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Algorithmic Data Science (Invited Talk)

2019
*
Symposium on Theoretical Aspects of Computer Science
*

The authors show that if the

doi:10.4230/lipics.stacs.2019.3
dblp:conf/stacs/Mutzel19
fatcat:4sq6azx2snb2tkhr4n5wchaoyq
*homomorphism*vectors are restricted to trees, then the feature vectors of the*homomorphism*counts of two graphs are identical if and only if the*Weisfeiler*-*Leman*algorithm ... Basic*Weisfeiler*-*Leman*The*Weisfeiler*-*Leman*algorithm (WL) simultaneously colours the vertices of the two given graphs iteratively. In the beginning, all vertices get the same colour c. ...##
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Lovász Meets Weisfeiler and Leman
[article]

2018
*
arXiv
*
pre-print

We lift the results for trees to an equivalence between numbers of

arXiv:1802.08876v2
fatcat:clduredu25azpfhzroddazj6ha
*homomorphisms*from graphs of tree width k, the k-dimensional*Weisfeiler*-*Leman*algorithm, and the level-k Sherali-Adams relaxation of our ... we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the*Weisfeiler*-*Leman*... XX:4 Lovász*Meets**Weisfeiler*and*Leman*Figure 1 Two fractionally non-isomorphic graphs with the same path*homomorphism*counts. Theorem 2. ...##
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Isomorphism Testing for Graphs Excluding Small Minors

2020
*
2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
*

*Weisfeiler*-

*Leman*Algorithm The

*Weisfeiler*-

*Leman*algorithm, originally introduced by

*Weisfeiler*and

*Leman*in its twodimensional form [32] , forms one of the most fundamental subroutines in the context ... Next, we define the 2-dimensional

*Weisfeiler*-

*Leman*algorithm. ... So let i ∈ [r] and consider the bipartite graph By the properties of the 2-dimensional

*Weisfeiler*-

*Leman*algorithm the graph B is biregular. ...

##
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Isomorphism Testing for Graphs Excluding Small Minors
[article]

2020
*
arXiv
*
pre-print

*Weisfeiler*-

*Leman*Algorithm The

*Weisfeiler*-

*Leman*algorithm, originally introduced by

*Weisfeiler*and

*Leman*in its twodimensional form [32] , forms one of the most fundamental subroutines in the context ... Next, we define the 2-dimensional

*Weisfeiler*-

*Leman*algorithm. ... So let i ∈ [r] and consider the bipartite graph By the properties of the 2-dimensional

*Weisfeiler*-

*Leman*algorithm the graph B is biregular. ...

##
###
Lovász Meets Weisfeiler and Leman

2018

We lift the results for trees to an equivalence between numbers of

doi:10.18154/rwth-2018-231956
fatcat:lwbwe7s6tfenrlosorutlwwcly
*homomorphisms*from graphs of tree width k, the k-dimensional*Weisfeiler*-*Leman*algorithm, and the level-k Sherali-Adams relaxation of our ... paper, we relate a beautiful theory by Lovász with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the*Weisfeiler*-*Leman*... Since Lovász*Meets**Weisfeiler*and*Leman*Now suppose HOM r (G) = HOM r (H) holds, and set v = HOM r (G). ...##
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Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs
[article]

2019
*
arXiv
*
pre-print

Over 50 years ago, Lovász proved that two graphs are isomorphic if and only if they admit the same number of

arXiv:1910.06958v2
fatcat:i2ckcwtqbvhzvhbab6hxuw3vy4
*homomorphisms*from any graph [Acta Math. Hungar. 18 (1967), pp. 321–328]. ... As there exist pairs of non-isomorphic graphs that are quantum isomorphic, this implies that*homomorphism*counts from planar graphs do not determine a graph up to isomorphism. ... Therefore if G ∼ = P H, then G and H are not distinguished by 2-dimensional*Weisfeiler*-*Leman*. ...##
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Graph isomorphism: Physical resources, optimization models, and algebraic characterizations
[article]

2020
*
arXiv
*
pre-print

As it turns out, the notion of DN N -isomorphism coincides with an equivalence relation on graphs introduced in 1968 by

arXiv:2004.10893v1
fatcat:wnophwxi5jbhbcf4msnn56co3u
*Weisfeiler*and*Leman*[29] , known today as the 2-dimensional*Weisfeiler*-*Leman*method ... Otherwise, we say that the graphs are not distinguished by the*Weisfeiler*-*Leman*method, which is an equivalence relation on graphs. ...##
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The Power of the Weisfeiler-Leman Algorithm to Decompose Graphs
[article]

2021
*
arXiv
*
pre-print

We prove that the 2-dimensional

arXiv:1908.05268v2
fatcat:qdxirpksw5apjcafis62soa5ai
*Weisfeiler*-*Leman*algorithm implicitly computes the decomposition of a graph into its 3-connected components. ... In an application of the results, we show the new upper bound of k on the*Weisfeiler*-*Leman*dimension of the class of graphs of treewidth at most k. ... The*Weisfeiler*-*Leman*Algorithm Let χ, χ ′ : V k → C be colorings of the k-tuples of vertices of G, where C is some finite set of colors. ...##
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Graph Isomorphism in Quasipolynomial Time
[article]

