Time of Anonymous Rendezvous in Trees: Determinism vs. Randomization

Elouasbi, Samir; Pełc, Andrzej

doi:10.1007/978-3-642-31104-8_25

Cited by 7 publications

(6 citation statements)

References 16 publications

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“…Many fundamental problems for cooperation of mobile agents have been studied. For example, the searching problem [4], the gossip problem [5], the election problem [6], and the gathering problem [1,2,3,6,7,8,9,10,11,12,13,14,15,16] have been studied.…”

Section: Related Workmentioning

confidence: 99%

“…In particular, the gathering problem has received a lot of attention and has been extensively studied in many topologies including trees [1,5,12,13,14,15], tori [1,8], and rings [1,2,3,6,7,9,10,11]. The gathering problem for rings has been extensively studied because algorithms for such highly symmetric topologies give techniques to treat the essential difficulty of the gathering problem such as breaking symmetry.…”

Section: Related Workmentioning

confidence: 99%

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Partial gathering of mobile agents in asynchronous unidirectional rings

Shibata

Kawai

Ooshita

et al. 2016

Theoretical Computer Science

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In this paper, we consider the partial gathering problem of mobile agents in asynchronous unidirectional rings equipped with whiteboards on nodes. The partial gathering problem is a new generalization of the total gathering problem. The partial gathering problem requires, for a given integer g, that each agent should move to a node and terminate so that at least g agents should meet at the same node. The requirement for the partial gathering problem is weaker than that for the (well-investigated) total gathering problem, and thus, we have interests in clarifying the difference on the move complexity between them. We propose three algorithms to solve the partial gathering problem. The first algorithm is deterministic but requires unique ID of each agent. This algorithm achieves the partial gathering in O(gn) total moves, where n is the number of nodes. The second algorithm is randomized and requires no unique ID of each agent (i.e., anonymous). This algorithm achieves the partial gathering in expected O(gn) total moves. The third algorithm is deterministic and requires no unique ID of each agent. For this case, we show that there exist initial configurations in which no algo-✩ The conference version of this paper is published

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Partial gathering of mobile agents in asynchronous unidirectional rings

Shibata

Kawai

Ooshita

et al. 2016

Theoretical Computer Science

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“…Rendezvous time (both deterministic and randomized) of anonymous agents in trees without marking nodes has also been very recently studied in [18]. It was shown therein that deterministic rendezvous in n-node trees can be always achieved in time O(n), but only when the memory size of the agents is at least linear.…”

Section: Related Workmentioning

confidence: 99%

“…We remark that our Algorithm 2 works for all non-symmetric starting configurations, i.e., configurations for which rendezvous is always feasible. It turns out that when the configuration is symmetric, rendezvous is not feasible when the agents start simultaneously, but becomes feasible when one of the agents starts with some non-zero delay [18]. The question of whether our time-space trade-off holds for the case of symmetric positions with non-zero delay remains open.…”

Section: The General Algorithmmentioning

confidence: 99%

Time versus space trade-offs for rendezvous in trees

2013

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International audienceTwo identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory of the agents. For agents with $k$ memory bits, we show that optimal rendezvous time is $\Theta(n+n^2/k)$ in $n$-node trees. More precisely, if $k \geq c\log n$, for some constant $c$, we design agents accomplishing rendezvous in arbitrary trees of size $n$ {(unknown to the agents)} in time $O(n+n^2/k)$, starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time $o(n+n^2/k)$, even in the class of lines of known length and even with simultaneous start. Finally, we prove that at least logarithmic memory is necessary for rendezvous, even for agents starting simultaneously in a $n$-node line

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“…(In the latter scenario, symmetry is broken by the use of the different labels of agents, and thus rendezvous is sometimes possible even for symmetric initial positions of the agents). Rendezvous time (both deterministic and randomized) of anonymous agents in trees without marking nodes has been studied in [17]. It was shown that deterministic rendezvous in n-node trees can be always achieved in time O(n), but only when the memory size of the agents is at least linear.…”

Section: Related Workmentioning

confidence: 99%

Time vs. space trade-offs for rendezvous in trees

Czyzowicz

Kosowski

Pełc

2012

Proceedings of the Twenty-Fourth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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. Time vs. space trade-offs for rendezvous in trees. [Research Report] 2011, pp.20. Time vs. space trade-offs for rendezvous in treesTwo identical (anonymous) mobile agents start from arbitrary nodes of an unknown tree and have to meet at some node. Agents move in synchronous rounds: in each round an agent can either stay at the current node or move to one of its neighbors. We consider deterministic algorithms for this rendezvous task. The main result of this paper is a tight trade-off between the optimal time of completing rendezvous and the size of memory of the agents. For agents with k memory bits, we show that optimal rendezvous time is Θ(n + n 2 /k) in n-node trees. More precisely, if k ≥ c log n, for some constant c, we design agents accomplishing rendezvous in arbitrary trees of unknown size n in time O(n + n 2 /k), starting with arbitrary delay. We also show that no pair of agents can accomplish rendezvous in time o(n + n 2 /k), even in the class of lines of known length and even with simultaneous start. Finally, we prove that at least logarithmic memory is necessary for rendezvous, even for agents starting simultaneously in a n-node line.

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Time of Anonymous Rendezvous in Trees: Determinism vs. Randomization

Cited by 7 publications

References 16 publications

Partial gathering of mobile agents in asynchronous unidirectional rings

Partial gathering of mobile agents in asynchronous unidirectional rings

Time versus space trade-offs for rendezvous in trees

Time vs. space trade-offs for rendezvous in trees

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