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Computational Geometry and Facility Location
 Proc. International Conference on Operations Research and Management Science
, 1990
"... this paper we briefly survey the most recent results in the area of facility location, concentrating on versions of the problem that are likely to be unfamiliar to the transportation and management science community and we explore the interaction between facility location problems and the field of c ..."
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Cited by 18 (3 self)
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this paper we briefly survey the most recent results in the area of facility location, concentrating on versions of the problem that are likely to be unfamiliar to the transportation and management science community and we explore the interaction between facility location problems and the field of computational geometry. Such versions of the problem include the standard models of points as customers and facilities but with geodesic rather than the traditional Minkowski metrics as measures of distance, as well as more complicated models of customers and facilities such as
Motion Planning of Legged Robots
, 1997
"... We study the problem of computing the free space of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. The robot is subject to two constraints: each leg has a maximal extension R #accessibility constraint# and the body of ..."
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Cited by 18 (1 self)
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We study the problem of computing the free space of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. The robot is subject to two constraints: each leg has a maximal extension R #accessibility constraint# and the body of the robot must lie above the convex hull of its feet #stability constraint#. Moreover, the robot can only put its feet on some regions, called the foothold regions. The free space positions of the body of the robot such that there exists a set of accessible footholds for which the robot is stable. We present an efficient algorithm that computes log n# time and O#n ##n## space for point footholds where ##n# is an extremely slowly growing function ###n# 3 for any practical value of n#. We also presentan when the foothold regions are pairwise disjoint polygons with n edges in total. This algorithm computes in O#n # 8 #n# log n# time using # 8 #n## space ## 8 #n# is also an extremely slowly growing function#. These results are close to optimal since#, # isalower bound for the size of .
Complete Algorithms for Feeding Polyhedral Parts using Pivot Grasps
, 1995
"... To rapidly feed industrial parts on an assembly line, Carlisle et. al. [7] proposed a flexible part feeding system that drops parts on a flat conveyor belt, determines position and orientation of each part with a vision system, and then moves them into a desired orientation. A robot arm with 4 degre ..."
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Cited by 18 (7 self)
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To rapidly feed industrial parts on an assembly line, Carlisle et. al. [7] proposed a flexible part feeding system that drops parts on a flat conveyor belt, determines position and orientation of each part with a vision system, and then moves them into a desired orientation. A robot arm with 4 degrees of freedom (DoF) is capable of moving parts through 6 DoF when equipped with a passive pivoting axis between the parallel jaws of its gripper. The idea is to grasp a part with 2 hard finger contacts such that it pivots, under gravity, into a desired orientation when lifted and replaced on the table. We refer to these actions as pivot grasps. This paper considers the planning problem. Given a polyhedral part shape, coefficient of friction and a pair of stable configurations as input, find pairs of grasp points that will cause the part to pivot from one stable configuration to the other. For some transitions, pivot grasps may not exist. For a part with n faces and m stable configurations, ...
Multiple Containment Methods
, 1994
"... We present three different methods for finding solutions to the 2D translationonly containment problem: find translations for k polygons that place them inside a given polygonal container without overlap. Both the container and the polygons to be placed in it may be nonconvex. First, we provide se ..."
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Cited by 13 (10 self)
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We present three different methods for finding solutions to the 2D translationonly containment problem: find translations for k polygons that place them inside a given polygonal container without overlap. Both the container and the polygons to be placed in it may be nonconvex. First, we provide several exact algorithms that improve results for k = 2 or k = 3. In particular, we give an algorithm for three convex polygons and a nonconvex container with running time in O(m 3 n log mn), where n is the number of vertices in the container, and m is the sum of the vertices of the k polygons. This is an improvement of a factor of n 2 over previous algorithms. Second, we give an approximation algorithm for k nonconvex polygons and a nonconvex container based on restriction and subdivision of the configuration space. Third, we develop a MIP (mixed integer programming) model for k nonconvex polygons and a nonconvex container.
Motorcycle Graphs and Straight Skeletons
, 2002
"... We present a new algorithm to compute a motorcycle graph. It runs in O(n p n log n) time when n is the size of the input. We give a new characterization of the straight skeleton of a polygon possibly with holes. ..."