2016
*
arXiv
*
pre-print

Luks's barrier situation is characterized by a

arXiv:1512.03547v2
fatcat:nfilvn466zhafloxxlyeqitmre
*homomorphism*ϕ that maps a given permutation group G onto S_k or A_k, the symmetric or alternating group of degree k, where k is not too small. ...*Weisfeiler*-*Leman*canonical refinement Classical WL refinement The classical*Weisfeiler*-*Leman*5 (WL) refinement [WeL, We] takes as input a binary configuration and refines it to a coherent configuration ... Coherent configurations are the stable configurations of the classical*Weisfeiler*-*Leman*canonical refinement process [WeL, We] R ⊆ Ω × Ω let R − = {(y, x) | (x, y) ∈ R}. ...##
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Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker's Conjecture confirmed
[article]

2021
*
arXiv
*
pre-print

If X = (V, E) is a graph then the

arXiv:2110.08492v2
fatcat:4xhyqqcryfgqlcxlbncntvc7nq
*Weisfeiler*-*Leman*color refinement process [WL68, We76] (see, e. g., [Ba16] ) efficiently constructs a CC X(X) = (V, c) such that Aut(X) = Aut(X(X)). ... The*homomorphism*ϕ ii is the identity on G i . The ϕ i,j are called the transition*homomorphisms*. ...##
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Nonlocal Games and Quantum Permutation Groups
[article]

2018
*
arXiv
*
pre-print

Part of this work was completed during the Focused Research

arXiv:1712.01820v2
fatcat:k4wjx4xjjvetjickjcn2i5i4i4
*Meeting*at Queen's University Belfast in October 2017, which was funded by the Heilbronn Institute for Mathematical Research. ... We remark that this coherent algebra can be computed in polynomial time via the (2-dimensional)*Weisfeiler*-*Leman*method [25] . ... It is also known that two graphs are equivalent if and only if they cannot be distinguished by the (2-dimensional)*Weisfeiler*-*Leman*algorithm. ...##
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Between primitive and 2-transitive: Synchronization and its friends

2017
*
EMS Surveys in Mathematical Sciences
*

Coherent configurations were introduced independently by Donald Higman [53, 54] in the USA and by

doi:10.4171/emss/4-2-1
fatcat:p4wgh52hhnghdcjau3wmokss2m
*Weisfeiler*and*Leman*[102] in the former Soviet Union to describe the orbits on pairs of a permutation ... Now 3-sets in the same S(L)*meet*in 0 or 2 points. So any image of the Fano plane*meets*each S(L) in at most (and hence exactly) one set. ...##
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On the automorphism groups of strongly regular graphs II

2015
*
Journal of Algebra
*

The

doi:10.1016/j.jalgebra.2014.09.007
fatcat:kev5vyn4fjd33llwwnjahyjhre
*Weisfeiler*-*Leman*refinement [61, 60] defines a refined coloring c by making c (x, y) = c (u, v) if and only if c(x, y) = c(u, v) and for all j, k < r we have p(x, y; i, j) = p(u, v; i, j). ... This map is a*homomorphism*, given that F is a functor. Proof of Theorem 22. Suppose (f, F ) is a functorial reduction from GI to the isomorphism problem for s. r. graphs. ...##
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On the automorphism groups of strongly regular graphs I

2014
*
Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14
*

The

doi:10.1145/2554797.2554830
dblp:conf/innovations/Babai14
fatcat:3zycmvaskrcbxjc4o37xthat4a
*Weisfeiler*-*Leman*refinement [61, 60] defines a refined coloring c by making c (x, y) = c (u, v) if and only if c(x, y) = c(u, v) and for all j, k < r we have p(x, y; i, j) = p(u, v; i, j). ... This map is a*homomorphism*, given that F is a functor. Proof of Theorem 22. Suppose (f, F ) is a functorial reduction from GI to the isomorphism problem for s. r. graphs. ...##
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СИБИРСКИЕ ЭЛЕКТРОННЫЕ МАТЕМАТИЧЕСКИЕ ИЗВЕСТИЯ Special issue: Graphs and Groups, Spectra and Symmetries-G2S2 2016 ON GRAPHS AND GROUPS, SPECTRA AND SYMMETRIES HELD ON AUGUST 15-28, 2016, NOVOSIBIRSK, RUSSIA

2016
unpublished

The importance of this notion was explained by the fact that if the coherent configuration of a graph is separable, then the isomorphism of this graph to any other graph can be tested by the

fatcat:do352qvjsbg7jf6ykjdccc6rfy
*Weisfeiler*-*Leman*... They as well as the young students emphasized how glad they were that mathematicians from so many countries had come all the way to Siberia to*meet*their Russian colleagues. ...
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