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“…From this result we concluded that computing the level-n-labels of all vertices is essentially enough for multiple robots to weakly meet and, with some additional effort, also to reconstruct the visibility graph of the polygon. Our solution improves on the previous result [4] where LB-robots additionally were allowed to measure angles very roughly (in fact only to distinguish between angles smaller and larger than π). The results in the present paper show that this additional capability is not necessary.…”

confidence: 61%

“…From this result we concluded that computing the level-n-labels of all vertices is essentially enough for multiple robots to weakly meet and, with some additional effort, also to reconstruct the visibility graph of the polygon. Our solution improves on the previous result [4] where LB-robots additionally were allowed to measure angles very roughly (in fact only to distinguish between angles smaller and larger than π). The results in the present paper show that this additional capability is not necessary.…”

confidence: 61%

“…It was previously shown that without initial knowledge about the size of the polygon, such a robot cannot infer the size of a polygon and thus cannot reconstruct its visibility graph [6]. If the robot is only allowed to move along the boundary of the polygon, it cannot reconstruct the visibility graph, even if the number of vertices n is known beforehand [4]. It is still an open question whether the knowledge of n helps in the general case where the robot is not restricted to move along the boundary.…”

confidence: 99%

“…Section 2). Bilò et al showed that such a robot cannot reconstruct the visibility graph of a polygon by moving along the boundary only, even if the number of vertices n is known, unless provided with additional capabilities [2]. We extend the model by allowing the robot to look-back after moving, i.e.…”

confidence: 99%