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

2019
*
arXiv
*
pre-print

We show that given access to a subroutine that decides if two weighted undirected

arXiv:1905.00073v1
fatcat:tgaxvjdqsbempmvodgiqip6zk4
*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*. ...##
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The Hardness of Code Equivalence over $\mathbb{F}_q$ and Its Application to Code-Based Cryptography
[chapter]

2013
*
Lecture Notes in Computer Science
*

The

doi:10.1007/978-3-642-38616-9_14
fatcat:eufpaexm7nhcdbh7xxbee7iiqi
*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. ...##
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LESS-FM: Fine-tuning Signatures from a Code-based Cryptographic Group Action
[article]

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 ...

##
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Symmetry in Integer Linear Programming
[chapter]

2009
*
50 Years of Integer Programming 1958-2008
*

An integer linear program (ILP)

doi:10.1007/978-3-540-68279-0_17
fatcat:vzpul5elmfdo3dt4dbflnbxx5u
*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*...##
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A general system for heuristic minimization of convex functions over non-convex sets

2017
*
Optimization Methods and Software
*

More examples include regressor selection, 3-SAT, circle packing, the travelling salesman problem (TSP), factor analysis modelling, inexact

doi:10.1080/10556788.2017.1304548
fatcat:6ss3u4j6rjevpddiwnalefkjdy
*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. ...##
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Fast Approximate Quadratic Programming for Graph Matching

2015
*
PLoS ONE
*

The

doi:10.1371/journal.pone.0121002
pmid:25886624
pmcid:PMC4401723
fatcat:75t3a4srxfgedfgmy7dllmc5ge
*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*...##
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A survey of homogeneous structures

2011
*
Discrete Mathematics
*

For example, if we

doi:10.1016/j.disc.2011.01.024
fatcat:fqpfnc25hjdajekkiyaeszw6ye
*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. ...##
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The complexity of classifying separable Banach spaces up to isomorphism

2009
*
Journal of the London Mathematical Society
*

) Polish groups up to topological

doi:10.1112/jlms/jdn068
fatcat:qkqib5jxdvftlkbmg2x3vfllby
*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. ...##
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Orbitopal fixing

2011
*
Discrete Optimization
*

We demonstrate the computational power of orbitopal fixing at the example of a

doi:10.1016/j.disopt.2011.07.001
fatcat:ms7ixpxb2raubnviw7vq4sahni
*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. ...##
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A General System for Heuristic Solution of Convex Problems over Nonconvex Sets
[article]

2016
*
arXiv
*
pre-print

We study several examples of well known nonconvex problems, and show that our general purpose heuristics

arXiv:1601.07277v1
fatcat:lqlfa3phgve4xkeq345auzuxjm
*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). ...##
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A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search
[chapter]

2019
*
Lecture Notes in Computer Science
*

Keywords: Abstract convex landscape · Abstract convex search · Convex

doi:10.1007/978-3-030-16711-0_12
fatcat:bscffzyxijc7baa46wgarkqu4a
*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 ...##
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Box-inequalities for quadratic assignment polytopes

2001
*
Mathematical programming
*

, and

doi:10.1007/s101070100251
fatcat:4ixsykdwvbhetdidmw56fupste
*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*. ...##
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Pseudo-Codeword Performance Analysis for LDPC Convolutional Codes
[article]

2006
*
arXiv
*
pre-print

Message-passing iterative decoders for low-density parity-check (LDPC) block

arXiv:cs/0609148v1
fatcat:fka6rdxjjrcofnkls6nvrkwkca
*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) . ...##
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Ioana's Superrigidity Theorem and Orbit Equivalence Relations

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

doi:10.1155/2013/387540
fatcat:p5y5e7n47nb5rcv567kwduxspu
*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*...##
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Rainbow cycles in flip graphs
[article]

2018
*
arXiv
*
pre-print

In addition, we consider two flip

arXiv:1712.07421v2
fatcat:sjtjbhhwbfc5tkgkuxeg62dxwi
*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*. ...
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