Time vs. space trade-offs for rendezvous in trees

Czyzowicz, Jurek; Kosowski, Adrian; Pełc, Andrzej

doi:10.1145/2312005.2312007

Cited by 8 publications

(11 citation statements)

References 37 publications

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“…This result is in fact incorrect in this formulation. Indeed, it has been recently proved in [15] that, for some port labeling of a line and some initial positions that are not symmetric with respect to this labeling, rendezvous with simultaneous start requires a logarithmic number of bits, while = 2 for the line. However, our positive result holds for agents starting from arbitrary non perfectly symmetrizable initial positions.…”

Section: Bibliographic Notementioning

confidence: 99%

“…In the recent paper [14] the authors showed that deterministic rendezvous can be solved in arbitrary n-node graphs using O(log n) memory bits (for arbitrary delay between starting times of the agents) and that this number of bits is necessary, even in rings and even for simultaneous start. Tradeoffs between time of rendezvous in trees and the size of memory of the agents are studied in [15]. The impact of memory size on the feasibility of the related task of tree exploration, for trees with unlabeled nodes, has been studied in [19,27].…”

Section: Related Workmentioning

confidence: 99%

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Delays Induce an Exponential Memory Gap for Rendezvous in Trees

Fraigniaud

Pełc

2013

ACM Trans. Algorithms

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The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. In this paper, we focus on rendezvous in trees, and, analogously to the efforts that have been made for solving the exploration problem with compact automata, we study the size of memory of mobile agents that permits to solve the rendezvous problem deterministically. We assume that the agents are identical, and move in synchronous rounds.We first show that if the delay between the starting times of the agents is arbitrary, then the lower bound on memory required for rendezvous is Ω(log n) bits, even for the line of length n. This lower bound meets a previously known upper bound of O(log n) bits for rendezvous in arbitrary graphs of size at most n. Our main result is a proof that the amount of memory needed for rendezvous with simultaneous start depends essentially on the number of leaves of the tree, and is exponentially less impacted by the number n of nodes. Indeed, we present two identical agents with O(log + log log n) bits of memory that solve the rendezvous problem in all trees with at most n nodes and at most leaves. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that Ω(log + log log n) bits of memory are required for rendezvous, even in the class of trees with degrees bounded by 3.

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Section: Bibliographic Notementioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Delays Induce an Exponential Memory Gap for Rendezvous in Trees

Fraigniaud

Pełc

2013

ACM Trans. Algorithms

Self Cite

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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%

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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“…In this section we consider the effect of limiting the memory of the agent. The task of rendezvous in tree networks has been studied in synchronous environments for agents with small memory and it was shown that logarithmic memory is required for rendezvous even on the line [14]. Note that this lower bound does not apply directly in our setting since the set of solvable instances of rendezvous is strictly larger in a synchronous environment than in an asynchronous one when the agents cannot mark the vertices.…”

Section: Agents Having Little Memorymentioning

confidence: 99%

“…In stronger models, e.g. 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].…”

Section: Introductionmentioning

confidence: 99%

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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Time vs. space trade-offs for rendezvous in trees

Cited by 8 publications

References 37 publications

Delays Induce an Exponential Memory Gap for Rendezvous in Trees

Delays Induce an Exponential Memory Gap for Rendezvous in Trees

Partial gathering of mobile agents in asynchronous unidirectional rings

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

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