Distributed Computing最新文献

Population protocols (Angluin et al. in PODC, 2004) are a model of distributed computation in which indistinguishable, finite-state agents interact in pairs to decide if their initial configuration, i.e., the initial number of agents in each state, satisfies a given property. In a seminal paper Angluin et al. classified population protocols according to their communication mechanism, and conducted an exhaustive study of the expressive power of each class, that is, of the properties they can decide (Angluin et al. in Distrib Comput 20(4):279-304, 2007). In this paper we study the correctness problem for population protocols, i.e., whether a given protocol decides a given property. A previous paper (Esparza et al. in Acta Inform 54(2):191-215, 2017) has shown that the problem is decidable for the main population protocol model, but at least as hard as the reachability problem for Petri nets, which has recently been proved to have non-elementary complexity. Motivated by this result, we study the computational complexity of the correctness problem for all other classes introduced by Angluin et al., some of which are less powerful than the main model. Our main results show that for the class of observation models the complexity of the problem is much lower, ranging from ${\Pi }_2^p$ to PSPACE.

We present a randomized distributed algorithm that computes a $\Delta$ -coloring in any non-complete graph with maximum degree $\Delta \ge 4$ in $O(log\Delta )+2^{O\left(\sqrt{loglogn}\right)}$ rounds, as well as a randomized algorithm that computes a $\Delta$ -coloring in $O\left({(loglogn)}^2\right)$ rounds when $\Delta \in [3,O(1\left)\right]$ . Both these algorithms improve on an $O({log}^{3}n/log\Delta )$ -round algorithm of Panconesi and Srinivasan (STOC'93), which has remained the state of the art for the past 25 years. Moreover, the latter algorithm gets (exponentially) closer to an $\Omega (loglogn)$ round lower bound of Brandt et al. (STOC'16).

Distributed proofs are mechanisms that enable the nodes of a network to collectively and efficiently check the correctness of Boolean predicates on the structure of the network (e.g., having a specific diameter), or on objects distributed over the nodes (e.g., a spanning tree). We consider well known mechanisms consisting of two components: a prover that assigns a certificate to each node, and a distributed algorithm called a verifier that is in charge of verifying the distributed proof formed by the collection of all certificates. We show that many network predicates have distributed proofs offering a high level of redundancy, explicitly or implicitly. We use this remarkable property of distributed proofs to establish perfect tradeoffs between the size of the certificate stored at every node, and the number of rounds of the verification protocol.

Population protocols are a model for distributed computing that is focused on simplicity and robustness. A system of n identical agents (finite state machines) performs a global task like electing a unique leader or determining the majority opinion when each agent has one of two opinions. Agents communicate in pairwise interactions with randomly assigned communication partners. Quality is measured in two ways: the number of interactions to complete the task and the number of states per agent. We present protocols for the majority problem that allow for a trade-off between these two measures. Compared to the only other trade-off result (Alistarh et al. in Proceedings of the 2015 ACM symposium on principles of distributed computing, Donostia-San Sebastián, 2015), we improve the number of interactions by almost a linear factor. Furthermore, our protocols can be made uniform (working correctly without any information on the population size n), yielding the first uniform majority protocols that stabilize in a subquadratic number of interactions.