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Limitations of Algebraic Approaches to Graph Isomorphism Testing [article]

Christoph Berkholz, Martin Grohe
2015 arXiv   pre-print
We compare this approach to recently studied linear and semidefinite programming approaches to isomorphism testing, which are known to be related to the combinatorial Weisfeiler-Lehman algorithm.  ...  The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system  ...  Acknowledgements We thank Anuj Dawar and Erkal Selman for many inspiring discussions in the initial phase of this project.  ... 
arXiv:1502.05912v1 fatcat:7ccppsernrhhvfhh77umjkj3yq

Efficiently Pinpointing SPARQL Query Containments [chapter]

Claus Stadler, Muhammad Saleem, Axel-Cyrille Ngonga Ngomo, Jens Lehmann
2018 Lecture Notes in Computer Science  
Solving the query containment problem can be reduced to the problem of deciding whether a sub graph isomorphism exists between the normalized algebra expressions of two queries.  ...  Several state-of-the-art methods are limited to matching two queries only, as well as only giving a boolean answer to whether a containment relation holds.  ...  The naive approach is to linearly scan all available views and test for whether a rewriting exists.  ... 
doi:10.1007/978-3-319-91662-0_16 fatcat:gclvxtqkmzbgdfmaga2uuvf4lm

Circuits, Logic and Games (Dagstuhl Seminar 15401)

Mikolaj Bojanczyk, Meena Mahajan, Thomas Schwentick, Heribert Vollmer, Marc Herbstritt
2016 Dagstuhl Reports  
with respect to the exchange of recent results, ideas and methodological approaches.  ...  The seminar focussed on the following specific topics: The algebraic approach to circuit complexity with its applications to finite model theory The logic-circuit connection, with a particular emphasis  ...  Limitations of Algebraic Approaches to Graph Isomorphism Testing We show that the strength of this algebraic approach is closely related to the Weisfeiler-Lehman algorithm or, equivalently, to the equivalence  ... 
doi:10.4230/dagrep.5.9.105 dblp:journals/dagstuhl-reports/BojanczykMSV15 fatcat:pv6oxt7lnvhkbczugwxmvumdxq

The Graph Isomorphism Problem (Dagstuhl Seminar 15511)

László Babai, Anuj Dawar, Pascal Schweitzer, Jacobo Torán, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 15511 "The Graph Isomorphism Problem".  ...  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.  ...  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  ... 
doi:10.4230/dagrep.5.12.1 dblp:journals/dagstuhl-reports/BabaiDST15 fatcat:meig4kvcgffnjiq5wpa6wjs6am

A Model Theory Approach to Structural Limits [article]

Jaroslav Nesetril
2013 arXiv   pre-print
Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.  ...  The goal of this paper is to unify two lines in a particular area of graph limits.  ...  Acknowledgments The authors would like to thanks the referee for his most valuable comments.  ... 
arXiv:1303.2865v1 fatcat:l5dhwyghw5c4zngmhoka5qpoya

Coclass theory for nilpotent semigroups via their associated algebras

Andreas Distler, Bettina Eick
2013 Journal of Algebra  
This differs from the group theory setting in that we additionally use certain algebras associated to the considered semigroups. We propose a series of conjectures on our suggested approach.  ...  If these become theorems, then this would reduce the classification of nilpotent semigroups of a fixed coclass to a finite calculation.  ...  We used it to investigate G 2,K computationally, applying the isomorphism test for associative nilpotent algebras over finite fields in [6] .  ... 
doi:10.1016/j.jalgebra.2012.09.042 fatcat:q274vlhe5zhmpndmun57quf2uu

Short Distance Analysis in Algebraic Quantum Field Theory [article]

Detlev Buchholz
1997 arXiv   pre-print
Within the framework of algebraic quantum field theory a general method is presented which allows one to compute and classify the short distance (scaling) limit of any algebra of local observables.  ...  The method has been tested in models. (Invited talk given at the International Congress of Mathematical Physics, July 1997, Brisbane)  ...  The graph of the function A thus provides the desired identification of observables at different scales. With this idea in mind one is led to the concept of scaling algebra.  ... 
arXiv:hep-th/9710094v1 fatcat:t7pgowfzqjcw7fsjfjnix4oxjq

A Novel Optimizing Network Architecture with Applications

Anand Rangarajan, Steven Gold, Eric Mjolsness
1996 Neural Computation  
Deterministic annealing in conjunction with self-amplification avoids poor local minima and ensures that a vertex of the hypercube is reached.  ...  We introduce a new technique, softassign, which is used to satisfy this constraint. Experimental results on different problems are presented and discussed.  ...  Acknowledgements We acknowledge the help of the reviewers (one in particular) in substantially improving the paper from an earlier version.  ... 
doi:10.1162/neco.1996.8.5.1041 fatcat:gphhy7bugvcyniq3lrv5gw6bny

