We consider a set of k autonomous robots that are endowed with visibility sensors (but that are otherwise unable to communicate) and motion actuators. Those robots must collaborate to reach a single vertex that is unknown beforehand, and to remain there hereafter. Previous works on gathering in ring-shaped networks suggest that there exists a tradeoff between the size of the set of potential initial configurations, and the power of the sensing capabilities of the robots (i.e. the larger the initial configuration set, the most powerful the sensor needs to be). We prove that there is no such trade off. We propose a gathering protocol for an odd number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non-atomic CORDA model with asynchronous fair scheduling. Our protocol allows the largest set of initial configurations (with respect to impossibility results) yet uses the weakest multiplicity detector to date. The time complexity of our protocol is O(n 2 ), where n denotes the size of the ring. Compared to previous work that also uses local weak multiplicity detection, we do not have the constraint that k < n/2 (here, we simply have 2 < k < n − 3).

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A loosely-stabilizing leader election protocol with polylogarithmic convergence time in the population protocol model is presented in this paper. In the population protocol model, which is a common abstract model of mobile sensor networks, it is known to be impossible to design a self-stabilizing leader election protocol. Thus, in our prior work, we introduced the concept of loose-stabilization, which is weaker than self-stabilization but has similar advantage as selfstabilization in practice. Following this work, several loosely-stabilizing leader election protocols are presented. The loosely-stabilizing leader election guarantees that, starting from an arbitrary configuration, the system reaches a safe configuration with a single leader within a relatively short time, and keeps the unique leader for an sufficiently long time thereafter. The convergence times of all the existing loosely-stabilizing protocols, i.e., the expected time to reach a safe configuration, are polynomial in n where n is the number of nodes (while the holding times to keep the unique leader are exponential in n). In this paper, a loosely-stabilizing protocol with polylogarithmic convergence time is presented. Its holding time is not exponential, but arbitrarily large polynomial in n.

In this article, we present the first leader election protocol in the population protocol model that stabilizes within Oðlog nÞ parallel time in expectation with Oðlog nÞ states per agent, where n is the number of agents. Given a rough knowledge m of lg n such that m ! lg n and m ¼ Oðlog nÞ, the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter. This protocol is time-optimal because it was recently proven that any leader election protocol requires Vðlog nÞ parallel time.

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In this paper, we present the first leader election protocol in the population protocol model that stabilizes O(log n) parallel time in expectation with O(log n) states per agent, where n is the number of agents. Given a rough knowledge m of the population size n such that m ≥ log 2 n and m = O(log n), the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter.

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