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The Quadtree and Related Hierarchical Data Structures
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LLS: a locality aware location service for mobile ad hoc networks
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How to meet asynchronously (almost) everywhere
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Asynchronous deterministic rendezvous in bounded terrains
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Almost optimal asynchronous rendezvous in infinite multidimensional grids
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Synchronous rendezvous for location-aware agents
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Decidability classes for mobile agents computing
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
How to meet asynchronously (almost) everywhere
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How to meet asynchronously at polynomial cost
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Deterministic polynomial approach in the plane
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Price of asynchrony in mobile agents computing
Theoretical Computer Science
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In this paper we study efficient rendezvous of two mobile agents moving asynchronously in the Euclidean 2d-space. Each agent has limited visibility, permitting it to see its neighborhood at unit range from its current location. Moreover, it is assumed that each agent knows its own initial position in the plane given by its coordinates. The agents, however, are not aware of each others position. The agents possess coherent compasses and the same unit of length, which permit them to consider their current positions within the same system of coordinates. The cost of the rendezvous algorithm is the sum of lengths of the trajectories of both agents. This cost is taken as the maximum over all possible asynchronous movements of the agents, controlled by the adversary. We propose an algorithm that allows the agents to meet in a local neighborhood of diameter O(d), where d is the original distance between the agents. This seems rather surprising since each agent is unaware of the possible location of the other agent. In fact, the cost of our algorithm is O(d2+ε), for any constant ε 0. This is almost optimal, since a lower bound of Ω(d2) is straightforward. The only up to date paper [12] on asynchronous rendezvous of bounded-visibility agents in the plane provides the feasibility proof for rendezvous, proposing a solution exponential in the distance d and in the labels of the agents. In contrast, we show here that, when the identity of the agent is based solely on its original location, an almost optimal solution is possible. An integral component of our solution is the construction of a novel type of non-simple space-filling curves that preserve locality. An infinite curve of this type visits specific grid points in the plane and provides a route that can be adopted by the mobile agents in search for one another. This new concept may also appear counter-intuitive in view of the result from [22] stating that for any simple space-filling curve, there always exists a pair of close points in the plane, such that their distance along the space-filling curve is arbitrarily large.