Corpus ID: 17625222

Dagstuhl Report 13082: Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices

@article{Beasely2013DagstuhlR1,
  title={Dagstuhl Report 13082: Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices},
  author={LeRoy Beasely and Troy Lee and Hartmut Klauck and Dirk Oliver Theis},
  journal={ArXiv},
  year={2013},
  volume={abs/1305.4147}
}
This report documents the program and the outcomes of Dagstuhl Seminar 13082 "Communication Complexity, Linear Optimization, and lower bounds for the nonnegative rank of matrices", held in February 2013 at Dagstuhl Castle. 
Heuristics for exact nonnegative matrix factorization
TLDR
Two heuristics for exact NMF are proposed, one inspired from simulated annealing and the other from the greedy randomized adaptive search procedure, able to compute exact nonnegative factorizations for several classes of nonnegative matrices and demonstrate their superiority over standard multi-start strategies. Expand
A universality theorem for nonnegative matrix factorizations
Let $A$ be a matrix with nonnegative real entries. A nonnegative factorization of size $k$ is a representation of $A$ as a sum of $k$ nonnegative rank-one matrices. The space of all suchExpand

References

SHOWING 1-10 OF 16 REFERENCES
An upper bound for nonnegative rank
  • Y. Shitov
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2014
We provide a nontrivial upper bound for the nonnegative rank of rank-three matrices which allows us to prove that ? 6 n / 7 ? linear inequalities suffice to describe a convex n-gon up to a linearExpand
Which nonnegative matrices are slack matrices
Abstract In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack matrix. TheExpand
Fooling-sets and rank in nonzero characteristic
TLDR
Dietzfel-binger, Hromkovic, and Schnitger (1996) showed that n ≤ (rkM)2, regardless of over which field the rank is computed, and asked whether the exponent on rkM can be improved. Expand
Real rank versus nonnegative rank
Abstract We consider the set of m × n nonnegative real matrices and define the nonnegative rank of a matrix A to be the minimum k such that A = BC where B is m × k and C is k × n . Given that theExpand
Common Information and Unique Disjointness
TLDR
An information-theoretic framework for establishing strong lower bounds on the nonnegative rank of matrices by means of common information by combining it with Hellinger distance estimations and an information theoretic variant of the fooling set method that allows to extend fooleding set lower bounds from extension complexity to approximate extension complexity are provided. Expand
An analog of the cook theorem for polytopes
We prove that the polytope M of any combinatorial optimization problem with a linear objective function is an affine image of some facet of the cut polytope whose dimension is polynomial with respectExpand
Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
TLDR
The power of lower bounds on positive semidefinite rank is characterized based on solely on the support of the matrix S, i.e., its zero/non-zero pattern. Expand
On the copositive representation of binary and continuous nonconvex quadratic programs
  • S. Burer
  • Mathematics, Computer Science
  • Math. Program.
  • 2009
TLDR
Any nonconvex quadratic program having a mix of binary and continuous variables as a linear program over the dual of the cone of copositive matrices is model, which reduces the dimension of the linear conic program. Expand
Fooling-sets and rank in nonzero characteristic (extended abstract)
An n\times n matrix M is called a fooling-set matrix of size n, if its diagonal entries are nonzero, whereas for every k\ne \ell we have M_{k,\ell} M_{\ell,k} = 0. Dietzfelbinger, Hromkovi\v{c}, andExpand
Clique versus independent set
TLDR
It is shown that a polynomial CS-separator is equivalent to thePolynomial Alon–Saks–Seymour Conjecture, asserting that if a graph has an edge-partition into k complete bipartite graphs, then its chromatic number is polynomially bounded in terms of k . Expand
...
1
2
...