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Graph Size Estimation [article]

Maciej Kurant, Carter T. Butts, Athina Markopoulou
<span title="2012-10-01">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Second, we introduce SafetyMargin, a method that corrects estimators for dependence in RW samples. Finally, we combine these two stand-alone techniques to obtain a RW-based graph size estimator.  ...  In this paper, we are interested in a fundamental property of this type - the graph size N, i.e., the number of its nodes.  ...  [20, 50] propose two graph size estimators that take as input a traceroute sample. Model-based Estimation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1210.0460v1">arXiv:1210.0460v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s2r7wg7hrbhj5f26xlkdfeu47u">fatcat:s2r7wg7hrbhj5f26xlkdfeu47u</a> </span>
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Direct estimation of sizes of higher-order graphs

John C. Collins, Andreas Freund
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2y36cnqlfjfbjkv7jqmcepxs5u" style="color: black;">Nuclear Physics B</a> </i> &nbsp;
With the aid of simple examples we show how to make simple estimates of the sizes of higher-order Feynman graphs.  ...  We show how to estimate the sizes of graphs by a direct examination of the integrands.  ...  One is to estimate the graphs without having explicit expressions for the graphs; one just searches for the possible singularities that would prevent the natural size of a graph from being its actual size  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0550-3213(97)00445-8">doi:10.1016/s0550-3213(97)00445-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ecssgwatrbehjkes6lu6o6av3q">fatcat:ecssgwatrbehjkes6lu6o6av3q</a> </span>
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An Estimator for Matching Size in Low Arboricity Graphs with Two Applications [article]

Hossein Jowhari
<span title="2020-11-25">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For planar graphs, we show the estimator does better and returns a 3.5 approximation of the matching size.  ...  In this paper, we present a new simple degree-based estimator for the size of maximum matching in bounded arboricity graphs.  ...  To estimate the matching size, we count the number of what we call locally superior vertices in the graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.11706v2">arXiv:2011.11706v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dpgnshnwovfe7my5ky57ts7wom">fatcat:dpgnshnwovfe7my5ky57ts7wom</a> </span>
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Estimating Population Size via Line Graph Reconstruction [chapter]

Bjarni V. Halldórsson, Dima Blokh, Roded Sharan
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We propose a novel graph theoretic method to estimate haplotype population size from genotype data.  ...  Conclusions: Our computational experiments show that when most of the sharings are true sharings the problem can be solved very fast and the estimated size is very close to the true size; when many of  ...  Background A fundamental problem in population studies is the estimation of the size of the underlying haplotype pool.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-33122-0_6">doi:10.1007/978-3-642-33122-0_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tovptn2hzbasto3lzm6lrfqh7u">fatcat:tovptn2hzbasto3lzm6lrfqh7u</a> </span>
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Estimating population size via line graph reconstruction

Bjarni V Halldórsson, Dima Blokh, Roded Sharan
<span title="">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/izdyn6hngbd35czi6err6qypqu" style="color: black;">Algorithms for Molecular Biology</a> </i> &nbsp;
We propose a novel graph theoretic method to estimate haplotype population size from genotype data.  ...  Conclusions: Our computational experiments show that when most of the sharings are true sharings the problem can be solved very fast and the estimated size is very close to the true size; when many of  ...  Background A fundamental problem in population studies is the estimation of the size of the underlying haplotype pool.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/1748-7188-8-17">doi:10.1186/1748-7188-8-17</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23829669">pmid:23829669</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3716786/">pmcid:PMC3716786</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fdyhbcz4fzfavokc5pe25z23lu">fatcat:fdyhbcz4fzfavokc5pe25z23lu</a> </span>
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On Estimating Maximum Matching Size in Graph Streams [article]

Sepehr Assadi, Sanjeev Khanna, Yang Li
<span title="2017-01-16">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the problem of estimating the maximum matching size in graphs whose edges are revealed in a streaming manner.  ...  On the lower bound front, we prove that any α-approximation algorithm for estimating matching size in dynamic graph streams requires Ω(√(n)/α^2.5) bits of space, even if the underlying graph is both sparse  ...  In general, what is the space-approximation tradeoff for estimating the matching size in graph streams?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.04364v1">arXiv:1701.04364v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/arpv4ufslranpbwe4weliv6evm">fatcat:arpv4ufslranpbwe4weliv6evm</a> </span>
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The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs [article]

