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Permutation Code Equivalence is not Harder than Graph Isomorphism when Hulls are Trivial [article]

Magali Bardet and Ayoub Otmani and Mohamed Saeed-Taha
2019 arXiv   pre-print
We show that given access to a subroutine that decides if two weighted undirected graphs are isomorphic, one may deterministically decide the permutation code equivalence provided that the underlying vector  ...  This problem is referred to as the permutation code equivalence.  ...  than 200 are equivalent or not.  ... 
arXiv:1905.00073v1 fatcat:tgaxvjdqsbempmvodgiqip6zk4

The Hardness of Code Equivalence over $\mathbb{F}_q$ and Its Application to Code-Based Cryptography [chapter]

Nicolas Sendrier, Dimitris E. Simos
2013 Lecture Notes in Computer Science  
The code equivalence problem is to decide whether two linear codes over Fq are identical up to a linear isometry of the Hamming space.  ...  In this paper, we review the hardness of code equivalence over Fq due to some recent negative results and argue on the possible implications in code-based cryptography.  ...  This Programme is supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission.  ... 
doi:10.1007/978-3-642-38616-9_14 fatcat:eufpaexm7nhcdbh7xxbee7iiqi

LESS-FM: Fine-tuning Signatures from a Code-based Cryptographic Group Action [article]

Alessandro Barenghi, Jean-François Biasse, Edoardo Persichetti, Paolo Santini
2021 IACR Cryptology ePrint Archive  
Code-based cryptographic schemes are highly regarded among the quantum-safe alternatives to current standards.  ...  In this paper, we revisit a recent work using an innovative approach for signing, based on the hardness of the code equivalence problem.  ...  The authors would also like to recognize support for this work; in particular, Jean-Francois Biasse is supported by NIST grant 60NANB17D184 and NSF grant 183980, while Edoardo Persichetti is supported  ... 
dblp:journals/iacr/BarenghiBPS21 fatcat:hgrutqv2sbaftdqtybdk4qjepi

Symmetry in Integer Linear Programming [chapter]

François Margot
2009 50 Years of Integer Programming 1958-2008  
An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem.  ...  The compiler is g++ version 4.3.0 20080428 (Red Hat 4.3.0-8). Results are obtained using only one processor.  ...  Few papers attempt to use an automatic symmetry detection algorithm at nodes of the tree, and when they do, results are unconvincing [88] , as the time spend in searching for additional symmetries is  ... 
doi:10.1007/978-3-540-68279-0_17 fatcat:vzpul5elmfdo3dt4dbflnbxx5u

A general system for heuristic minimization of convex functions over non-convex sets

S. Diamond, R. Takapoui, S. Boyd
2017 Optimization Methods and Software  
More examples include regressor selection, 3-SAT, circle packing, the travelling salesman problem (TSP), factor analysis modelling, inexact graph isomorphism, and many more.  ...  When Z = {0, 1} q , the problem (1) is a general mixed integer convex program, that is, a convex optimization problem in which some variables are constrained to be Boolean.  ...  We do not claim that our heuristics give state-of-the-art results for any particular problem.  ... 
doi:10.1080/10556788.2017.1304548 fatcat:6ss3u4j6rjevpddiwnalefkjdy

Fast Approximate Quadratic Programming for Graph Matching

Joshua T. Vogelstein, John M. Conroy, Vince Lyzinski, Louis J. Podrazik, Steven G. Kratzer, Eric T. Harley, Donniell E. Fishkind, R. Jacob Vogelstein, Carey E. Priebe, Mark R. Muldoon
2015 PLoS ONE  
The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent.  ...  With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm.  ...  Indeed, the indefinite formulation (and not the convex formulation) has the property that when matching asymmetric isomorphic graphs, the unique global minimum of the indefinite relaxation is the isomorphism  ... 
doi:10.1371/journal.pone.0121002 pmid:25886624 pmcid:PMC4401723 fatcat:75t3a4srxfgedfgmy7dllmc5ge

A survey of homogeneous structures

Dugald Macpherson
2011 Discrete Mathematics  
For example, if we are talking about graphs, or digraphs, or partial orders, it is assumed that the language has a single binary relation symbol.  ...  Beyond this, I have tried to give definitions if they are needed. A good background source in model theory is [81] .  ...  They note that since there are continuum many homogeneous digraphs, some such are templates with undecidable CSP.  ... 
doi:10.1016/j.disc.2011.01.024 fatcat:fqpfnc25hjdajekkiyaeszw6ye

The complexity of classifying separable Banach spaces up to isomorphism

Valentin Ferenczi, Alain Louveau, Christian Rosendal
2009 Journal of the London Mathematical Society  
) Polish groups up to topological isomorphism, and (5) Schauder bases up to permutative equivalence.  ...  It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it.  ...  Therefore this also means that isometry on B is simpler than permutative equivalence of bases.  ... 
doi:10.1112/jlms/jdn068 fatcat:qkqib5jxdvftlkbmg2x3vfllby

