On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks

2025-05-22

AI Summary

This paper addresses the local mutual exclusion problem for distributed nodes in anonymous dynamic networks: each node, upon issuing a lock request, must exclusively access itself and all its persistent neighbors. To tackle adversarial edge dynamics and asynchronous communication, we propose the first randomized local mutual exclusion algorithm with provable runtime guarantees. Our approach employs a semi-synchronous/asynchronous concurrent model, formalizes persistent neighbors, and introduces an open-rounds analytical framework. The main contribution is the first derivation of an expected convergence time upper bound of $O(nDelta^3)$, overcoming the prior absence of runtime analysis for this problem. Moreover, the algorithm strictly ensures mutual exclusion and lockout-freedom. These results yield the first provably efficient solution for local coordination in dynamic distributed systems.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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$(nDelta^3)$ 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).

Problem

• Analyzing runtime of local mutual exclusion in dynamic networks
• Ensuring exclusive locks on nodes and persistent neighbors
• Adversarial edge dynamics and anonymous nodes considered

Innovation

• Randomized algorithm for dynamic networks
• Ensures mutual exclusion and lockout freedom
• O(nΔ³) expected runtime for locking