Graham Cormode and Hossein Jowhari and Morteza Monemizadeh and S. Muthukrishnan
<span title="2016-11-14">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
arboricity graph, we present a one-pass algorithm that uses space O (c^10/3n^2/3) and returns an O(c)-estimator for the size of the maximum matching.  ...  Estimating the size of the maximum matching is a canonical problem in graph algorithms, and one that has attracted extensive study over a range of different computational models.  ...  returns an O(c)-estimator for the size of the maximum matching.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1608.03118v2">arXiv:1608.03118v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qds4khoq3beohpdsxs2mduibqq">fatcat:qds4khoq3beohpdsxs2mduibqq</a> </span>
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Estimating clique size by coloring the nodes of auxiliary graphs

Sándor Szabó
<span title="2018-12-01">2018</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3eqv6evtubbcxlmaovdwd4jg2i" style="color: black;">Acta Universitatis Sapientiae: Informatica</a> </i> &nbsp;
Applying this procedure to a suitably constructed auxiliary graph one may further improve the clique size estimate of the original graph.  ...  It is a common practice to find upper bound for clique number via legal coloring of the nodes of the graph. We will point out that with a little extra work we may lower this bound.  ...  The basic procedure In this section first we describe a procedure to estimate the clique size of a finite simple graph G = (V, E).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/ausi-2018-0008">doi:10.2478/ausi-2018-0008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ysdstsidd5hxbpvtdbgeox2fwm">fatcat:ysdstsidd5hxbpvtdbgeox2fwm</a> </span>
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Pre-synthesis Queue Size Estimation of Streaming Data Flow Graphs

S. Mondal, S. Memik, N. Bellas
<span title="">2006</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hss6rlelz5by5nc6dnosoj2luu" style="color: black;">2006 14th Annual IEEE Symposium on Field-Programmable Custom Computing Machines</a> </i> &nbsp;
Procedure for Queue Size Estimation Given, an unscheduled streaming data flow graph G = (V, E), and a set of resource constraints R, our goal is to estimate, the total number of registers in the queues  ...  Data Flow Graphs (DFGs) are widely used for representing such behavioral descriptions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/fccm.2006.59">doi:10.1109/fccm.2006.59</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fccm/MondalMB06.html">dblp:conf/fccm/MondalMB06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wcs3wxbl2bdo7akpss6dg3nsry">fatcat:wcs3wxbl2bdo7akpss6dg3nsry</a> </span>
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Estimating the size of correcting codes using extremal graph problems [chapter]

Sergiy Butenko, Panos Pardalos, Ivan Sergienko, Vladimir Shylo, Petro Stetsyuk
<span title="">2009</span> <i title="Springer New York"> Springer Optimization and Its Applications </i> &nbsp;
Finding estimates of the size of correcting codes is important from both theoretical and practical perspectives.  ...  We solve the problem of finding the largest correcting codes using previously developed algorithms for optimization problems in graphs. We report new exact solutions and estimates.  ...  We use efficient approaches to the maximum independent set and graph coloring problems to deal with the problem of estimating the largest code sizes.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-0-387-98096-6_12">doi:10.1007/978-0-387-98096-6_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gatotxuh5neljgrapds643zs6u">fatcat:gatotxuh5neljgrapds643zs6u</a> </span>
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B-Graph Sampling to Estimate the Size of a Hidden Population

Marinus Spreen, Stefan Bogaerts
<span title="2015-12-01">2015</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ft4lrnuwljb3tembi3q4ksjcwi" style="color: black;">Journal of Official Statistics</a> </i> &nbsp;
Link-tracing designs are often used to estimate the size of hidden populations by utilizing the relational links between their members.  ...  frame members can be estimated using Chao's and Zelterman's estimators for sparse data.  ...  Compared to the estimations of the population size from the original study, the B-graph sampling design gives comparable point estimates (500þ 427 ¼ 927; 550þ 427 ¼ 977; 490þ 427 ¼ 917), implying that  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1515/jos-2015-0042">doi:10.1515/jos-2015-0042</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnkopgy4yvhrbhjsqbmgom5kjm">fatcat:pnkopgy4yvhrbhjsqbmgom5kjm</a> </span>
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Distributed network size estimation and average degree estimation and control in networks isomorphic to directed graphs

