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Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph [PDF]
INFORMS Journal on Computing, 2022 The minimum rank of a graph G is the minimum of the ranks of all symmetric adjacency matrices of G. We present a new combinatorial bound for the minimum rank of an arbitrary graph G based on enumerating certain subsets of vertices of G satisfying matroid
Logan Smith +2 more
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Subgraph Complementation and Minimum Rank [PDF]
The Electronic Journal of Combinatorics, 2021 Any finite simple graph $G = (V,E)$ can be represented by a collection $\mathscr{C}$ of subsets of $V$ such that $uv\in E$ if and only if $u$ and $v$ appear together in an odd number of sets in $\mathscr{C}$.
Calum Buchanan +2 more
semanticscholar +5 more sources
On the Hardness of the Decoding and the Minimum Distance Problems for Rank Codes [PDF]
IEEE Transactions on Information Theory, 2016 In this paper we give a randomized reduction for the Rank Syndrome Decoding problem and Rank Minimum Distance problem for rank codes. Our results are based on an embedding from linear codes equipped with Hamming distance unto linear codes over an extension field equipped with the rank metric.
Philippe Gaborit, Gilles Zémor
exaly +5 more sources
A Minimum Rank Approach for Reduction of Environmental Noise in Near-Field Array Antenna Diagnosis [PDF]
Journal of Imaging, 2019 A method to filter out the contribution of interference sources in array diagnosis is proposed. The interference-affected near field measured on a surface is treated as a (complex-data) image.
Marco Donald Migliore +4 more
doaj +2 more sources
Materials Research Express, 2022 Technique for order preference by similarity to ideal solution (TOPSIS) is a well-known multi attribute decision making (MADM) method and it has been widely used in materials selection.
Won-Chol Yang +4 more
doaj +2 more sources
The minimum rank problem for circulants [PDF]
Linear Algebra and its Applications, 2015 The minimum rank problem is to determine for a graph G the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacency matrix of G .
Louis Deaett, Seth A. Meyer
semanticscholar +4 more sources
Words of Minimum Rank in Deterministic Finite Automata [PDF]
International Conference on Developments in Language Theory, 2019 The rank of a word in a deterministic finite automaton is the size of the image of the whole state set under the mapping defined by this word. We study the length of shortest words of minimum rank in several classes of complete deterministic finite automata, namely, strongly connected and Eulerian automata. A conjecture bounding this length is known as
J. Kari, A. Ryzhikov, Anton Varonka
semanticscholar +4 more sources
MINIMUM RANK OF GRAPHS WITH LOOPS
The Electronic Journal of Linear Algebra, 2015 A loop graph $\mf G$ is a finite undirected graph that allows loops but does not allow multiple edges. The set $\sym(\lG)$ of real symmetric matrices associated with a loop graph $\lG$ of order $n$ is the set of symmetric matrices $A=[a_{ij}]\in\Rnn ...
Chassidy Bozeman +7 more
semanticscholar +4 more sources
Minimum rank with zero diagonal
The Electronic Journal of Linear Algebra, 2014 Associated with a simple graph G is a family of real, symmetric zero diagonal matrices with the same nonzero pattern as the adjacency matrix of G. The minimum of the ranks of the matrices in this family is denoted mr0(G).
Cheryl Grood +6 more
semanticscholar +5 more sources
Graph theory versus minimum rank for index coding [PDF]
2014 IEEE International Symposium on Information Theory, 2014 We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far 1. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic ...
Karthikeyan Shanmugam +2 more
semanticscholar +4 more sources