Deterministic rendezvous in networks: A comprehensive survey

Pełc, Andrzej

doi:10.1002/net.21453

Cited by 95 publications

(53 citation statements)

References 49 publications

(113 reference statements)

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“…The agents start from their initial configuration and may gain some knowledge on the topology of the graph only as a result of its path traversals. The task to be performed varies and may include exploration [2,12,20,26], map construction [10,14,18], gathering [13,19,32,40] or leader election [5,6,28]. In this work we focus on the task of capturing a fast fugitive hiding in the graph.…”

Section: Introductionmentioning

confidence: 99%

Distributed graph searching with a sense of direction

2014

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In this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function ω provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least ω(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has ω ≡ 1. We assume that with a graph G to be searched, there is associated a partition (V 1 , . . . , V t ) of its vertex set such that edges are allowed only within each V i and between two consecutive V i 's. We provide an algorithm for distributed monotone connected edge searching of such graphs, where the searchers are initially placed on an arbitrary vertex of G and have no a priori knowledge on G, but they have a sense of direction that lets them recognize whether an edge incident to already explored vertex in V i leads to a vertex in one of V i−1 , V i or V i+1 . Starting from any vertex the algorithm uses at most 3·max i=1,...,t ω(V i )+1 searchers, where ω(V i ) = v∈V i ω(v). We also prove that this algorithm is best possible up to a small additive constant, that is, each distributed searching algorithm in worst case must use 3 · max i=1,...,t ω(V i ) − 1 searchers for some graphs.

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Section: Introductionmentioning

confidence: 99%

Distributed graph searching with a sense of direction

2014

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“…when the agents have distinct identifiers [12,17] or, when they are synchronous [13,14], or if the environment is restricted to specific topologies such as the ring [20,23], grid [4] or tree [14] topologies, then it becomes easier to solve rendezvous and the set of solvable instances may become relatively larger. For results on rendezvous in such models, please see the recent survey [24]. Another significant difference between the results in this paper and those of [24] is that we allow the agents to meet only at a node, whereas most results from the above paper also allow meeting on an edge when two agents are traversing it from opposite sides 1 .…”

Section: Introductionmentioning

confidence: 93%

“…For results on rendezvous in such models, please see the recent survey [24]. Another significant difference between the results in this paper and those of [24] is that we allow the agents to meet only at a node, whereas most results from the above paper also allow meeting on an edge when two agents are traversing it from opposite sides 1 . The rendezvous problem has also been studied in a completely different model where the agents move in a continuous terrain [19] or in a graph [22] but have global visibility.…”

Section: Introductionmentioning

confidence: 93%

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

2013

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We consider the rendezvous problem of gathering two or more identical agents that are initially scattered among the nodes of an unknown graph. We discuss some of the recent results for this problem focusing only on deterministic algorithms for the general case when the graph topology is unknown, the nodes of the graph may not be uniquely labeled and the agents may not be synchronized with each other. In this scenario, the objective is to solve rendezvous whenever deterministically feasible, while optimizing on the amount of movement by the agents or the memory required (for the nodes or the agents) in the worst case. Further we also investigate some special scenarios such as (i) when the graph contains some dangerous nodes or, (ii) when there is no consistent ordering on the edges of a node. We present positive results, complexity analysis and some general techniques for dealing with such worst case scenarios for the symmetric rendezvous problem.

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“…also [3,4,6,11]. Deterministic rendezvous in networks has been surveyed in [46]. Several authors considered geometric scenarios (rendezvous in an interval of the real line, e.g., [11,12], or in the plane, e.g., [7,8]).…”

Section: Related Workmentioning

confidence: 99%

Tradeoffs between cost and information for rendezvous and treasure hunt

Miller

Pełc

2015

Journal of Parallel and Distributed Computing

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In rendezvous, two agents traverse network edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target situated at an unknown node of the network. We study tradeoffs between the amount of information (advice) available a priori to the agents and the cost (number of edge traversals) of rendezvous and treasure hunt. Our goal is to find the smallest size of advice which enables the agents to solve these tasks at some cost C in a network with e edges. This size turns out to depend on the initial distance D and on the ratio

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Deterministic rendezvous in networks: A comprehensive survey

Cited by 95 publications

References 49 publications

Distributed graph searching with a sense of direction

Distributed graph searching with a sense of direction

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

Tradeoffs between cost and information for rendezvous and treasure hunt

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