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An Application of Catalan Numbers on Cayley Tree of Order 2: Single Polygon Counting
"... Abstract. In this paper, we consider a problem on finding the number of different single connected component containing a fixed root for a given number of vertices on semi-infinite Cayley tree. The solution of this problem is the well known Catalan numbers. The result is then extended to the complet ..."
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Cited by 1 (0 self)
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Abstract. In this paper, we consider a problem on finding the number of different single connected component containing a fixed root for a given number of vertices on semi-infinite Cayley tree. The solution of this problem is the well known Catalan numbers. The result is then extended
QSplat: A Multiresolution Point Rendering System for Large Meshes
, 2000
"... Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing and p ..."
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Cited by 502 (8 self)
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Advances in 3D scanning technologies have enabled the practical creation of meshes with hundreds of millions of polygons. Traditional algorithms for display, simplification, and progressive transmission of meshes are impractical for data sets of this size. We describe a system for representing
Probabilistic Counting Algorithms for Data Base Applications
, 1985
"... This paper introduces a class of probabilistic counting lgorithms with which one can estimate the number of distinct elements in a large collection of data (typically a large file stored on disk) in a single pass using only a small additional storage (typically less than a hundred binary words) a ..."
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Cited by 444 (6 self)
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This paper introduces a class of probabilistic counting lgorithms with which one can estimate the number of distinct elements in a large collection of data (typically a large file stored on disk) in a single pass using only a small additional storage (typically less than a hundred binary words
The Digital Michelangelo Project: 3D Scanning of Large Statues
, 2000
"... We describe a hardware and software system for digitizing the shape and color of large fragile objects under non-laboratory conditions. Our system employs laser triangulation rangefinders, laser time-of-flight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merg ..."
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Cited by 488 (8 self)
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, merging, and viewing scanned data. As a demonstration of this system, we digitized 10 statues by Michelangelo, including the well-known figure of David, two building interiors, and all 1,163 extant fragments of the Forma Urbis Romae, a giant marble map of ancient Rome. Our largest single dataset
Approximate Frequency Counts over Data Streams
- VLDB
, 2002
"... We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algorithms can e ..."
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Cited by 418 (1 self)
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We present algorithms for computing frequency counts exceeding a user-specified threshold over data streams. Our algorithms are simple and have provably small memory footprints. Although the output is approximate, the error is guaranteed not to exceed a user-specified parameter. Our algorithms can
Improved Localization of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach
- J. Cogn. Neurosci
, 1993
"... We describe a comprehensive linear approach to the prob- lem of imaging brain activity with high temporal as well as spatial resolution based on combining EEG and MEG data with anatomical constraints derived from MRI images. The "inverse problem" of estimating the distribution of dipole st ..."
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Cited by 263 (19 self)
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formulation. ;m explicit polygonal model of the cortical manifold is first constructed :,s follows: (1) slice data in three onhogon;,l pJ:,ncs of section (needle-shaped voxels) are combined with a linear aleblurring technique to make a single high.resolution 3-D image (cubic voxels), (2) the image
Out-of-Core Simplification of Large Polygonal Models
, 2000
"... We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative ve ..."
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Cited by 159 (10 self)
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We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative
IP Multicast Channels: Express Support for Large-scale Single-source Applications
, 1999
"... In the IP multicast model, a set of hosts can be aggregated into a group of hosts with one address, to which any host can send. However, Internet TV, distance learning, file distribution and other emerging large-scale multicast applications strain the current realization of this model, which lacks a ..."
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Cited by 201 (4 self)
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has exactly one explicitly designated source, and zero or more channel subscribers. A single protocol supports both channel subscription and efficient collection of channel information such as subscriber count. We argue that EXPRESS addresses the aforementioned problems, justifying this multicast
Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
- SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 156 (3 self)
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The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time
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