Time-Optimal Leader Election in Population Protocols

Sudo, Yuichi; Ooshita, Fukuhito; Izumi, Taisuke; Kakugawa, Hirotsugu; Masuzawa, Toru

doi:10.1109/tpds.2020.2991771

Cited by 13 publications

(28 citation statements)

References 18 publications

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“…We initiate the study of the limits of time efficiency or the time/space trade-offs for SSLE in the standard population protocol model, in the complete interaction graph. The most related protocol, of Cai, Izumi, and Wada [22] (Silent-n-state-SSR, Protocol 1), given for complete graphs, uses exactly states and Θ( 2 ) expected parallel time , exponentially slower than the polylog( )-time non-self-stabilizing existing solutions [14,36,37,43,55]. Our main results are two faster protocols, each making a different time/space tradeoff.…”

Section: Contributionmentioning

confidence: 88%

“…We note that any protocol solving SSLE requires Ω(log ) time: from any configuration where all agents are leaders, by a coupon collector argument, it takes Ω(log ) time for − 1 of them to interact and become followers. (This argument uses the self-stabilizing assumption that "all-leaders" is a valid initial configuration; otherwise, for initialized leader election, it requires considerably more care to prove an Ω(log ) time lower bound [55]. )…”

Section: Contributionmentioning

confidence: 99%

“…Leader election has recently been shown to be solvable with optimal (log ) parallel time and (log log ) states [14], improving on recent work meeting this space bound in time (log 2 ) [36] and (log log log ) [37]. Another work presents a simpler (log )-time, (log )-state protocol [55]. It may appear obvious that any leader election protocol requires Ω(log ) time, but this requires a nontrivial proof [54].…”

Section: Introductionmentioning

confidence: 97%

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Time-Optimal Self-Stabilizing Leader Election in Population Protocols

Burman

Chen

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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We consider the standard population protocol model, where (a priori) indistinguishable and anonymous agents interact in pairs according to uniformly random scheduling. The self-stabilizing leader election problem requires the protocol to converge on a single leader agent from any possible initial configuration. We initiate the study of time complexity of population protocols solving this problem in its original setting: with probability 1, in a complete communication graph. The only previously known protocol by Cai, Izumi, and Wada [Theor. Comput. Syst. 50] runs in expected parallel time Θ( 2 ) and has the optimal number of states in a population of agents. The existing protocol has the additional property that it becomes silent, i.e., the agents' states eventually stop changing.Observing that any silent protocol solving self-stabilizing leader election requires Ω( ) expected parallel time, we introduce a silent protocol that uses optimal ( ) parallel time and states. Without any silence constraints, we show that it is possible to solve self-stabilizing leader election in asymptotically optimal expected parallel time of (log ), but using at least exponential states (a quasipolynomial number of bits). All of our protocols (and also that of Cai et al.) work by solving the more difficult ranking problem: assigning agents the ranks 1, . . . , .

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Section: Contributionmentioning

confidence: 88%

Section: Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

Time-Optimal Self-Stabilizing Leader Election in Population Protocols

Burman

Chen

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

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“…However, there are example large count systems with stochastic effects not observed in ODE simulation, and where τ -leaping introduces systematic inaccuracies that disrupt the fundamental qualitative behavior of the system, demonstrating the need for exact stochastic simulation. A simple such example is the 3-state rock-paper-scissors oscillator: The population protocol literature furnishes more examples, with problems such as leader election [4,7,9,10,15,17,19,20,32,33] and single-molecule detection [3,16], 5 that crucially use small counts in a very large population, a regime not modelled correctly by ODEs. See also [26] for examples of CRNs with qualitative stochastic behavior not captured by ODEs, yet that behavior appears only in population sizes too large to simulate with Gillespie.…”

Section: Issues With Other Speedup Methodsmentioning

confidence: 99%

ppsim: A software package for efficiently simulating and visualizing population protocols

