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### Matching: A Well-Solved Class of Integer Linear Programs [chapter]

Jack Edmonds, Ellis L. Johnson
<span title="">2003</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;
A main purpose of this work is to give a good algorithm for a certain welldescribed class of integer linear programming problems, called matching problems (or the matching problem).  ...  In the process, we derive a description of a system of linear inequalities whose polyhedron is the convex hull of the admissible solution vectors to the given matching problem.  ...  By contrast with general integer linear programming, the matching problem is well-solved. (7) Theorem.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36478-1_3">doi:10.1007/3-540-36478-1_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qj24yu3wgbhyff76ovehgcasly">fatcat:qj24yu3wgbhyff76ovehgcasly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120128214124/http://www.eecs.umich.edu/~pettie/matching/Edmonds-Ellis-Matching-A-well-solved-class-of-integer-programs.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/a1/cd/a1cd9b09f1b0686e02eacbf2a3421ff36df11f6e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36478-1_3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Nonlinear Bipartite Matching [article]

Yael Berstein, Shmuel Onn
<span title="2006-05-23">2006</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the problem of optimizing nonlinear objective functions over bipartite matchings.  ...  and maximization, and a randomized algorithm for optimizing arbitrary objectives.  ...  By solving the linear programs minimizing and maximizing w k x over Π 4 for k = 1, 2 (step 1 of the algorithm above) we get s 1 = s 2 = 0, t 1 = 3, t 2 = 4, and so the smallest grid containing vert(Π 4  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/0605610v1">arXiv:math/0605610v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dump3rwizzexxdmp42hqnpqpte">fatcat:dump3rwizzexxdmp42hqnpqpte</a> </span>
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### Nonlinear bipartite matching

Yael Berstein, Shmuel Onn
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/s6sw62lf6zcxrghfhvjqhycu5y" style="color: black;">Discrete Optimization</a> </i> &nbsp;
We study the problem of optimizing nonlinear objective functions over bipartite matchings.  ...  and maximization, and a randomized algorithm for optimizing arbitrary objectives.  ...  The first author was supported in part by an Irwin and Joan Jacobs Scholarship and by a scholarship from the Graduate School of the Technion.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.disopt.2007.11.002">doi:10.1016/j.disopt.2007.11.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4ghq2ypz6vecpbrxhafx3t5ymq">fatcat:4ghq2ypz6vecpbrxhafx3t5ymq</a> </span>
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### A Discrete Optimization Description for the Solutions in the Matching Problem

Walied H. Sharif
<span title="2006-01-01">2006</span> <i title="Science Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2lsiqmywajba3cmrphqr452nfu" style="color: black;">Journal of Mathematics and Statistics</a> </i> &nbsp;
The general mixed-integer programming problem is given together with the definition of the convex hull of the integer solutions.  ...  This study was concerned with the characterization of solutions in the matching problem.  ...  This class is not well defined but can be said to include integer programs with linear programming relaxations, i.e. up to several thousand rows and columns, but with a small number of integer variables  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3844/jmssp.2006.351.353">doi:10.3844/jmssp.2006.351.353</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lxp3wx2pnfhwhaaiimkjpric5q">fatcat:lxp3wx2pnfhwhaaiimkjpric5q</a> </span>
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### Simultaneous Matchings [chapter]

Khaled Elbassioni, Irit Katriel, Martin Kutz, Meena Mahajan
<span title="">2005</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;
In this paper we study the following generalisation of the X-perfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection F ⊆ 2 X of k subsets  ...  of X, find a subset M ⊆ E of the edges such that for each C ∈ F, the edge set M ∩ (C × D) is a C-perfect matching in G (or report that no such set exists).  ...  Write α = |R|, β = |C| and A = A(k), and consider the pair of primal-dual linear programs given by (1) over ξ ∈ R α and y ∈ R β .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11602613_12">doi:10.1007/11602613_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bp2pstjafjbkbgktmjs5txp4tm">fatcat:bp2pstjafjbkbgktmjs5txp4tm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830074125/http://people.mpi-inf.mpg.de/alumni/d1/2009/mkutz/pubs/ElbKatKutMah_SimMatch.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/07/23/0723de26c66dde59a654e7812790b4dbe42781c8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11602613_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Factorized graph matching

