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## Randomness and Computation Joint Workshop “New Horizons in Computing ” and “Statistical Mechanical Approach to Probabilistic

### Citations

2192 | Randomized Algorithms - Motwani, Raghavan - 1995 |

615 |
Spatial Tessellations: Concepts and Applications of Voronoi Diagrams
- Okabe, Boots, et al.
- 1992
(Show Context)
Citation Context ...oint x such that the Voronoi region of x is as large as possible. The area of Voronoi regions has been considered before in the context of games, such as the Voronoi game [1, 5] or the Hotelling game =-=[15]-=-. As far as we know, the only previous paper discussing maximizing the Voronoi region of a new point is by Dehne et al. [9], who show that the area function has only a single local maximum inside a re... |

497 | Art Gallery Theorems and Algorithms
- O’Rourke
- 1987
(Show Context)
Citation Context ..., and wish to find a set of points (guards) so that each point of P is seen by least one guard. This problem is NP-hard. Art-gallery problems have attracted a lot of research in the last thirty years =-=[16, 17]-=-. A natural heuristic for solving art-gallery problems is to use a greedy approach based on area: We first find a guard that maximizes the area seen, next find a guard that sees the maximal area not s... |

432 | Applications of random sampling in computational geometry - Clarkson, Shor - 1989 |

124 | Art gallery and illumination problems, in
- Urrutia
- 1999
(Show Context)
Citation Context ..., and wish to find a set of points (guards) so that each point of P is seen by least one guard. This problem is NP-hard. Art-gallery problems have attracted a lot of research in the last thirty years =-=[16, 17]-=-. A natural heuristic for solving art-gallery problems is to use a greedy approach based on area: We first find a guard that maximizes the area seen, next find a guard that sees the maximal area not s... |

64 |
On a class of O(n 2 ) problems in computational geometry
- Gajentaan, Overmars
- 1995
(Show Context)
Citation Context ...algorithm that finds a (1 − δ)-approximation in time O((n 2 /δ 4 ) log 3 (n/δ)) with high probability. We also show that approximating the largest visible polygon up to a constant factor is 3sum-hard =-=[11]-=-, implying that our algorithm is probably close to optimal as far as the dependency on n is concerned. Our second problem is motivated by the task of placing a new supermarket such that it takes over ... |

40 | The Probabilistic Method. Wiley Interscience, 2d edition, 2000. [2] R. Avenhaus. Montmort's problem, Burnside's lemma and Bell's - Alon, Spencer - 2005 |

38 | Matching convex shapes with respect to the symmetric difference
- Alt, Fuchs, et al.
- 1998
(Show Context)
Citation Context ... P and Q under translations or rigid motions. The area of overlap (or the area of the symmetric difference) of two planar regions is a natural measure of their similarity that is insensitive to noise =-=[3, 7]-=-. Mount et al. [13] first studied the function mapping a translation vector to the area of overlap of a translated simple polygon P with another simple polygon Q, showing that it is continuous and pie... |

38 | Guarding galleries where no point sees a small area - Valtr - 1998 |

29 | Computing the maximum overlap of two convex polygons under translations,
- Berg, Devillers, et al.
- 1998
(Show Context)
Citation Context ... P and Q under translations or rigid motions. The area of overlap (or the area of the symmetric difference) of two planar regions is a natural measure of their similarity that is insensitive to noise =-=[3, 7]-=-. Mount et al. [13] first studied the function mapping a translation vector to the area of overlap of a translated simple polygon P with another simple polygon Q, showing that it is continuous and pie... |

23 | Path planning in 0/1/∞ weighted regions with applications - Gewali, Meng, et al. - 1988 |

20 | The one-round Voronoi game
- Cheong, Har-Peled, et al.
- 2002
(Show Context)
Citation Context ...ur task is indeed to find a point x such that the Voronoi region of x is as large as possible. The area of Voronoi regions has been considered before in the context of games, such as the Voronoi game =-=[1, 5]-=- or the Hotelling game [15]. As far as we know, the only previous paper discussing maximizing the Voronoi region of a new point is by Dehne et al. [9], who show that the area function has only a singl... |

18 | On the area of overlap of translated polygons.
- Mount, Silverman, et al.
- 1996
(Show Context)
Citation Context ...ations or rigid motions. The area of overlap (or the area of the symmetric difference) of two planar regions is a natural measure of their similarity that is insensitive to noise [3, 7]. Mount et al. =-=[13]-=- first studied the function mapping a translation vector to the area of overlap of a translated simple polygon P with another simple polygon Q, showing that it is continuous and piecewise polynomial o... |

12 | Maximizing the overlap of two planar convex sets under rigid motions,”
- Ahn, Cheong, et al.
- 2007
(Show Context)
Citation Context ...ea of overlap of two collections of triangles in time O(n 8 ). A (1 − ε)approximation algorithm for the case of convex polygons with running time O((log n)/ε + (1/ε) log(1/ε)) was given by Ahn et al. =-=[2]-=-. Finally, de Berg et al. [8] consider the case where P and Q are disjoint unions of m and n unit disks, with m ≤ n. They compute a (1 − ε)-approximation for the maximal area of overlap of P and Q und... |

11 | Maximizing a Voronoi region: The convex case
- Dehne, Klein, et al.
- 2002
(Show Context)
Citation Context ...the context of games, such as the Voronoi game [1, 5] or the Hotelling game [15]. As far as we know, the only previous paper discussing maximizing the Voronoi region of a new point is by Dehne et al. =-=[9]-=-, who show that the area function has only a single local maximum inside a region where the set of Voronoi 1 Joint work with Alon Efrat and Sariel Har-Peled. An earlier version of this work has appear... |

9 | Competitive facility location along a highway
- Ahn, Cheng, et al.
- 2001
(Show Context)
Citation Context ...ur task is indeed to find a point x such that the Voronoi region of x is as large as possible. The area of Voronoi regions has been considered before in the context of games, such as the Voronoi game =-=[1, 5]-=- or the Hotelling game [15]. As far as we know, the only previous paper discussing maximizing the Voronoi region of a new point is by Dehne et al. [9], who show that the area function has only a singl... |

4 |
Tsoukalas. Optimum placement of guards
- Ntafos, Z
- 1994
(Show Context)
Citation Context ... first find a guard that maximizes the area seen, next find a guard that sees the maximal area not seen by the first guard, and so on until each point of P is seen by some guard. Ntafos and Tsoukalas =-=[14]-=- show how to find, for any δ > 0, a guard that sees an area of size (1 − δ)µopt. Their algorithm requires O(n 5 /δ 2 ) time in the worst case. We give a probabilistic algorithm that finds a (1 − δ)-ap... |

2 |
Maximizing the area of overlap of two unions of convex homothets under translation
- Berg, Giannopoulos, et al.
- 2003
(Show Context)
Citation Context ...ons of triangles in time O(n 8 ). A (1 − ε)approximation algorithm for the case of convex polygons with running time O((log n)/ε + (1/ε) log(1/ε)) was given by Ahn et al. [2]. Finally, de Berg et al. =-=[8]-=- consider the case where P and Q are disjoint unions of m and n unit disks, with m ≤ n. They compute a (1 − ε)-approximation for the maximal area of overlap of P and Q under translations in time O((nm... |