Efficient size estimation and impossibility of termination in uniform dense population protocols

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 exact value $\lfloor \log n \rfloor$). Our first main result is a uniform protocol for calculating $\log(n) \pm O(1)$ 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 converging but not terminating: it does not signal when the estimate is close to the true value of $\log n$. If it could be made terminating, this would allow composition with protocols, such as those for leader election or majority, that require a size estimate initially, to make them uniform (though with a small probability of failure). We do show how our main protocol can be indirectly composed with others in a simple and elegant way, based on the leaderless phase clock, 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 $\Omega(n)$ 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.Comment: Using leaderless phase cloc

The Computational Power of Beeps

In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by focusing on randomized leader election. We prove a lower bound on the states required to solve this problem with a given error bound, probability precision, and (when relevant) network size lower bound. We then show the bound tight with a matching upper bound. Noting that our optimal upper bound is slow, we describe two faster algorithms that trade some state optimality to gain efficiency. We then turn our attention to more general classes of problems by proving that once you have enough states to solve leader election with a given error bound, you have (within constant factors) enough states to simulate correctly, with this same error bound, a logspace TM with a constant number of unary input tapes: allowing you to solve a large and expressive set of problems. These results identify a key simplicity threshold beyond which useful distributed computation is possible in the beeping model.Comment: Extended abstract to appear in the Proceedings of the International Symposium on Distributed Computing (DISC 2015

Clustering algorithm in initialization of multi-hop wireless sensor networks

In most application scenarios of wireless sensor networks (WSN), sensor nodes are usually deployed randomly and do not have any knowledge about the network environment or even their ID's at the initial stage of their operations. In this paper, we address the clustering problems with a newly deployed multi-hop WSN where most existing clustering algorithms can hardly be used due to the absence of MAC link connections among the nodes. We propose an effective clustering algorithm based on a random contention model without the prior knowledge of the network and the ID's of nodes. Computer simulations have been used to show the effectiveness of the algorithm with a relatively low complexity if compared with existing schemes

Stellar Consensus by Instantiation

Stellar introduced a new type of quorum system called a Federated Byzantine Agreement System. A major difference between this novel type of quorum system and a threshold quorum system is that each participant has its own, personal notion of a quorum. Thus, unlike in a traditional BFT system, designed for a uniform notion of quorum, even in a time of synchrony one well-behaved participant may observe a quorum of well-behaved participants, while others may not. To tackle this new problem in a more general setting, we abstract the Stellar Network as an instance of what we call Personal Byzantine Quorum Systems. Using this notion, we streamline the theory behind the Stellar Network, removing the clutter of unnecessary details, and refute the conjecture that Stellar\u27s notion of intact set is optimally fault-tolerant. Most importantly, we develop a new consensus algorithm for the new setting