Feng Zhou, F. De la Torre
<span title="">2012</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ilwxppn4d5hizekyd3ndvy2mii" style="color: black;">2012 IEEE Conference on Computer Vision and Pattern Recognition</a> </i> &nbsp;
Graph matching plays a central role in solving correspondence problems in computer vision.  ...  for graph matching and reveals the connection among several methods; (3) Using the factorization we derive a new approximation of the original problem that improves state-of-the-art algorithms in graph  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cvpr.2012.6247667">doi:10.1109/cvpr.2012.6247667</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cvpr/ZhouT12.html">dblp:conf/cvpr/ZhouT12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/22e3rphoc5bhbftu56wuh7fk5a">fatcat:22e3rphoc5bhbftu56wuh7fk5a</a> </span>
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### Factorized Graph Matching

Feng Zhou, Fernando De la Torre
<span title="2016-09-01">2016</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3px634ph3vhrtmtuip6xznraqi" style="color: black;">IEEE Transactions on Pattern Analysis and Machine Intelligence</a> </i> &nbsp;
Graph matching plays a central role in solving correspondence problems in computer vision.  ...  for graph matching and reveals the connection among several methods; (3) Using the factorization we derive a new approximation of the original problem that improves state-of-the-art algorithms in graph  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tpami.2015.2501802">doi:10.1109/tpami.2015.2501802</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/26595909">pmid:26595909</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i6ucfen5p5hmdewwindbkmzd3e">fatcat:i6ucfen5p5hmdewwindbkmzd3e</a> </span>
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### Matroid matching

Jon Lee, Maxim Sviridenko, Jan Vondrak
<span title="">2010</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the 42nd ACM symposium on Theory of computing - STOC &#39;10</a> </i> &nbsp;
We also give a 3/2-approximation for the weighted version of a special case of matroid matching, the matchoid problem.  ...  Unweighted matroid matching for linearly-represented matroids was solved by Lovász, and the problem is known to be intractable for general matroids.  ...  This inequality is valid for all integer feasible solutions of the linear-programming relaxation (4.8-4.10).  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1806689.1806741">doi:10.1145/1806689.1806741</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/LeeSV10.html">dblp:conf/stoc/LeeSV10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yg52hfvqdjeqjows6b6pfo2by4">fatcat:yg52hfvqdjeqjows6b6pfo2by4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130409135407/http://theory.stanford.edu/~jvondrak/data/matroid-parity-SICOMP.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/62/fc/62fcc755fc440f41db8273f6f4004bcf091ab2e4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1806689.1806741"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

### Fractional matroid matchings

John H Vande Vate
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g6u5fful5vcr3a7gppc6y47el4" style="color: black;">Journal of combinatorial theory. Series B (Print)</a> </i> &nbsp;
problem is hard, then solving the linear program will be hard as well.  ...  The matroid matching problem generalizes several well-solved problems in combinatorial optimization including the matroid intersection problem and the graphic matching problem.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(92)90037-x">doi:10.1016/0095-8956(92)90037-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/auliqi2wjfcsddb6rbvk6z4rky">fatcat:auliqi2wjfcsddb6rbvk6z4rky</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924222848/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/1d4/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDk1ODk1NjkyOTAwMzd4.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/26/3e/263e429fdd3a2389e62e67624d8813ed1eae594a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0095-8956(92)90037-x"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

### Hierarchical Matching of Non-rigid Shapes [chapter]

Dan Raviv, Anastasia Dubrovina, Ron Kimmel
<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;
The complexity of a matching process is exponential by nature, but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth two-manifolds.  ...  The majority of the methods addressing this problem boil down to a minimization of a distortion measure.  ...  Acknowledgment This research was supported by European Communitys FP7-ERC program, grant agreement no. 267414.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-24785-9_51">doi:10.1007/978-3-642-24785-9_51</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vjk3ohr4nrbs3fulmawcudvgum">fatcat:vjk3ohr4nrbs3fulmawcudvgum</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922001434/http://www.cs.technion.ac.il/~ron/PAPERS/RavDubKimSSVM11.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/6f/16/6f16996a86e291e261a021352f8fd5e6f9acd42d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-24785-9_51"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Online resource matching for heterogeneous grid environments

