Deterministic Symmetric Rendezvous in Arbitrary Graphs: Overcoming Anonymity, Failures and Uncertainty

Chalopin, Jérémie; Das, Shantanu; Widmayer, Peter

doi:10.1007/978-1-4614-6825-7_12

Cited by 5 publications

(3 citation statements)

References 25 publications

(35 reference statements)

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“…Networks. Whether for CA over graphs [26], multi-agent modeling [11] or agent-based distributed algorithms [10], it is common to work with graphs whose nodes have numbered neighbours. Thus our 'graphs' or networks are the usual, connected, undirected, possibly infinite, bounded-degree graphs, but with a few additional twists:…”

Section: In a Nutshell : Reversible Causal Graph Dynamicsmentioning

confidence: 99%

Reversibility vs Local Creation/Destruction

Arrighi

Durbec

Emmanuel

2019

Reversible Computation

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Consider a network that evolves reversibly, according to nearest neighbours interactions. Can its dynamics create/destroy nodes? On the one hand, since the nodes are the principal carriers of information, it seems that they cannot be destroyed without jeopardising bijectivity. On the other hand, there are plenty of global functions from graphs to graphs that are non-vertex-preserving and bijective. The question has been answered negatively-in three different ways. Yet, in this paper we do obtain reversible local node creation/destruction-in three relaxed settings, whose equivalence we prove for robustness. We motivate our work both by theoretical computer science considerations (reversible computing, cellular automata extensions) and theoretical physics concerns (basic formalisms for discrete quantum gravity). ACM Subject Classification

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Section: In a Nutshell : Reversible Causal Graph Dynamicsmentioning

confidence: 99%

Reversibility vs Local Creation/Destruction

Arrighi

Durbec

Emmanuel

2019

Reversible Computation

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“…Fault-tolerant aspects of the rendezvous problem have been investigated in [11,15,16,20,22]. Faulty unmovable tokens were considered in the context of the task of gathering many agents at one node.…”

Section: Related Workmentioning

confidence: 99%

Fault-Tolerant Rendezvous in Networks

Chalopin

Dieudonné

Labourel

et al. 2014

Automata, Languages, and Programming

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Two mobile agents, starting from different nodes of an unknown network, have to meet at a node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to delay faults: if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability 0 < p < 1), unbounded adversarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most c consecutive rounds, where c is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals.For random faults, we show an algorithm with cost polynomial in the size n of the network and polylogarithmic in the larger label L, which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not possible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost O(nℓ), where ℓ is the smaller label, working in arbitrary trees, and we show that Ω(ℓ) is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in n, and logarithmic in the bound c and in the larger label L.

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“…The symmetric version of this strategy is for each robot to randomly choose to visit every vertex or wait for a fixed length of time. Another symmetric approach is for robots to move randomly between several unique vertices that they have identified [10], [11], [12].…”

Section: Introductionmentioning

confidence: 99%