Tradeoffs between cost and information for rendezvous and treasure hunt

Miller, Avery; Pełc, Andrzej

doi:10.1016/j.jpdc.2015.06.004

Cited by 14 publications

(2 citation statements)

References 55 publications

(91 reference statements)

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“…Most of the literature on rendezvous considered finite graphs and assumed the synchronous scenario, where agents move in rounds. In [21] the authors studied tradeoffs between the amount of information a priori available to the agents and time of treasure hunt and of rendezvous. In [24], the authors presented rendezvous algorithms with time polynomial in the size of the graph and the length of agent's labels.…”

Section: Related Workmentioning

confidence: 99%

Deterministic treasure hunt and rendezvous in arbitrary connected graphs

Pattanayak,

Pelc

2024

Information Processing Letters

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Section: Related Workmentioning

confidence: 99%

Deterministic treasure hunt and rendezvous in arbitrary connected graphs

Pattanayak,

Pelc

2024

Information Processing Letters

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“…As we mentioned, the neighborhood rendezvous problem can be seen as a relaxation of rendezvous in complete graphs, and thus we can regard our result as the one extending the graph classes allowing fast rendezvous (using a stronger assumption of vertex identifiers). There are also several studies [9]- [11] for achieving fast rendezvous using side information coming from oracles (so-called advice). In this model, agents cannot see the whole map of G, but instead can know the (partial) information on their initial locations.…”

Section: Related Workmentioning

confidence: 99%

Fast Neighborhood Rendezvous

Eguchi

Kitamura

IZUMI

2022

IEICE Trans. Inf. & Syst.

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In the rendezvous problem, two computing entities (called agents) located at different vertices in a graph have to meet at the same vertex. In this paper, we consider the synchronous neighborhood rendezvous problem, where the agents are initially located at two adjacent vertices. While this problem can be trivially solved in O(Δ) rounds (Δ is the maximum degree of the graph), it is highly challenging to reveal whether that problem can be solved in o(Δ) rounds, even assuming the rich computational capability of agents. The only known result is that the time complexity of O( √ n) rounds is achievable if the graph is complete and agents are probabilistic, asymmetric, and can use whiteboards placed at vertices. Our main contribution is to clarify the situation (with respect to computational models and graph classes) admitting such a sublinear-time rendezvous algorithm. More precisely, we present two algorithms achieving fast rendezvous additionally assuming bounded minimum degree, unique vertex identifier, accessibility to neighborhood IDs, and randomization. The first algorithm runs within Õ( √ nΔ/δ + n/δ) rounds for graphs of the minimum degree larger than √ n, where n is the number of vertices in the graph, and δ is the minimum degree of the graph. The second algorithm assumes that the largest vertex ID is O(n), and achieves Õ n √ δ-round time complexity without using whiteboards. These algorithms attain o(Δ)-round complexity in the case of δ = ω( √ n log n) and δ = ω(n 2/3 log 4/3 n) respectively. We also prove that four unconventional assumptions of our algorithm, bounded minimum degree, accessibility to neighborhood IDs, initial distance one, and randomization are all inherently necessary for attaining fast rendezvous. That is, one can obtain the Ω(n)-round lower bound if either one of them is removed.

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Impact of knowledge on the cost of treasure hunt in trees

2021

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Treasure hunt is finding a hidden inert target by a mobile agent. We consider deterministic algorithms for treasure hunt in trees. Our goal is to establish the impact of different kinds of initial knowledge given to the agent on the cost of treasure hunt, defined as the total number of edge traversals until the agent reaches the treasure. The agent can be initially given either a complete map of the tree rooted at its starting node, with all port numbers marked, or a blind map of the tree rooted at its starting node but without port numbers. It may also be given, or not, the distance from the root to the treasure. This yields four different knowledge types that are partially ordered by their precision. The penalty of a less precise knowledge type  2 over a more precise knowledge type  1 measures intuitively the worst-case ratio of the cost of an algorithm supplied with knowledge of type  2 over the cost of an algorithm supplied with knowledge of type  1 . Our main results establish penalties for comparable knowledge types in this partial order. For knowledge types with known distance, the penalty for having a blind map over a complete map turns out to be very large. By contrast, for unknown distance, the penalty of having a blind map over having a complete map is small. When a map is provided (either complete or blind), the penalty of not knowing the distance over knowing it is medium.

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Tradeoffs between cost and information for rendezvous and treasure hunt

Cited by 14 publications

References 55 publications

Deterministic treasure hunt and rendezvous in arbitrary connected graphs

Deterministic treasure hunt and rendezvous in arbitrary connected graphs

Fast Neighborhood Rendezvous

Impact of knowledge on the cost of treasure hunt in trees

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