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The Graph Isomorphism Problem (Dagstuhl Seminar 15511)

László Babai, Anuj Dawar, Pascal Schweitzer, Jacobo Torán, Marc Herbstritt
<span title="2016-04-11">2016</span> <i title="Schloss Dagstuhl Leibniz-Zentrum für Informatik GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u2phfyhrhje7xnnubtp3vfklcu" style="color: black;">Dagstuhl Reports</a> </i> &nbsp;
The goal of the seminar was to bring together researchers working on the numerous topics closely related to the Isomorphism Problem to foster their collaboration.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 15511 "The Graph Isomorphism Problem".  ...  On Tinhofer's Linear Programming Approach to Isomorphism Testing Oleg Verbitsky ( Exploring a linear programming approach to Graph Isomorphism, Tinhofer [1] defined the concept of a compact graph: A graph  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.12.1">doi:10.4230/dagrep.5.12.1</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/dagstuhl-reports/BabaiDST15.html">dblp:journals/dagstuhl-reports/BabaiDST15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/meig4kvcgffnjiq5wpa6wjs6am">fatcat:meig4kvcgffnjiq5wpa6wjs6am</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220119071859/https://drops.dagstuhl.de/opus/volltexte/2016/5802/pdf/dagrep_v005_i012_p001_s15511.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/4c/4c/4c4c411171281a6d099ac1643ef742f6101159ca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.12.1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Graph Isomorphism, Color Refinement, and Compactness [article]

V. Arvind, Johannes Köbler, Gaurav Rattan, Oleg Verbitsky
<span title="2015-05-04">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Tinhofer noted that isomorphism testing for compact graphs can be done quite efficiently by linear programming.  ...  Tinhofer (1991) explored a linear programming approach to Graph Isomorphism and defined compact graphs: A graph is compact if its fractional automorphisms polytope is integral.  ...  Thus, the applicability range for Tinhofer's linear programming approach to isomorphism testing is at least as large as for the combinatorial approach based on color refinement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.01255v3">arXiv:1502.01255v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pivgpwx3zbd7pila44ocsuaqty">fatcat:pivgpwx3zbd7pila44ocsuaqty</a> </span>
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Algorithmic Data Science (Invited Talk)

Petra Mutzel, Michael Wagner
<span title="2019-03-12">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/npfxqbtrtjcmndol3ijtu4shem" style="color: black;">Symposium on Theoretical Aspects of Computer Science</a> </i> &nbsp;
I like to call for more participation in algorithmic data science by our community. Now we have the opportunity to shape this new emerging field.  ...  Algorithmic Data Science Skiena [45] wrote a great book that gives a nice introduction into data science focusing on the skills and principles needed for the whole process including data integration,  ...  More precisely, they show that the levels of the Sherali-Adams hierarchy of linear programming relaxations applied to Tinhofer's equation system interleave with the levels of k-dimensional Weisfeiler-Leman  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.stacs.2019.3">doi:10.4230/lipics.stacs.2019.3</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stacs/Mutzel19.html">dblp:conf/stacs/Mutzel19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4sq6azx2snb2tkhr4n5wchaoyq">fatcat:4sq6azx2snb2tkhr4n5wchaoyq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200229024654/https://drops.dagstuhl.de/opus/volltexte/2019/10242/pdf/LIPIcs-STACS-2019-3.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/f2/59/f2598e4f7b6d73de0031f1e4f538ae52ffc1d24b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.stacs.2019.3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Lovász Meets Weisfeiler and Leman [article]

Holger Dell, Martin Grohe, Gaurav Rattan
<span title="2018-05-22">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
linear program.  ...  There is a natural system of linear equations whose nonnegative integer solutions correspond to the isomorphisms between two graphs.  ...  Limitations of algebraic approaches to graph isomorphism testing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.08876v2">arXiv:1802.08876v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/clduredu25azpfhzroddazj6ha">fatcat:clduredu25azpfhzroddazj6ha</a> </span>
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Pebble Games and Linear Equations [article]

Martin Grohe, Martin Otto
<span title="2015-03-24">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The correspondence between basic colour refinement and fractional isomorphism, due to Tinhofer (1986, 1991) and Ramana, Scheinerman and Ullman (1994), is re-interpreted as the base level of Sherali-Adams  ...  Our results are driven by considerably simplified accounts of the underlying combinatorics and linear algebra.  ...  Acknowledgements We are most grateful to Albert Atserias for his valuable comments on an earlier draft of this exposition.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.1990v3">arXiv:1204.1990v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o3txb6phuvc4npyfl3hmuziori">fatcat:o3txb6phuvc4npyfl3hmuziori</a> </span>
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Sherali-Adams Relaxations of Graph Isomorphism Polytopes [article]

Peter N. Malkin
<span title="2011-07-20">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This algorithm generalizes the classic vertex classification algorithm and generalizes the work of Tinhofer on polyhedral methods for graph automorphism testing.  ...  We investigate the Sherali-Adams lift & project hierarchy applied to a graph isomorphism polytope whose integer points encode the isomorphisms between two graphs.  ...  Introduction Classical combinatorial optimization problems have been traditionally approached by means of linear programming relaxations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1107.0632v2">arXiv:1107.0632v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k74txpbxtzejxhq6scssepm5em">fatcat:k74txpbxtzejxhq6scssepm5em</a> </span>
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Dagstuhl Reports, Volume 5, Issue 12, December 2015, Complete Issue [article]

<span title="2016-04-18">2016</span>
In other words, the applicability range for Tinhofer's linear programming approach to isomorphism testing is at least as large as for the combinatorial approach based on color refinement.  ...  Verbitsky, "On Tinhofer's Linear Programming Approach to Isomorphism Testing", in Proc. of the 40th Int'l Symp. on Mathematical Foundations of Computer Science (MFCS'15), LNCS, Vol. 9235, pp. 26-37, Springer  ...  A competition on top of political debates with additional data coming from tweets.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.12">doi:10.4230/dagrep.5.12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qpht63qmfne7rfremmrbliqtw4">fatcat:qpht63qmfne7rfremmrbliqtw4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220123034334/https://drops.dagstuhl.de/opus/volltexte/2016/5811/pdf/dagrep-v005-i012-complete.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/27/3b/273be8cb1b3ede1e7a8aeefaadd92be9f86485e2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Lovász Meets Weisfeiler and Leman

Holger Dell, Martin Grohe, Gaurav Rattan
<span title="">2018</span>
linear program.  ...  There is a natural system of linear equations whose nonnegative integer solutions correspond to the isomorphisms between two graphs.  ...  To use it as an isomorphism test, we compare the color patterns of two graphs. If they are different, we say that color refinement distinguishes the graphs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.18154/rwth-2018-231956">doi:10.18154/rwth-2018-231956</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lwbwe7s6tfenrlosorutlwwcly">fatcat:lwbwe7s6tfenrlosorutlwwcly</a> </span>
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