Homotopy theory and distributed computing
Homotopy theory and distributed computing
Algebraic topology has proved to be a very useful tool in addressing the computability of rendezvous problems in distributed computing. To date the tools used include the fundamental group and ordinary homology. This paper introduces more sophisticated techniques from homotopy theory involving the Hilton-Milnor Theorem in order to analyze whether rendezvous problems are solvable. A criterion is proved that ensures a solution given certain hypotheses. Families of examples are given when the hypotheses are satisfied and when they are not satisfied; these include new cases when homology alone suffices to ensure a solution and cases when homology needs to be supplemented by additional properties to obtain a solution.
distributed computing, rendezvous task, homotopy theory, geometric realization
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Liu, Xingwu
574ccdd3-f28a-40bc-ba28-f13014baff00
Wu, Jie
2ae4aab0-b362-47bd-b494-e25fb2ea0889
Yue, Yunguang
e9a715bd-e5ff-454f-bb78-e12b19b8063c
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Liu, Xingwu
574ccdd3-f28a-40bc-ba28-f13014baff00
Wu, Jie
2ae4aab0-b362-47bd-b494-e25fb2ea0889
Yue, Yunguang
e9a715bd-e5ff-454f-bb78-e12b19b8063c
Theriault, Stephen, Liu, Xingwu, Wu, Jie and Yue, Yunguang
(2026)
Homotopy theory and distributed computing.
Foundations of Data Science.
(doi:10.3934/fods.2026011).
Abstract
Algebraic topology has proved to be a very useful tool in addressing the computability of rendezvous problems in distributed computing. To date the tools used include the fundamental group and ordinary homology. This paper introduces more sophisticated techniques from homotopy theory involving the Hilton-Milnor Theorem in order to analyze whether rendezvous problems are solvable. A criterion is proved that ensures a solution given certain hypotheses. Families of examples are given when the hypotheses are satisfied and when they are not satisfied; these include new cases when homology alone suffices to ensure a solution and cases when homology needs to be supplemented by additional properties to obtain a solution.
Text
DC2 revised
- Accepted Manuscript
More information
Accepted/In Press date: 26 April 2026
e-pub ahead of print date: 6 May 2026
Keywords:
distributed computing, rendezvous task, homotopy theory, geometric realization
Identifiers
Local EPrints ID: 512351
URI: http://eprints.soton.ac.uk/id/eprint/512351
ISSN: 2639-8001
PURE UUID: f92f53ff-78ab-4fdb-876e-39d37e256adb
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Date deposited: 25 Jun 2026 16:48
Last modified: 20 Aug 2026 01:51
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Contributors
Author:
Xingwu Liu
Author:
Jie Wu
Author:
Yunguang Yue
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