We investigate the importance of quorum sensing in the success of house-hunting of emigrating Temnothorax ant colonies. Specifically, we show that the absence of the quorum sensing mechanism leads to failure of consensus during emigrations. We tackle this problem through the lens of distributed computing by viewing it as a natural distributed consensus algorithm. We develop an agent-based model of the house-hunting process, and use mathematical tools such as conditional probability, concentration bounds and Markov mixing time to rigorously prove the negative impact of not employing the quorum sensing mechanism on emigration outcomes. Our main result is a high probability bound for failure of consensus without quorum sensing in a two-new-nest environment, which we further extend to the general multiple-new-nest environments. We also show preliminary evidence that appropriate quorum sizes indeed help with consensus during emigrations. Our work provides theoretical foundations to analyze why Temnothorax ants evolved to utilize the quorum rule in their house-hunting process.
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Quorum subsumption for heterogeneous quorum systems
Byzantine quorum systems provide higher throughput than proof-of-work and incur modest energy consumption. Further, their modern incarnations incorporate personalized and heterogeneous trust. Thus, they are emerging as an appealing candidate for global financial infrastructure. However, since their quorums are not uniform across processes anymore, the properties that they should maintain to support abstractions such as reliable broadcast and consensus are not well-understood. It has been shown that the two properties quorum intersection and availability are necessary. In this paper, we prove that they are not sufficient. We then define the notion of quorum subsumption, and show that the three conditions together are sufficient: we present reliable broadcast and consensus protocols, and prove their correctness for quorum systems that provide the three properties.
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- Award ID(s):
- 1942711
- PAR ID:
- 10491935
- Editor(s):
- Oshman, Rotem
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Journal Name:
- Leibniz International Proceedings in Informatics (LIPIcs):37th International Symposium on Distributed Computing (DISC 2023)
- Subject(s) / Keyword(s):
- Distributed Systems Impossibility Results Byzantine fault tolerance Computing methodologies → Distributed algorithms Computer systems organization → Availability Computer systems organization → Reliability
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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