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On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks

Authors Anya Chaturvedi , Joshua J. Daymude , Andréa W. Richa

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Concurrency
  • Software and its engineering → Mutual exclusion
Keywords
  • Mutual exclusion
  • dynamic networks
  • message passing
  • concurrency

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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(nΔ³) open rounds of its lock request in expectation, where n is the number of nodes in the dynamic network, Δ 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).

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Anya Chaturvedi, Joshua J. Daymude, and Andréa W. Richa. On the Runtime of Local Mutual Exclusion for Anonymous Dynamic Networks. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SAND.2025.15

Author Details

Anya Chaturvedi
  • School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, USA
Joshua J. Daymude
  • School of Computing and Augmented Intelligence, Biodesign Center for Biocomputing, Security and Society, Arizona State University, Tempe, AZ, USA
Andréa W. Richa
  • School of Computing and Augmented Intelligence, Biodesign Center for Biocomputing, Security and Society, Arizona State University, Tempe, AZ, USA

Funding

  • Chaturvedi, Anya: NSF (CCF-2312537) and U.S. ARO (MURI W911NF-19-1-0233).
  • Daymude, Joshua J.: NSF (CCF-2312537).
  • Richa, Andréa W.: NSF (CCF-2312537, CCF-2106917) and U.S. ARO (MURI W911NF-19-1-0233).

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