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25
Distributed control of robotic networks: a mathematical approach to motion coordination algorithms
, 2009
"... (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 ..."
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Cited by 38 (1 self)
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(i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including errors, suggestions, evaluations, and teaching or research uses. 2 “Distributed Control of Robotic Networks ” by F. Bullo, J. Cortés and S. Martínez
On Finding a Guard that Sees Most and a Shop that Sells Most
- In Proc. 15th ACM-SIAM Sympos. Discrete Algorithms
, 2003
"... We present a near-quadratic time algorithm that computes a point inside a simple polygon P having approximately the largest visibility polygon inside P , and near-linear time algorithm for nding the point that will have approximately the largest Voronoi region when added to an n-point set. We a ..."
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Cited by 28 (3 self)
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We present a near-quadratic time algorithm that computes a point inside a simple polygon P having approximately the largest visibility polygon inside P , and near-linear time algorithm for nding the point that will have approximately the largest Voronoi region when added to an n-point set. We apply the same technique to nd the translation that approximately maximizes the area of intersection of two polygonal regions in near-quadratic time.
Locating guards for visibility coverage of polygons
- in Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX
, 2007
"... All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 17 (2 self)
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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Terrain Guarding is NP-Hard
, 2009
"... A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. ..."
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Cited by 8 (0 self)
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A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if every point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. Using a reduction from PLANAR 3-SAT we prove that the decision version of this problem is NP-hard. This solves a significant open problem and complements recent positive approximability results for the optimization problem. 1
Efficient sensor placement for surveillance problems
"... Abstract. We study the problem of covering a two-dimensional spatial region P, cluttered with occluders, by sensors. A sensor placed at a location p covers a point x in P if x lies within sensing radius r from p and x is visible from p, i.e., the segment px does not intersect any occluder. The goal ..."
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Cited by 5 (1 self)
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Abstract. We study the problem of covering a two-dimensional spatial region P, cluttered with occluders, by sensors. A sensor placed at a location p covers a point x in P if x lies within sensing radius r from p and x is visible from p, i.e., the segment px does not intersect any occluder. The goal is to compute a placement of the minimum number of sensors that cover P. We propose a landmark-based approach for covering P. Suppose P has ς holes, and it can be covered by h sensors. Given a small parameter ε> 0, let λ: = λ(h, ε) = (h/ε) log ς. We prove that one can compute a set L of O(λ log λ log (1/ε)) landmarks so that if a set S of sensors covers L, then S covers at least (1 − ε)-fraction of P. It is surprising that so few landmarks are needed, and that the number does not depend on the number of vertices in P. We then present efficient randomized algorithms, based on the greedy approach, that, with high probability, compute O ( ˜ hlog λ) sensor locations to cover L; here ˜ h ≤ h is the number sensors needed to cover L. We propose various extensions of our approach, including: (i) a weight function over P is given and S should cover at least (1−ε) of the weighted area of P, and (ii) each point of P is covered by at least t sensors, for a given parameter t ≥ 1. 1
Optimizing Autonomous Pipeline Inspection
- IEEE Trans. on Robotics
, 2011
"... Abstract—This paper studies the optimal inspection of au-tonomous robots in a complex pipeline system. We solve a 3-D region-guarding problem to suggest the necessary inspection spots. The proposed hierarchical integer linear programming optimiza-tion algorithm seeks the fewest spots necessary to co ..."
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Cited by 4 (2 self)
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Abstract—This paper studies the optimal inspection of au-tonomous robots in a complex pipeline system. We solve a 3-D region-guarding problem to suggest the necessary inspection spots. The proposed hierarchical integer linear programming optimiza-tion algorithm seeks the fewest spots necessary to cover the entire given 3-D region. Unlike most existing pipeline inspection systems that focus on designing mobility and control of the explore robots, this paper focuses on global planning of the thorough and auto-matic inspection of a complex environment. We demonstrate the efficacy of the computation framework using a simulated environ-ment, where scanned pipelines and existing leaks, clogs, and defor-mation can be thoroughly detected by an autonomous prototype robot. Index Terms—Autonomous pipeline inspection, 3-D region guarding. I.
