Communication Complexity of Consensus in Anonymous Message Passing Systems

Fusco, Emanuele G.

doi:10.1007/978-3-642-25873-2_14

Cited by 4 publications

(2 citation statements)

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“…It is well-known (cf. e.g., [29]) that the sum of degrees on a shortest path between any two nodes in an n-node graph is bounded above by 3n. Hence p 1 + • • • + p D ≤ 3n.…”

Section: Algorithmmentioning

confidence: 99%

Fast rendezvous with advice

Miller

Pełc

2015

Theoretical Computer Science

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Two mobile agents (robots), starting from different nodes of an n-node network at possibly different times, have to meet at the same node. This problem is known as rendezvous. Agents move in synchronous rounds using a deterministic algorithm. In each round, an agent decides to either remain idle or to move to one of the adjacent nodes. Each agent has a distinct integer label from the set {1, . . . , L}, which it can use in the execution of the algorithm, but it does not know the label of the other agent. The main efficiency measure of a rendezvous algorithm's performance is its time , i.e., the number of rounds from the start of the later agent until the meeting. If D is the distance between the initial positions of the agents, then Ω(D) is an obvious lower bound on the time of rendezvous. However, if each agent has no initial knowledge other than its label, time O(D) is usually impossible to achieve. We study the minimum amount of information that has to be available a priori to the agents to achieve rendezvous in optimal time Θ(D). Following the standard paradigm of algorithms with advice, this information is provided to the agents at the start by an oracle knowing the entire instance of the problem, i.e., the network, the starting positions of the agents, their wake-up rounds, and both of their labels. The oracle helps the agents by providing them with the same binary string called advice, which can be used by the agents during their navigation. The length of this string is called the size of advice. Our goal is to find the smallest size of advice which enables the agents to meet in time Θ(D). We show that this optimal size of advice is Θ(D log(n/D)+log log L). The upper bound is proved by constructing an advice string of this size, and providing a natural rendezvous algorithm using this advice that works in time Θ(D) for all networks. The matching lower bound, which is the main contribution of this paper, is proved by exhibiting classes of networks for which it is impossible to achieve rendezvous in time Θ(D) with smaller advice.

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“…It is well-known (cf. e.g., [29]) that the sum of degrees on a shortest path between any two nodes in an n-node graph is bounded above by 3n. Hence p 1 + • • • + p D ≤ 3n.…”

Section: Algorithmmentioning

confidence: 99%

Fast rendezvous with advice

Miller

Pełc

2015

Theoretical Computer Science

Self Cite

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“…One can think of various other "anonymous" models, i.e., which do not involve node identities. In particular, there is a large literature on distributed computing in networks without node identities, where symmetry breaking is enabled thanks to locally disjoint port numbers (see, e.g., [18]). We consider the anonymous LOCAL model to isolate the role of node identities from other symmetry breaking mechanisms.…”

Section: Model and Objectivesmentioning

confidence: 99%

On the Impact of Identifiers on Local Decision

Fraigniaud

Halldórsson

Korman

2012

Lecture Notes in Computer Science

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The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local computation, i.e., when nodes can gather information only from nodes at bounded distances, some insight regarding the role of identities has been established. For instance, it was shown that, for large classes of construction problems, the role of the identities can be rather small. However, for theidentities to play no role, some other kinds of mechanisms for breaking symmetry must be employed, such as edge-labeling or sense of direction. When it comes to local distributed decision problems, the specification of the decision task does not seem to involve symmetry breaking. Therefore, it is expected that, assuming nodes can gather sufficient information about their neighborhood, one could get rid of the identities, without employing extra mechanisms for breaking symmetry. We tackle this question in the framework of the $\local$ model. Let $\LD$ be the class of all problems that can be decided in a constant number of rounds in the $\local$ model. Similarly, let $\LD^*$ be the class of all problems that can be decided at constant cost in the anonymous variant of the $\local$ model, in which nodes have no identities, but each node can get access to the (anonymous) ball of radius $t$ around it, for any $t$, at a cost of $t$. It is clear that $\LD^*\subseteq \LD$. We conjecture that $\LD^*=\LD$. In this paper, we give several evidences supporting this conjecture. In particular, we show that it holds for hereditary problems, as well as when the nodes know an arbitrary upper bound on the total number of nodes. Moreover, we prove that the conjecture holds in the context of non-deterministic local decision, where nodes are given certificates (independent of the identities, if they exist), and the decision consists in verifying these certificates. In short, we prove that $\NLD^*=\NLD$.Comment: Principles of Distributed Systems, 16th International Conference, Dec 2012, Rome, Ital

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