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36
Randomized Query Processing in Robot Motion Planning
, 1995
"... The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot motion planning. The attractiveness of the scheme stems from its general applicability to virtually any motionplanning problem, and its empirically observed success. In th ..."
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Cited by 32 (10 self)
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The subject of this paper is the analysis of a randomized preprocessing scheme that has been used for query processing in robot motion planning. The attractiveness of the scheme stems from its general applicability to virtually any motionplanning problem, and its empirically observed success. In this paper we initiate a theoretical basis for explaining this empirical success. Under a simple assumption about the configuration space, we show that it is possible to perform a preprocessing step following which queries can be answered quickly. En route, we pose and give solutions to related problems on graph connectivity in the evasiveness model, and artgallery theorems. Robotics Laboratory, Department of Computer Science, Stanford University, Stanford, CA 943052140. Partially supported by ARPA grant N0001492J1809 and ONR grant N000149410721. y Robotics Laboratory, Department of Computer Science, Stanford University, Stanford, CA 943052140. Partially supported by ARPA grant N0...
Visibility Analysis and Sensor Planning in Dynamic Environments
 IN EUROPEAN CONFERENCE ON COMPUTER VISION
, 2004
"... We analyze visibility from static sensors in a dynamic scene with moving obstacles (people). Such analysis is considered in a probabilistic sense in the context of multiple sensors, so that visibility from even one sensor might be sufficient. Additionally, we analyze worstcase scenarios for high ..."
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Cited by 29 (3 self)
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We analyze visibility from static sensors in a dynamic scene with moving obstacles (people). Such analysis is considered in a probabilistic sense in the context of multiple sensors, so that visibility from even one sensor might be sufficient. Additionally, we analyze worstcase scenarios for highsecurity areas where targets are noncooperative. Such visibility analysis provides important performance characterization of multicamera systems. Furthermore, maximization of visibility in a given region of interest yields the optimum number and placement of cameras in the scene. Our analysis has applications in surveillance  manual or automated  and can be utilized for sensor planning in places like museums, shopping malls, subway stations and parking lots. We present several example scenes  simulated and real  for which interesting camera configurations were obtained using the formal analysis developed in the paper.
Optimum Guard Covers and mWatchmen Routes for Restricted Polygons
 International Journal of Computational Geometry and Applications
, 1993
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Computing Camera Viewpoints in an Active Robot WorkCell
 International Journal of Robotics Research
, 1999
"... This paper presents a dynamic sensor planning system, capable of planning the locations and settings of vision sensors for use in an environment containing objects moving in known ways. The key component of this research is the computation of the camera position, orientation, and optical settings to ..."
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Cited by 20 (2 self)
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This paper presents a dynamic sensor planning system, capable of planning the locations and settings of vision sensors for use in an environment containing objects moving in known ways. The key component of this research is the computation of the camera position, orientation, and optical settings to be used over a time interval. A new algorithm is presented for viewpoint computation which ensures that the feature detectability constraints of focus, resolution, fieldofview, and visibility are satisfied. A five degreeoffreedom Cartesian robot carrying a CCD camera in a hand/eye configuration and surrounding the workcell of a Puma 560 robot was constructed for performing sensor planning experiments. The results of these experiments, demonstrating the use of this system in a robot workcell, are presented. The research described in this paper was performed while this author was at the Columbia University Department of Computer Science. y This work was supported in part by DARPA con...
Containment Algorithms for Nonconvex Polygons with Applications to Layout
, 1995
"... Layout and packing are NPhard geometric optimization problems of practical importance for which finding a globally optimal solution is intractable if P!=NP. Such problems appear in industries such as aerospace, ship building, apparel and shoe manufacturing, furniture production, and steel construct ..."
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Cited by 13 (5 self)
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Layout and packing are NPhard geometric optimization problems of practical importance for which finding a globally optimal solution is intractable if P!=NP. Such problems appear in industries such as aerospace, ship building, apparel and shoe manufacturing, furniture production, and steel construction. At their core, layout and packing problems have the common geometric feasibility problem of containment: find a way of placing a set of items into a container. In this thesis, we focus on containment and its applications to layout and packing problems. We demonstrate that, although containment is NPhard, it is fruitful to: 1) develop algorithms for containment, as opposed to heuristics, 2) design containment algorithms so that they say "no" almost as fast as they say "yes", 3) use geometric techniques, not just mathematical programming techniques, and 4) maximize the number of items for which the algorithms are practical. Our approach to containment is based on a new restrict/evaluate...
