a taxonomy of nine important DG classes. Our results show that self-stabilizing leader election can only be achieved in the classes where all processes are sources. Furthermore, even pseudo-stabilizing leader election cannot be solved in all remaining classes, except in the class where at least one process is a timely source. We illustrate that result by proposing a pseudo-stabilizing leader election algorithm for the latter class. We also show that in this last case, the convergence time of pseudo-stabilizing leader election algorithms cannot be bounded. Nevertheless, we show that our solution is speculative since its convergence time can be bounded when the dynamics is not too erratic, precisely when all processes are timely sources.

On Implementing Stabilizing Leader Election with Weak Assumptions on Network Dynamics † ‡

“…⊈ (1) This first part of the proof compares DGs with a source (resp. a sink) against all to all DGs.…”

“…Nevertheless, we show † This study has been partially supported by the French anr project ANR-22-CE25-0008-01 (SkyData). ‡ A preliminary version of this paper has been published in the proceedings of PODC'2021 [1].…”

Simple, strict, proper, happy: A study of reachability in temporal graphs

“…There has been a large number of studies related to temporal reachability in the past decade, seen from various perspectives, e.g. k-connectivity and separators [27,24,19], components [7,4,2,30], feasibility of distributed tasks [14,25,3,9], schedule design [11], data structures [12,32,30,10], reachability minimization [21], reachability with additional constraints [12,15], temporal spanners [4,2,16,8], path enumeration [22], random graphs [6,17], exploration [26,20,23], and temporal flows [1,31], to name a few (many more exist). Over the course of these studies, it has become clear that temporal connectivity differs significantly from classical reachability in static graphs.…”