The art gallery theorem for polyominoes
, 2012
"... We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P. ..."
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We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P. In particular, we show that ⌊m+1 3 ⌋ point guards are always sufficient and sometimes necessary to cover an m-polyomino, possibly with holes. When m ≤ 3n 4 − 4, the sufficiency condition yields a strictly lower guard number than ⌊n 4⌋, given by the art gallery theorem for orthogonal polygons.
Generalized Watchman Route Problem with Discrete View Cost
"... In this paper, we introduce a generalized version of the Watchman Route Problem (WRP) where the objective is to plan a continuous closed route in a polygon (possibly with holes) and a set of discrete viewpoints on the planned route such that every point on the polygon boundary is visible from at lea ..."
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In this paper, we introduce a generalized version of the Watchman Route Problem (WRP) where the objective is to plan a continuous closed route in a polygon (possibly with holes) and a set of discrete viewpoints on the planned route such that every point on the polygon boundary is visible from at least one viewpoint. The total cost to minimize is a weighted sum of the view cost, proportional to the number of viewpoints, and the travel cost, the total length of the route. We call this problem the Watchman Route Problem with Discrete View Cost or the Generalized Watchman Route Problem (GWRP). In this paper, we consider a restricted version of GWRP that arises naturally in inspection tasks in robotic applications, where each polygon edge is entirely visible from at least one planned viewpoint. We call it Whole Edge Covering GWRP. This whole edge covering restriction is not trivial in that WEC-GWRP has the same NPhardness and inapproximability as GWRP. The algorithm we propose first constructs a graph that connects O(n 12) number of sample viewpoints in the polygon, where n is the number of polygon vertices; and then solves the corresponding View Planning Problem with Combined View and Traveling Cost, using an LP-relaxation based algorithm we introduced in [19]. We show that our algorithm has an approximation ratio in the order of either the view frequency, defined as the maximum number of sample viewpoints that cover a polygon edge, or a polynomial of log n, whichever is smaller. 1
A Pseudopolynomial Time O(log n)-Approximation Algorithm for Art Gallery Problems
"... Abstract. In this paper, we give a O(log copt)-approximation algorithm for the point guard problem where copt is the optimal number of guards. Our algorithm runs in time polynomial in n, the number of walls of the art gallery and the spread ∆, which is defined as the ratio between the longest and sh ..."
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Cited by 3 (0 self)
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Abstract. In this paper, we give a O(log copt)-approximation algorithm for the point guard problem where copt is the optimal number of guards. Our algorithm runs in time polynomial in n, the number of walls of the art gallery and the spread ∆, which is defined as the ratio between the longest and shortest pairwise distances. Our algorithm is pseudopolynomial in the sense that it is polynomial in the spread ∆ as opposed to polylogarithmic in the spread ∆, which could be exponential in the number of bits required to represent the vertex positions. The special subdivision procedure in our algorithm finds a finite set of potential guard-locations such that the optimal solution to the art gallery problem where guards are restricted to this set is at most 3copt. We use a set cover cum VC-dimension based algorithm to solve this restricted problem approximately. 1
Approximating the Obstacle Number for a Graph Drawing Efficiently
- CCCG
, 2011
"... An obstacle representation for a (straight-line) graph drawing consists of the positions of the graph vertices together with a set of polygonal obstacles such that every line segment between a pair of non-adjacent vertices intersects some obstacle, while the vertices and edges of the drawing avoid a ..."
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An obstacle representation for a (straight-line) graph drawing consists of the positions of the graph vertices together with a set of polygonal obstacles such that every line segment between a pair of non-adjacent vertices intersects some obstacle, while the vertices and edges of the drawing avoid all the obstacles. The obstacle number obs(D) for a graph drawing D is the least number of obstacles in an obstacle representation for it. We present an efficient algorithm for computing the obstacle number for a given graph drawing D with approximation ratio O(log obs(D)). This is achieved by showing that the V-C dimension is bounded for the family of hypergraphs of the underlying transversal problem, and using results from epsilon net theory.