Compatible Geometric Matchings
, 2007
"... This paper studies noncrossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also noncrossing. Our first result states that for any two perfect matchings M and M ′ of the same set of n points, for some k ∈ O(log n), there ..."
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Cited by 13 (8 self)
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This paper studies noncrossing geometric perfect matchings. Two such perfect matchings are compatible if they have the same vertex set and their union is also noncrossing. Our first result states that for any two perfect matchings M and M ′ of the same set of n points, for some k ∈ O(log n), there is a sequence of perfect matchings M = M0, M1,..., Mk = M ′ , such that each Mi is compatible with Mi+1. This improves the previous best bound of k ≤ n − 2. We then study the conjecture: every perfect matching with an even number of edges has an edgedisjoint compatible perfect matching. We introduce a sequence of stronger conjectures that imply this conjecture, and prove the strongest of these conjectures in the case of perfect matchings that consist of vertical and horizontal segments. Finally, we prove that every perfect matching with n edges has an edgedisjoint compatible matching with approximately
Grasping nonstretchable cloth polygons
, 2009
"... In this paper, we examine nonstretchable 2D polygonal cloth, and place bounds on the number of fingers needed to immobilize it. For any nonstretchable cloth polygon, it is always necessary to pin all the convex vertices. We show that for some shapes, more fingers are necessary. No more than one th ..."
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Cited by 8 (0 self)
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In this paper, we examine nonstretchable 2D polygonal cloth, and place bounds on the number of fingers needed to immobilize it. For any nonstretchable cloth polygon, it is always necessary to pin all the convex vertices. We show that for some shapes, more fingers are necessary. No more than one third of the concave vertices need to be pinned for simple polygons, and no more than one third of the concave vertices plus two fingers per hole are necessary for polygons with holes. 1
Minimal Simplicial Dissections and Triangulations of Convex 3Polytopes
 DISCRETE COMPUT. GEOM
, 2000
"... This paper addresses three questions related to minimal triangulations of a threedimensional convex polytope P . . Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices? . Can a dissection of P use fewer tetrahedra than ..."
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Cited by 7 (3 self)
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This paper addresses three questions related to minimal triangulations of a threedimensional convex polytope P . . Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices? . Can a dissection of P use fewer tetrahedra than a triangulation? . Does the size of a minimal triangulation depend on the geometric realization of P? The main result of this paper is that all these questions have an affirmative answer. Even stronger, the gaps of size produced by allowing interior vertices or by using dissections may be linear in the number of points.
The Complexity Of Finding Small Triangulations Of Convex 3Polytopes
, 2000
"... The problem of finding a triangulation of a convex threedimensional polytope with few tetrahedra is NPhard. We discuss other related complexity results. ..."
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Cited by 7 (0 self)
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The problem of finding a triangulation of a convex threedimensional polytope with few tetrahedra is NPhard. We discuss other related complexity results.
WorstCaseOptimal Algorithms for Guarding Planar Graphs and Polyhedral Surfaces
, 2003
"... We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requiremen ..."
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Cited by 6 (0 self)
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We present an optimal \Theta (n)time algorithm for the selection of a subset of the vertices of an nvertex plane graph G so that each of the faces of G is covered by (i.e. incident with) one or more of the selected vertices. At most bn=2c vertices are selected, matching the worstcase requirement. Analogous results for edgecovers are developed for two different notions of &quot;coverage&quot;. In particular,our lineartime algorithm selects at most n \Gamma 2 edges to strongly cover G, at most bn=3c diagonals to cover G, and in the case where G has no quadrilateral faces, at most bn=3c edges to cover G. All these bounds are optimal in the worstcase. Most of our results flow from the study of a relaxation of thefamiliar notion of a 2coloring of a plane graph which we call a facerespecting 2coloring that permits