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On the Complexity of the Rank Syndrome Decoding Problem [PDF]
IEEE Transactions on Information Theory, 2016 In this paper we propose two new generic attacks on the Rank Syndrome Decoding (RSD) problem Let $C$ be a random $[n,k]$ rank code over $GF(q^m)$ and let $y=x+e$ be a received word such that $x \in C$ and the $Rank(e)=r$. The first attack is combinatorial and permits to recover an error $e$ of rank weight $r$ in $min(O((n-k)^3m^3q^{r\lfloor\frac{km}{n}\
Philippe Gaborit, Olivier Ruatta
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The Rank-One Quadratic Assignment Problem
INFORMS Journal on Computing, 2021In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running ...
Yang Wang 0030 +5 more
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RANK PROBLEMS FOR COMPOSITE TRANSFORMATIONS
International Journal of Algebra and Computation, 1995Let (X, F) be a pair consisting of a finite set X and a set F of transformations of X, and, let <F> and F(l) denote, respectively, the semigroup generated by F and the part of <F> consisting of the transformations determined by a generator sequence of length no more than a given integer l.
Pavel Goralcik, Václav Koubek
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Psychometrika, 1957
Observed rankings of objects can be treated as arising from a time dependent probability process. Under such circumstances, associations observed are an indication of the character of this underlying process. In the particular example treated in some detail here, a quantity related to Kendall's tau is found to have an important role and its properties ...
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Observed rankings of objects can be treated as arising from a time dependent probability process. Under such circumstances, associations observed are an indication of the character of this underlying process. In the particular example treated in some detail here, a quantity related to Kendall's tau is found to have an important role and its properties ...
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An algorithm for rank aggregation problem
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farzad Didehvar, Changiz Eslahchi
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Factorization as a rank 1 problem
Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149), 2003Tomasi and Kanade (1992) introduced the factorization method for recovering 3D structure from 2D video. In their formulation, the 3D shape and 3D motion are computed by using an SVD to approximate a matrix that is rank 3 in a noiseless situation. In this paper we reformulate the problem using the fact that the x and y coordinates of each feature are ...
Pedro M. Q. Aguiar, José M. F. Moura
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Social Ranking Problem Based on Rankings of Restricted Coalitions
2021Evaluations of individuals; such as workers, researchers, team-sports athletes, etc.; are often based on the performance of their coalitions. The present paper will study the so-called ordinal social ranking problem; i.e., to determine the ordinal ranking of individuals according to the ordinal rankings of their coalitions.
Takahiro Suzuki, Masahide Horita
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