Papers by Mahsa Eftekhari
A stable majority population protocol using logarithmic time and states
ArXiv, 2020
We study population protocols, a model of distributed computing appropriate for modeling well-mix... more We study population protocols, a model of distributed computing appropriate for modeling well-mixed chemical reaction networks and other physical systems where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied majority problem is that of determining in an initial population of n agents, each with one of two opinions A or B, whether there are more A, more B, or a tie. A stable protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of A, B, or T, from which the consensus cannot change. We describe a protocol that solves this problem using O(logn) states (log logn + O(1) bits of memory) and optimal expected time O(logn). The number of states O(logn) is known to be optimal for the class of stable protocols that are “output dominant” and “monotone” [2]. These are two natural constraints satisfied by our protocol, m...
Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing, 2021
We study population protocols, a model of distributed computing where agents exchange information... more We study population protocols, a model of distributed computing where agents exchange information in pairwise interactions, but have no control over their schedule of interaction partners. The well-studied majority problem is that of determining in an initial population of n agents, each with one of two opinions A or B, whether there are more A, more B, or a tie. A stable protocol solves this problem with probability 1 by eventually entering a configuration in which all agents agree on a correct consensus decision of A, B, or T, from which the consensus cannot change. We describe a protocol that solves this problem using O(log n) states (log log n + O(1) bits of memory) and optimal expected time O(log n). The number of states O(log n) is known to be optimal for the class of polylogarithmic time stable protocols that are "output dominant'' and "monotone''. These are two natural constraints satisfied by our protocol, making it simultaneously time- and state-o...
e standard population protocol model assumes that when two agents interact, each observes the ent... more e standard population protocol model assumes that when two agents interact, each observes the entire state of the other agent. We initiate the study of the message complexity for population protocols, where the state of an agent is divided into an externally-visible message and an internal component, where only the message can be observed by the other agent in an interaction. We consider the case of O (1) message complexity. When time is unrestricted, we obtain an exact characterization of the stably computable predicates based on the number of internal states s(n): If s(n) = o(n) then the protocol computes a semilinear predicate (unlike the original model, which can compute non-semilinear predicates with s(n) = O (log n)), and otherwise it computes a predicate decidable by a nondeterministic O (n log s(n))-space-bounded Turing machine. We then consider time complexity, introducing novel O (polylog(n)) expected time protocols for junta/leader election and general purpose broadcast correct with high probability, and approximate and exact population size counting correct with probability 1. Finally, we show that the main constraint on the power of bounded-message-size protocols is the size of the internal states: with unbounded internal states, any computable function can be computed with probability 1 in the limit by a protocol that uses only one-bit messages.
The population protocol model describes a network of n anonymous agents who cannot control with w... more The population protocol model describes a network of n anonymous agents who cannot control with whom they interact. The agents collectively solve some computational problem through random pairwise interactions, each agent updating its own state in response to seeing the state of the other agent. They are equivalent to the model of chemical reaction networks, describing abstract chemical reactions such as A + B → C +D, when the latter is subject to the restriction that all reactions have two reactants and two products, and all rate constants are 1. The counting problem is that of designing a protocol so that n agents, all starting in the same state, eventually converge to states where each agent encodes in its state an exact or approximate description of population size n. In this survey paper, we describe recent algorithmic advances on the counting problem.
Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing - PODC '19, 2019
We study uniform population protocols: networks of anonymous agents whose pairwise interactions a... more We study uniform population protocols: networks of anonymous agents whose pairwise interactions are chosen at random, where each agent uses an identical transition algorithm that does not depend on the population size n. Many existing polylog(n) time protocols for leader election and majority computation are nonuniform: to operate correctly, they require all agents to be initialized with an approximate estimate of n (specifically, the value log n). Our first main result is a uniform protocol for calculating log(n) ± O(1) with high probability in O(log 2 n) time and O(log 4 n) states (O(log log n) bits of memory). The protocol is not terminating: it does not signal when the estimate is close to the true value of log n. If it could be made terminating with high probability, this would allow composition with protocols requiring a size estimate initially. We do show how our main protocol can be indirectly composed with others in a simple and elegant way, based on leaderless phase clocks, demonstrating that those protocols can in fact be made uniform. However, our second main result implies that the protocol cannot be made terminating, a consequence of a much stronger result: a uniform protocol for any task requiring more than constant time cannot be terminating even with probability bounded above 0, if infinitely many initial configurations are dense: any state present initially occupies Ω(n) agents. (In particular no leader is allowed.) Crucially, the result holds no matter the memory or time permitted. Finally, we show that with an initial leader, our size-estimation protocol can be made terminating with high probability, with the same asymptotic time and space bounds.
We study population protocols: networks of anonymous agents that interact under a scheduler that ... more We study population protocols: networks of anonymous agents that interact under a scheduler that picks pairs of agents uniformly at random. The _size counting problem_ is that of calculating the exact number $n$ of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem in sublinear time. The protocol converges in $O(\log n \log \log n)$ time and uses $O(n^{60})$ states ($O(1) + 60 \log n$ bits of memory per agent) with probability $1-O(\frac{\log \log n}{n})$. The time complexity is also $O(\log n \log \log n)$ in expectation. The time to converge is also $O(\log n \log \log n)$ in expectation. Crucially, unlike most published protocols with $\omega(1)$ states, our protocol is _uniform_: it uses the same transition algorithm for any population size, so does not need an estimate of the population size to be embedded into the algorithm. A sub-protocol is the first uniform sublinear-time leader election po...
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Papers by Mahsa Eftekhari