Doty¹,

Severson²

2021

Preprint

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We introduce ppsim [2], a software package for efficiently simulating population protocols, a widely-studied subclass of chemical reaction networks (CRNs) in which all reactions have two reactants and two products. Each step in the dynamics involves picking a uniform random pair from a population of n molecules to collide and have a (potentially null) reaction. In a recent breakthrough, Berenbrink, Hammer, Kaaser, Meyer, Penschuck, and Tran [ESA 2020] discovered a population protocol simulation algorithm quadratically faster than the naïve algorithm, simulating Θ( √ n) reactions in constant time, while preserving the exact stochastic dynamics.ppsim implements this algorithm, with a tightly optimized Cython implementation that can exactly simulate hundreds of billions of reactions in seconds. It dynamically switches to the CRN Gillespie algorithm for efficiency gains when the number of applicable reactions in a configuration becomes small. As a Python library, ppsim also includes many useful tools for data visualization in Jupyter notebooks, allowing robust visualization of time dynamics such as histogram plots at time snapshots and averaging repeated trials.Finally, we give a framework that takes any CRN with only bimolecular (2 reactant, 2 product) or unimolecular (1 reactant, 1 product) reactions, with arbitrary rate constants, and compiles it into a continuous-time population protocol. This lets ppsim exactly sample from the chemical master equation (unlike approximate heuristics such as τ -leaping or LNA), while achieving asymptotic gains in running time. In linked Jupyter notebooks, we demonstrate the efficacy of the tool on some protocols of interest in molecular programming, including the approximate majority CRN and CRN models of DNA strand displacement reactions.

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“…ree empirical techniques were employed in a cohesive way for calculating the proper status of leaders in a polynomial period. Another model for leader node selection was introduced in [48] based on employing the probabilistic grounded framework. e work had presented the improvements on the energy consumption and the consistency problem of channel communication.…”

Section: Related Workmentioning

confidence: 99%

Head Node Selection Algorithm in Cloud Computing Data Center

Kanwal

Iqbal

Irtaza

et al. 2021

Mathematical Problems in Engineering

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Cloud computing provides multiple services such as computational services, data processing, and resource sharing through multiple nodes. These nodes collaborate for all prementioned services in the data center through the head/leader node. This head node is responsible for reliability, higher performance, latency, and deadlock handling and enables the user to access cost-effective computational services. However, the optimal head nodes’ selection is a challenging problem due to consideration of resources such as memory, CPU-MIPS, and bandwidth. The existing methods are monolithic, as they select the head nodes without taking the resources of the nodes. Still, there is a need for the candidate node which can be selected as a head node in case of head node failure. Therefore, in this paper, we proposed a technique, i.e., Head Node Selection Algorithm (HNSA), for optimal head node selection from the data center, which is based on the genetic algorithm (GA). In our proposed method, there are three modules, i.e., initial population generation, head node selection, and candidate node selection. In the first module, we generate the initial population by randomly mapping the task on different servers using a scheduling algorithm. After that, we compute the overall cost and the cost of each node based on resources. In the second module, the best optimal nodes are selected as a head node by applying the genetic operations such as crossover, mutation, and fitness function by considering the available resources. In the selected optimal nodes, one node is chosen as a head node and the other is considered as a candidate node. In the third module, the candidate node becomes the head node in the case of head node failure. The proposed method HNSA is compared against the state-of-the-art algorithms such as Bees Life Algorithm (BLA) and Heterogeneous Earliest Finished Time (HEFT). The simulation analysis shows that the proposed HNSA technique performs better in terms of execution time, memory utilization, service level sgreement (SLA) violation, and energy consumption.

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Time-Optimal Leader Election in Population Protocols

Cited by 13 publications

References 18 publications

Time-Optimal Self-Stabilizing Leader Election in Population Protocols

Time-Optimal Self-Stabilizing Leader Election in Population Protocols

ppsim: A software package for efficiently simulating and visualizing population protocols

Head Node Selection Algorithm in Cloud Computing Data Center

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