Flag Algebras: A First Glance [article]

Marcel K. de Carli Silva, Fernando Mário de Oliveira Filho, Cristiane Maria Sato
2016 arXiv   pre-print
The theory of flag algebras, introduced by Razborov in 2007, has opened the way to a systematic approach to the development of computer-assisted proofs in extremal combinatorics.  ...  It makes it possible to derive bounds for parameters in extremal combinatorics with the help of a computer, in a semi-automated manner.  ...  Let H be a collection of graphs. A graph G is H-free if no induced subgraph of G is isomorphic to a graph in H.  ... 
arXiv:1607.04741v1 fatcat:ah2nk2sk5vhqjhwtwxuld4zaia

The polynomial algorithm for graphs' isomorphism testing [article]

Aleksandr Golubchik
2002 arXiv   pre-print
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.  ...  Acknowledgements I would like to express many thanks to Dr. M.Tabachnikov for the proposal (in 1983) to solve this problem, to Dr.V.Grinberg for productive contacts, to Dr.  ...  M.Klin for acquainting with contemporary achievements in this field and to my sons Dr. S. Golubchik and R. Golubchik for priceless computer assistance.  ... 
arXiv:math/0202085v1 fatcat:7e5c5lidsjdrxnwm475ayyypw4

A categorical manifesto

Joseph A. Goguen
1991 Mathematical Structures in Computer Science  
., adjoints de ne their results uniquely up to isomorphism, i.e., abstractly" in just this sense.  ...  A corollary of the rst guideline given in Section 1 is that two objects are abstractly the same" i they are isomorphic; see Section 1.1.  ...  In the Lawvere approach to universal algebra 49 , an algebra is a functor from a theory T to Set.  ... 
doi:10.1017/s0960129500000050 fatcat:m5fxdfgc7zedbkngxfaubasiwi

Genetic-based search for error-correcting graph isomorphism

Yuan-Kai Wang, Kuo-Chin Fan, Jorng-Tzong Horng
1997 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
This paper presents a genetic-based search approach that adopts genetic algorithms as the searching criteria to solve the problem of error-correcting graph isomorphism.  ...  Error-correcting graph isomorphism has been found useful in numerous pattern recognition applications.  ...  In this paper, a genetic-based search approach is proposed to solve the problem of error-correcting graph isomorphism.  ... 
doi:10.1109/3477.604100 pmid:18255899 fatcat:zlgkbq5y6nb4di7v4e2qzzj2bu

First-order limits, an analytical perspective

Jaroslav Nešetřil, Patrice Ossona de Mendez
2016 European journal of combinatorics (Print)  
In this paper we present a novel approach to graph (and structural) limits based on model theory and analysis.  ...  As an application, it leads to new intermediate examples of structural convergence and to a "grand conjecture" dealing with sparse graphs. We survey the recent developments.  ...  We now view our approach as a natural approach, which lies midway between functional analysis approach to quantum theory and limits of graphs.  ... 
doi:10.1016/j.ejc.2015.07.012 fatcat:bd5u5kga6fd3xioa6cpbqrpkny

Top quark pairs at two loops and Reduze 2 [article]

Andreas von Manteuffel, Cedric Studerus
2012 arXiv   pre-print
New graph matroid based algorithms allow to calculate shift relations between Feynman integrals in a fully automated way.  ...  It provides a fully distributed variant of Laporta's algorithm to reduce loop integrals.  ...  Acknowledgments This work was supported in part by the Research Center Elementary Forces and Mathematical Foundations (EMG) of the Johannes-Gutenberg-Universität Mainz, the German Research Foundation (  ... 
arXiv:1210.1436v1 fatcat:q4rk3hdfdbapzfjqifgimoqxie

Limitations of the Invertible-Map Equivalences [article]

Anuj Dawar, Erich Grädel, Moritz Lichter
2021 arXiv   pre-print
We show here that the two approaches can be unified to prove that CFI-structures over the rings ℤ_2^i are indistinguishable with respect to ≡^IM_k,ℙ, for the set ℙ of all primes.  ...  These ≡^IM_k,Q-equivalences, for a natural number k and a set of primes Q, refine the well-known Weisfeiler-Leman equivalences used in algorithms for graph isomorphism.  ...  These equivalence relations get finer with increasing k and approach isomorphism in the limit.  ... 
arXiv:2109.07218v1 fatcat:6br2oify5jgzpholxim77qrexy
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