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Optimal Spanners for AxisAligned Rectangles
 COMPUTATIONAL GEOMETRY, THEORY AND APPLICATIONS
, 2004
"... The dilation of a geometric graph is the maximum, over all pairs of points in the graph, of the ratio of the Euclidean length of the shortest path between them in the graph and their Euclidean distance. We consider a generalized version of this notion, where the nodes of the graph are not points ..."
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Cited by 4 (2 self)
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but axisparallel rectangles in the plane. The arcs in the graph are horizontal or vertical segments connecting a pair of rectangles, and the distance measure we use is the L 1 distance. The dilation of a pair of points is then de ned as the length of the shortest rectilinear path between them
Cuttings for Disks and AxisAligned Rectangles in ThreeSpace
"... We present new asymptotically tight bounds on cuttings, a fundamental data structure in computational geometry. For n objects in space and a parameter r ∈ N, an 1 rcutting is a covering of the space with simplices such that the interior of each simplex intersects at most n/rcutting of objects. For ..."
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. For n pairwise disjoint disks in R3 and a parameter r ∈ N, we construct a 1 r size O(r2). For n axisaligned rectangles in R3, we construct a 1 rcutting of size O(r3/2). As an application related to multipoint location in threespace, we present tight bounds on the cost of spanning trees across
Finding the Largest AxisAligned Rectangle in a Polygon in ...
 In Proc. 13th Canad. Conf. Comput. Geom
, 2001
"... We consider the problem of nding the largest area axisaligned rectangle contained in an n vertex polygon. We present an algorithm that solves this problem in O(n log n) time. This is an improvement by a factor of O(log n) over the best known algorithm. Our method of achieving this improvement is no ..."
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Cited by 4 (0 self)
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We consider the problem of nding the largest area axisaligned rectangle contained in an n vertex polygon. We present an algorithm that solves this problem in O(n log n) time. This is an improvement by a factor of O(log n) over the best known algorithm. Our method of achieving this improvement
Tracking an Extended Object Modeled as an AxisAligned Rectangle
"... Abstract: In many tracking applications, the extent of the target object is neglected and it is assumed that the received measurements stem from a point source. However, modern sensors are able to supply several measurements from different scattering centers on the target object due to their highre ..."
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resolution capability. As a consequence, it becomes necessary to incorporate the target extent into the estimation procedure. This paper introduces a new method for tracking the smallest enclosing rectangle of an extended object with an unknown shape. At each time step, a finite set of noisy position measurements
Approximation Algorithms for finding Independent Sets of AxisAligned Rectangles
, 2005
"... A hotel has one conference room and many groups wishing to schedule meetings in that room during the week. They want to allow as many groups as possible to use the room given the time constraints of the meetings. We can represent each proposed meeting as an interval on the real line. Then selecting ..."
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A hotel has one conference room and many groups wishing to schedule meetings in that room during the week. They want to allow as many groups as possible to use the room given the time constraints of the meetings. We can represent each proposed meeting as an interval on the real line. Then selecting the maximum number of disjoint intervals is equivalent to scheduling as many
Hellytype theorems for hollow axisaligned boxes
 PROC. AMER. MATH. SOC
, 1999
"... A hollow axisaligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axisaligned boxes have nonempty intersection, then the whole collection has nonempty intersection; and if any 5 of a collection of hollow ..."
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Cited by 2 (2 self)
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of hollow axisaligned rectangles in R 2 have nonempty intersection, then the whole collection has nonempty intersection. The values 2 d for d ≥ 3 and 5 for d = 2 are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if 2 d were lowered to 2
Empty Rectangles and Graph Dimension
, 2005
"... We consider rectangle graphs whose edges are defined by pairs of points in diagonally opposite corners of empty axisaligned rectangles. The maximum number of edges of such a graph on n points is shown to be ⌊ 1 4 n2 + n − 2⌋. This number also has other interpretations: • It is the maximum number ..."
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Cited by 3 (2 self)
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We consider rectangle graphs whose edges are defined by pairs of points in diagonally opposite corners of empty axisaligned rectangles. The maximum number of edges of such a graph on n points is shown to be ⌊ 1 4 n2 + n − 2⌋. This number also has other interpretations: • It is the maximum number
Kinetic Connectivity of Rectangles
 In Proc. 15th Annu. ACM Sympos. Comput. Geom
, 1999
"... We develop a kinetic data structure (KDS) for maintaining the connectivity of a set of axisaligned rectangles moving in the plane. In the kinetic framework, each rectangle is assumed to travel along a lowdegree algebraic path, specified by a flight planif the flight plan changes, the data struc ..."
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Cited by 13 (1 self)
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We develop a kinetic data structure (KDS) for maintaining the connectivity of a set of axisaligned rectangles moving in the plane. In the kinetic framework, each rectangle is assumed to travel along a lowdegree algebraic path, specified by a flight planif the flight plan changes, the data
A learning theory approach to noninteractive database privacy
 In Proceedings of the 40th annual ACM symposium on Theory of computing
, 2008
"... In this paper we demonstrate that, ignoring computational constraints, it is possible to release synthetic databases that are useful for accurately answering large classes of queries while preserving differential privacy. Specifically, we give a mechanism that privately releases synthetic data usefu ..."
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Cited by 220 (25 self)
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. This algorithm does not release synthetic data, but instead another data structure capable of representing an answer for each query. We also give an efficient algorithm for releasing synthetic data for the class of interval queries and axisaligned rectangles of constant dimension over discrete domains. 1.
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"... With an infinite hypothesis set H, the error bounds of the previous lecture are not informative. Is efficient learning from a finite sample possible when H is infinite? Our example of axisaligned rectangles shows that it is possible. Can we reduce the infinite case to a finite set? Project on finit ..."
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With an infinite hypothesis set H, the error bounds of the previous lecture are not informative. Is efficient learning from a finite sample possible when H is infinite? Our example of axisaligned rectangles shows that it is possible. Can we reduce the infinite case to a finite set? Project
Results 1  10
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