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“…Online variants of TSP (for a single agent) have been studied in various contexts. For example, the geometric setting of exploring grid graphs with and without holes is considered by [10,11,14,15,17], where a variety of competitive algorithms with constant competitive ratios is provided. A related setting is studied in [4], where an agent has to explore a graph while being attached to the starting point by a rope of restricted length.…”

confidence: 99%

“…This should be contrasted with previous algorithms with limited visibility, e.g. [6,7,9,10] in which only a particular class of terrains with obstacles is explored, e.g., terrains without narrow corridors or terrains composed of complete identical squares. This can be done at cost O (A).…”

confidence: 95%

“…Moreover, for particular shapes of obstacles (convex and with bounded aspect ratio) the optimal competitive ratio Θ( √ k ) has been proven in [3]. Exploration of polygons by a robot with limited vision has been studied, e.g., in [6][7][8][9][10][11]. In [6] the authors described an on-line algorithm with competitive ratio 1 + 3(Π S/ A), where Π is a quantity depending on the perimeter of the polygon, S is the area seen by the robot, and A is the area of the polygon.…”

confidence: 99%

“…Exploration of polygons by a robot with limited vision has been studied, e.g., in [9,10,11,13,14,15]. In [9] the authors described an on-line algorithm with competitive ratio 1 + 3(ΠS/A), where Π is a quantity depending on the perimeter of the polygon, S is the area seen by the robot, and A is the area of the polygon.…”

confidence: 99%