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Cited by 13 (1 self)
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We present a new algorithm to compute a motorcycle graph. It runs in O(n p n log n) time when n is the size of the input. We give a new characterization of the straight skeleton of a polygon possibly with holes.
An OutputSensitive Convex Hull Algorithm for Planar Objects
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
"... ..."
Guarding a terrain by two watchtowers
 In Proc. 21st Annu. ACM Sympos. Computational Geometry
, 2005
"... Given a polyhedral terrain T with n vertices, the twowatchtower problem for T asks to find two vertical segments, called watchtowers, of smallest common height, whose bottom endpoints (bases) lie on T, and whose top endpoints guard T, in the sense that each point on T is visible from at least one o ..."
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Cited by 10 (1 self)
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Given a polyhedral terrain T with n vertices, the twowatchtower problem for T asks to find two vertical segments, called watchtowers, of smallest common height, whose bottom endpoints (bases) lie on T, and whose top endpoints guard T, in the sense that each point on T is visible from at least one of them. There are three versions of the problem, discrete, semidiscrete, and continuous, depending on whether two, one, or none of the two bases are restricted to be among the vertices of T, respectively. In this paper we present the following results for the twowatchtower problem in R 2 and R 3: (1) We show that the discrete twowatchtowers problem in R 2 can be solved in O(n 2 log 4 n) time, significantly improving previous solutions. The algorithm works, without increasing its asymptotic running time, for the semicontinuous version, where one of the towers is allowed to be placed anywhere on T. (2) We show that the continuous twowatchtower problem in R 2 can be solved in O(n 3 α(n)log 3 n) time, again significantly improving previous results. (3) Still in R 2, we show that the continuous version of the problem of guarding a finite set P ⊂ T of m points by two watchtowers of smallest common height can be solved in O(mnlog 4 n) time.
Sweeping Lines and Line Segments with a Heap
, 1997
"... Given n line segments in the plane, the BentleyOttmann sweep maintains the exact ordering of the intersections of the segments with a vertical line, as this line sweeps the plane from left to right. To accomplish this, every intersection between two segments must be processed, and the running time ..."
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Cited by 10 (2 self)
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Given n line segments in the plane, the BentleyOttmann sweep maintains the exact ordering of the intersections of the segments with a vertical line, as this line sweeps the plane from left to right. To accomplish this, every intersection between two segments must be processed, and the running time of the sweep can be (n 2). In this paper, it is shown how a heap on the intersections can be maintained during the sweep. This new type of sweep processes O(n log² n)intersections when sweeping over lines and O(n p n log n) intersections when sweeping over line segments. Alower bound of (n log n) is also established.
Multicriteria Network Location Problems with Sum Objectives
, 1996
"... In this paper network location problems with several objectives are discussed, where every single objective is a classical median objective function. We will look at the problem of finding Pareto optimal locations and lexicographically optimal locations. It is shown that for Pareto optimal locations ..."
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Cited by 7 (4 self)
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In this paper network location problems with several objectives are discussed, where every single objective is a classical median objective function. We will look at the problem of finding Pareto optimal locations and lexicographically optimal locations. It is shown that for Pareto optimal locations in undirected networks no node dominance result can be shown. Structural results as well as efficient algorithms for these multicriteria problems are developed. In the special case of a tree network a generalization of Goldman's dominance algorithm for finding Pareto locations is presented.
Translating a Regular Grid over a Point Set
 COMPUT. GEOM. THEORY APPL
, 2003
"... We consider the problem of translating a (finite or infinite) square grid G over a set S of n points in the plane in order to maximize some objective function. We say that a grid cell is koccupied if it contains k or more points of S. The main set of problems we study have to do with translating ..."
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Cited by 6 (1 self)
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We consider the problem of translating a (finite or infinite) square grid G over a set S of n points in the plane in order to maximize some objective function. We say that a grid cell is koccupied if it contains k or more points of S. The main set of problems we study have to do with translating an infinite grid so that the number of koccupied cells is maximized or minimized. For these problems we obtain running times of the form O(kn polylog (n)). We also consider the problem of translating a nite size grid, with m cells, in order to maximize the number of koccupied cells. Here we obtain a running time of the form O(knm polylog (nm)). In solving