2012
DOI: 10.1007/978-3-642-33536-5_7
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Abstract: We propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration (exploration for short) of a grid-shaped network by a team of k asynchronous oblivious robots in the asynchronous non-atomic model, so-called CORDA.In more details, we first consider the ATOM model. We show that it is impossible to explore a grid of at least three nodes with less than three robots. Next, we show that it is impossible to explore a (2, 2)-Grid with less than 4 robots, and a (3, 3)-Grid with l… Show more

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Cited by 51 publications
(40 citation statements)
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“…This impossibility result extends to four robots in the deterministic setting, while five robots are sufficient to explore and stop a ring deterministically [12]. By contrast, it was recently pointed out that in the general case three robots are necessary and sufficient to explore an n × m grid-shaped network with m > 3 [4]. So, with respect to the required number of robots to explore and stop a graph, grid exploration is easier that ring exploration.…”
Section: Introductionmentioning
confidence: 97%
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“…This impossibility result extends to four robots in the deterministic setting, while five robots are sufficient to explore and stop a ring deterministically [12]. By contrast, it was recently pointed out that in the general case three robots are necessary and sufficient to explore an n × m grid-shaped network with m > 3 [4]. So, with respect to the required number of robots to explore and stop a graph, grid exploration is easier that ring exploration.…”
Section: Introductionmentioning
confidence: 97%
“…Assuming visibility capabilities, anonymous and oblivious robots, the three main problems that have been studied in the discrete robot model are gathering [9][10][11] (all robots are requested to reach a single node, not known beforehand), exploration with stop [4][5][6][7]12] (all nodes must be visited by at least one robot, and eventually all robots must stop moving forever), and exclusive perpetual exploration [1,2] (all nodes must be visited by all robots infinitely often, and no node or edge should be occupied by more than one robot at any time).…”
Section: Introductionmentioning
confidence: 99%
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“…First, they are restricted to the simpler SSYNC model rather than the more general and more complex ASYNC model. Second, they are either specific to a hardcoded topology (e.g., a 3 grid [18]) that prevents easy reuse in more generic situations, or make additional assumptions about configurations and protocols to be verified (e.g. unambiguous protocols [19]) that prevent combinatorial explosion but forbid reuse for proof-challenging protocols, which would most benefit from automatic verification.…”
Section: Introductionmentioning
confidence: 99%
“…In this context, typical problems are terminating exploration [2,3,4,5,6], exclusive perpetual exploration [7,8,9], exclusive searching [10,9], and gathering [9,11,12]. Here, we study the terminating exploration (or simply exploration) problem, which requires that robots collectively explore the whole graph and stop upon completion.…”
Section: Introductionmentioning
confidence: 99%