Orbitopal fixing

Volker Kaibel, Matthias Peinhardt, Marc E. Pfetsch
2011 Discrete Optimization  
We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem.  ...  It does, however, not explicitly add inequalities to the model. Instead, it uses certain fixing rules for variables.  ...  Acknowledgments We are grateful to Andreas Loos for discussions on the complexity of optimizing linear functions over covering orbitopes that lead to the basic idea for the proof of Theorem 5.  ... 
doi:10.1016/j.disopt.2011.07.001 fatcat:ms7ixpxb2raubnviw7vq4sahni

A General System for Heuristic Solution of Convex Problems over Nonconvex Sets [article]

Steven Diamond, Reza Takapoui, Stephen Boyd
2016 arXiv   pre-print
We study several examples of well known nonconvex problems, and show that our general purpose heuristics are effective in finding approximate solutions to a wide variety of problems.  ...  employ convex relaxations, convex restrictions, local neighbor search methods, and the alternating direction method of multipliers (ADMM), require the solution of a modest number of convex problems, and are  ...  Inexact graph isomorphism Two (undirected) graphs are isomorphic if we can permute the vertices of one so it is the same as the other (i.e., the same pairs of vertices are connected by edges).  ... 
arXiv:1601.07277v1 fatcat:lqlfa3phgve4xkeq345auzuxjm

A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search [chapter]

Marcos Diez García, Alberto Moraglio
2019 Lecture Notes in Computer Science  
Keywords: Abstract convex landscape · Abstract convex search · Convex hull closure · Geometric crossover · Recombination P-structure  ...  One of the main goals behind this unification is to develop an analytical method that verifies if a problem s landscape belongs to certain abstract convex landscape classes, where certain recombination-based  ...  for general recombination P-structures not just string crossovers, and no assumptions are made on selection  ... 
doi:10.1007/978-3-030-16711-0_12 fatcat:bscffzyxijc7baa46wgarkqu4a

Box-inequalities for quadratic assignment polytopes

Michael Jünger, Volker Kaibel
2001 Mathematical programming  
, and trivial facets.  ...  Computational experiments with a cutting plane algorithm based on these inequalities show that they are very useful with respect to the goal of solving quadratic assignment problems to optimality or to  ...  is that they are each invariant under permuting the rows or the columns of the (hyper)graph.  ... 
doi:10.1007/s101070100251 fatcat:4ixsykdwvbhetdidmw56fupste

Pseudo-Codeword Performance Analysis for LDPC Convolutional Codes [article]

Roxana Smarandache, Ali E. Pusane, Pascal O. Vontobel, Daniel J. Costello Jr
2006 arXiv   pre-print
Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords.  ...  every pseudo-codeword in the convolutional code induces a pseudo-codeword in the block code with pseudo-weight no larger than that of the convolutional code's pseudo-codeword.  ...  a vector that fulfills the equations of a graph cover rather than the graph itself. and whose Tanner graph is shown in Fig. 1 (left) .  ... 
arXiv:cs/0609148v1 fatcat:fka6rdxjjrcofnkls6nvrkwkca

Ioana's Superrigidity Theorem and Orbit Equivalence Relations

Samuel Coskey
2013 ISRN Algebra  
) and set theory (Borel reducibility); and (iii) a streamlined proof of Simon Thomas's theorem that the classification of torsion-free abelian groups of finite rank is intractable.  ...  introduction to rigidity, including a crash course in Borel cocycles and a summary of some of the best-known superrigidity theorems; (ii) some easy applications of superrigidity, both to ergodic theory (orbit equivalence  ...  When this is the case, we will often conflate the two, saying alternately that certain actions are orbit equivalent or that certain equivalence relations are "orbit equivalent. " Borel bireducibility is  ... 
doi:10.1155/2013/387540 fatcat:p5y5e7n47nb5rcv567kwduxspu

Rainbow cycles in flip graphs [article]

Stefan Felsner, Linda Kleist, Torsten Mütze, Leon Sering
2018 arXiv   pre-print
In addition, we consider two flip graphs on classes of non-geometric objects: the flip graph of permutations of {1,2,...,n} and the flip graph of k-element subsets of {1,2,...,n}.  ...  An r-rainbow cycle in this graph is a cycle in which every inner edge of the triangulation appears exactly r times. This notion of a rainbow cycle extends in a natural way to other flip graphs.  ...  Acknowledgements We thank Manfred Scheucher for his quick assistance in running computer experiments that helped us to find rainbow cycles in small flip graphs.  ... 
arXiv:1712.07421v2 fatcat:sjtjbhhwbfc5tkgkuxeg62dxwi
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