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Comparing Images Using the Hausdorff Distance
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide ef ..."
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Cited by 659 (10 self)
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(translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover
Labeling Schemes for Small Distances in Trees
, 2003
"... We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distan ..."
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Cited by 33 (2 self)
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We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone
GPSLess Low Cost Outdoor Localization for Very Small Devices.
 IEEE Personal Communications Magazine,
, 2000
"... AbstractInstrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where ..."
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Cited by 1000 (27 self)
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AbstractInstrumenting the physical world through large networks of wireless sensor nodes, particularly for applications like environmental monitoring of water and soil, requires that these nodes be very small, light, untethered and unobtrusive. The problem of localization, i.e., determining where
Quantum Electrodynamics at Extremely Small Distances
, 804
"... The asymptotics of the GellMann – Low function in QED can be determined exactly, β(g) = g at g → ∞, where g = e 2 is the running fine structure constant. It solves the problem of pure QED at small distances L and gives the behavior g ∼ L −2. According to Landau, Abrikosov, Khalatnikov [1], relatio ..."
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Cited by 1 (1 self)
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The asymptotics of the GellMann – Low function in QED can be determined exactly, β(g) = g at g → ∞, where g = e 2 is the running fine structure constant. It solves the problem of pure QED at small distances L and gives the behavior g ∼ L −2. According to Landau, Abrikosov, Khalatnikov [1
On Small Distances of Small 2Groups
 COMMENT. MATH. UNIV. CAROLINAE
, 2001
"... The paper reports the results of a search for pairs of groups of order n that can be placed in the distance n²/4 for the case when n 2 {16, 32}. The constructions that are used are of the general character and some of their properties are discussed as well. ..."
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Cited by 5 (2 self)
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The paper reports the results of a search for pairs of groups of order n that can be placed in the distance n²/4 for the case when n 2 {16, 32}. The constructions that are used are of the general character and some of their properties are discussed as well.
The Closest Substring problem with small distances
, 2005
"... In the CLOSEST SUBSTRING problem k strings s1,..., sk are given, and the task is to find a string s of length L such that each string si has a consecutive substring of length L whose distance is at most d from s. The problem is motivated by applications in computational biology. We present two algo ..."
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Cited by 18 (2 self)
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In the CLOSEST SUBSTRING problem k strings s1,..., sk are given, and the task is to find a string s of length L such that each string si has a consecutive substring of length L whose distance is at most d from s. The problem is motivated by applications in computational biology. We present two
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 893 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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that respect the metric of the (possibly weighted) graph. Given a graph G we map its vertices to a normed space in an attempt to (i) Keep down the dimension of the host space and (ii) Guarantee a small distortion, i.e., make sure that distances between vertices in G closely match the distances between
QuasiPerfect Codes With Small Distance
, 2005
"... The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasiperfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance R and S and covering radius P and Q, respectively. We discuss the blockwise di ..."
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Cited by 3 (0 self)
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The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasiperfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance R and S and covering radius P and Q, respectively. We discuss the blockwise
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