Iman Shames, Themistoklis Charalambous, Christoforos N. Hadjicostis, Mikael Johansson
<span title="">2012</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/76cqjdra2zg5rgo2v5aqxsklkq" style="color: black;">2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)</a> </i> &nbsp;
is described by a directed graph.  ...  In this work, we present asynchronous distributed algorithms, based on ratio consensus, that can be used to accurately estimate the number of nodes in a multi-component system whose communication topology  ...  The problem of estimating the number of nodes in a graph has been already considered under the umbrella term of network size estimation (see, for example, [6] - [8] and references there-in).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/allerton.2012.6483452">doi:10.1109/allerton.2012.6483452</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/allerton/ShamesCHJ12.html">dblp:conf/allerton/ShamesCHJ12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zi2qk3xav5bdvnfzo2ufsdvtoy">fatcat:zi2qk3xav5bdvnfzo2ufsdvtoy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140513124934/http://www.eng.ucy.ac.cy:80/hadjicostis/various/allerton2012.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e5/f4/e5f4ed00980ac6649ef24bfa9c402afcc68dc559.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/allerton.2012.6483452"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

The Sparse Awakens: Streaming Algorithms for Matching Size Estimation in Sparse Graphs

Graham Cormode, Hossein Jowhari, Morteza Monemizadeh, S. Muthukrishnan, Marc Herbstritt
<span title="2017-08-31">2017</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uot5qmdbz5g6rasdd5kuoonkzu" style="color: black;">European Symposium on Algorithms</a> </i> &nbsp;
Estimating the size of the maximum matching is a canonical problem in graph analysis, and one that has attracted extensive study over a range of different computational models.  ...  an O(α)-estimator for the size of the maximum matching on the condition that the number edge deletions in the stream is bounded by O(αn).  ...  Table 1 1 Known results for estimating the size of a maximum matching in data streams. Reference Graph class Stream Approx.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.esa.2017.29">doi:10.4230/lipics.esa.2017.29</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/esa/CormodeJMM17.html">dblp:conf/esa/CormodeJMM17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ehrv3bs7zvf6rmeli6s6p46x3y">fatcat:ehrv3bs7zvf6rmeli6s6p46x3y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220119060516/https://drops.dagstuhl.de/opus/volltexte/2017/7849/pdf/LIPIcs-ESA-2017-29.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/64/1b/641bf5eb3bb46828e1dce7df91c29ced78b2dc85.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.esa.2017.29"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Streaming Algorithms for Estimating the Matching Size in Planar Graphs and Beyond [chapter]

Hossein Esfandiari, Mohammad T Hajiaghayi, Vahid Liaghat, Morteza Monemizadeh, Krzysztof Onak
<span title="2014-12-22">2014</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. Consider a graph G = (V, E) with n vertices and m edges.  ...  When the underlying graph is planar, we present a simple and elegant streaming algorithm that with high probability estimates the size of a maximum matching within a constant factor usingÕ(n 2/3 ) space  ...  Algorithm 1 1 Maximum Matching Estimator Input: A stream of edges of the graph e 1 , . . . , e m . Output: An estimation M of the size of a maximum matching M * .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973730.81">doi:10.1137/1.9781611973730.81</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/EsfandiariHLMO15.html">dblp:conf/soda/EsfandiariHLMO15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/367czouodvfrlbckoekeg3z64u">fatcat:367czouodvfrlbckoekeg3z64u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705073021/http://iuuk.mff.cuni.cz/%7Emonemi/EstimMatch.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/63/2c/632c6bfaa258aae7958bd192b2a00db8a33cc516.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973730.81"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Graph-Based 3D Multi-Person Pose Estimation Using Multi-View Images [article]

Size Wu, Sheng Jin, Wentao Liu, Lei Bai, Chen Qian, Dong Liu, Wanli Ouyang
<span title="2021-09-13">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For 3D pose estimation, the Pose Regression Graph Module (PRG) learns both the multi-view geometry and structural relations between human joints.  ...  This paper studies the task of estimating the 3D human poses of multiple persons from multiple calibrated camera views.  ...  [35] to generate 3D bounding boxes with the fixed orientation and size, and apply the 3D pose estimator [35] to generate initial 3D poses.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.05885v1">arXiv:2109.05885v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/slivz6tknbbxdjyaz4qv2gl4si">fatcat:slivz6tknbbxdjyaz4qv2gl4si</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210920103639/https://arxiv.org/pdf/2109.05885v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/76/69/7669c64268f405c1b59a9bb862356b1fefc25257.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.05885v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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