On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks

TL;DR

This paper analyzes the runtime of a randomized local mutual exclusion algorithm in dynamic networks, proving that nodes acquire locks within expected polynomial time bounds despite adversarial conditions.

Contribution

It provides the first runtime analysis of a local mutual exclusion algorithm in anonymous dynamic networks under adversarial edge dynamics.

Findings

Nodes lock within O(nΔ^3) open rounds in expectation.

The analysis applies to semi-synchronous and asynchronous models.

Locks are guaranteed despite adversarial network changes.

Abstract

Algorithms for mutual exclusion aim to isolate potentially concurrent accesses to the same shared resources. Motivated by distributed computing research on programmable matter and population protocols where interactions among entities are often assumed to be isolated, Daymude, Richa, and Scheideler (SAND`22) introduced a variant of the local mutual exclusion problem that applies to arbitrary dynamic networks: each node, on issuing a lock request, must acquire exclusive locks on itself and all its persistent neighbors, i.e., the neighbors that remain connected to it over the duration of the lock request. Assuming adversarial edge dynamics, semi-synchronous or asynchronous concurrency, and anonymous nodes communicating via message passing, their randomized algorithm achieves mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1). However, they did not analyze their algorithm's runtime. In this paper, we prove that any node will successfully lock itself and its persistent neighbors within O$(n\Delta^3)$ open rounds of its lock request in expectation, where $n$ is the number of nodes in the dynamic network, $\Delta$ is the maximum degree of the dynamic network, rounds are normalized to the execution time of the ``slowest'' node, and ``closed'' rounds when some persistent neighbors are already locked by another node are ignored (i.e., only ``open" rounds are considered).