Finding the Shortest Watchman Route in a Simple Polygon

Carlsson, Svante; Jönsson, Håkan; Nilsson, Bengt J.

doi:10.1007/pl00009467

Cited by 66 publications

(39 citation statements)

References 18 publications

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“…The basic version of the coverage problem with just one robot with unlimited visual range operating in a simple polygon without obstacles has an exact polynomial time solution (Carlsson et al 1999;Tan 2001). But, extending the problem to support robots' limited visual range, obstacles in the environment, or allowing multiple robots make the corresponding decision problems NP-hard (Nilsson 1995).…”

Section: Complexity Analyses Of the Algorithmsmentioning

confidence: 99%

Multi-robot repeated area coverage

2013

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We address the problem of repeated coverage of a target area, of any polygonal shape, by a team of robots having a limited visual range. Three distributed Clusterbased algorithms, and a method called Cyclic Coverage are introduced for the problem. The goal is to evaluate the performance of the repeated coverage algorithms under the effects of the variables: Environment Representation, and the Robots' Visual Range. A comprehensive set of performance metrics are considered, including the distance the robots travel, the frequency of visiting points in the target area, and the degree of balance in workload distribution among the robots. The Cyclic Coverage approach, used as a benchmark to compare the algorithms, produces optimal or near-optimal solutions for the single robot case under some criteria. The results can be used as a framework for choosing an appropriate combination of repeated coverage algorithm, environment representation, and the robots' visual range based on the particular scenario and the metric to be optimized.

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Section: Complexity Analyses Of the Algorithmsmentioning

confidence: 99%

Multi-robot repeated area coverage

2013

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“…A watchman route in a polygon P (either a simple polygon or a polygon with holes, also known as a polygonal domain) is a closed curve inside P such that every point in P is visible from at least one point of the route. For simple polygons, the shortest route can be found in O(n 4 log n) time [6,10,36], and a 2-approximation can be computed in linear time [37]. For polygons with holes the problem cannot be approximated in polynomial time to within a factor of c log n, for a suitable constant c > 0, assuming that P = NP [28].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, our result for lines shows that some instances of TSP with neighborhoods (TSPN) and with obstacles are polynomially solvable (the obstacles are the open faces of the input line arrangement), while obviously TSPN without obstacles is generally NP-hard. It is worth mentioning that TSPN for a set of lines in the plane (with no obstacles) is solvable in polynomial time as a special case of the watchman route in a simple polygon [6,10,24,36,38].…”

Section: Introductionmentioning

confidence: 99%

Watchman routes for lines and line segments

Dumitrescu

Mitchell

Żyliński

2014

Computational Geometry

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Given a set L of non-parallel lines in the plane, a watchman route (tour) for L is a closed curve contained in the union of the lines in L such that every line is visited (intersected) by the route; we similarly define a watchman route (tour) for a connected set S of line segments. The watchman route problem for a given set of lines or line segments is to find a shortest watchman route for the input set, and these problems are natural special cases of the watchman route problem in a polygon with holes (a polygonal domain).In this paper, we show that the problem of computing a shortest watchman route for a set of n non-parallel lines in the plane is polynomially tractable, while it becomes NP-hard in 3D. We give an alternative NP-hardness proof of this problem for line segments in the plane and obtain a polynomial-time approximation algorithm with ratio O(log 3 n). Additionally, we consider some special cases of the watchman route problem on line segments, for which we provide exact algorithms or improved approximations.

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“…Related Work. Placing static guards to see a polygonal domain is the famous Art Gallery Problem [20]; finding a route for a single guard that sees a domain is the subject in the Watchman Route Problem [17,10] (heuristics for multiple watchmen in polygons are given in [21]). In these problems the guards are not required to spot moving targets (they just need to see any static target); catching evading objects in polygons is known as the Walkability Problem [23].…”

Section: Introductionmentioning

confidence: 99%