V.K. Naik, C. Liu, L. Yang, J. Wagner
<span title="">2005</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ujjptpi7mjgmfdad3mk3fcer3y" style="color: black;">CCGrid 2005. IEEE International Symposium on Cluster Computing and the Grid, 2005.</a> </i> &nbsp;
In this paper, we first present a linear programming based approach for modeling and solving the resource matching problem in grid environments with heterogeneous resources.  ...  We then propose a web service style architecture for on-line matching of independent jobs with resources in a grid environment and describe a prototype implementation.  ...  Resource matching as an integer programming problem Integer programming is a technique for solving certain kinds of problems: maximizing the value of an objective function subject to constraints, where  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ccgrid.2005.1558620">doi:10.1109/ccgrid.2005.1558620</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ccgrid/NaikLYW05.html">dblp:conf/ccgrid/NaikLYW05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gknnymuscbgzjkaux6xuvc6xbu">fatcat:gknnymuscbgzjkaux6xuvc6xbu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100617194922/http://people.cs.uchicago.edu/~chliu/doc/CCGrid-Harmony-final.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/d9/3a/d93a877ddc1e378457150bd311cbe6be6b2967eb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ccgrid.2005.1558620"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

### Computing Minimum-Weight Perfect Matchings

William Cook, André Rohe
<span title="">1999</span> <i title="Institute for Operations Research and the Management Sciences (INFORMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ko3yoz32wja7tmqwbgqqjmfyxa" style="color: black;">INFORMS journal on computing</a> </i> &nbsp;
As a benchmark of the algorithm's performance, solving a 100,000 node geometric instance on a 200 Mhz Pentium-Pro computer takes approximately 3 minutes.  ...  We make several observations on the implementation of Edmonds' blossom algorithm for solving minimum-weight perfect-matching problems and we present computational results for geometric problem instances  ...  Goemans for his remarks about perfect matchings in Delaunay triangulations.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1287/ijoc.11.2.138">doi:10.1287/ijoc.11.2.138</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vvzuaszn6vgj5ilk6sereiw7zq">fatcat:vvzuaszn6vgj5ilk6sereiw7zq</a> </span>
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### Temporal Matching [article]

Julien Baste, Binh-Minh Bui-Xuan, Antoine Roux
<span title="2019-02-07">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce the notion of temporal matching of a link stream to be an independent γ-edge set belonging to the link stream.  ...  We show that the problem of computing a temporal matching of maximum size is NP-hard as soon as γ>1. We depict a kernelization algorithm parameterized by the solution size for the problem.  ...  Acknowledgements: We are grateful to Clémence Magnien for helpful pointers and valuable pieces of advice.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1812.08615v2">arXiv:1812.08615v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xqeilk2eqjgarddrzkdohrmdxu">fatcat:xqeilk2eqjgarddrzkdohrmdxu</a> </span>
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### Graph unification and matching [chapter]

Detlef Plump, Annegret Habel
<span title="">1996</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;
It is shown that a restricted form of graph unification corresponds to solving linear Diophantine equations, and hence is decidable.  ...  The matching concept suggests a new graph rewriting approach which is very simple to describe and which generalizes the well-known double-pnshout approach.  ...  Thus, the general unification problem of type 0 reduces to the problem of solving homogeneous and inhomogeneous linear Diophantine equations in non-negative integers.  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-61228-9_80">doi:10.1007/3-540-61228-9_80</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bxy2itmdgjcaznqvxisltnpc2i">fatcat:bxy2itmdgjcaznqvxisltnpc2i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190305001336/http://pdfs.semanticscholar.org/cc72/69c5fa0aafc40307bd21e5df641ff281c3c3.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/cc/72/cc7269c5fa0aafc40307bd21e5df641ff281c3c3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-61228-9_80"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

### Matching Interdiction [article]

Rico Zenklusen
<span title="2008-04-22">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
weight of a maximum weight matching in the remaining graph is minimized.  ...  Furthermore, we present a pseudo-polynomial algorithm for solving the matching interdiction problem on graphs with bounded treewidth.  ...  A tree decomposition can easily be converted (in linear time) into a nice tree decomposition of the same width and with a linear growth in size [8] .  ...
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0804.3583v1">arXiv:0804.3583v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y7rkc2ktkvd5rdgtnh46ppi4kq">fatcat:y7rkc2ktkvd5rdgtnh46ppi4kq</a> </span>
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