175 research outputs found
A note on the relationship between the Graphical Traveling Salesman Polyhedron, the Symmetric Traveling Salesman Polytope, and the Metric Cone
In this short communication, we observe that the Graphical Traveling Salesman
Polyhedron is the intersection of the positive orthant with the Minkowski sum
of the Symmetric Traveling Salesman Polytope and the polar of the metric cone.
This follows almost trivially from known facts. There are two reasons why we
find this observation worth communicating none-the-less: It is very surprising;
it helps to understand the relationship between these two important families of
polyhedra.Comment: short communication (3 pages), Discrete Appl. Mat
Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix
The positive semidefinite rank of a nonnegative -matrix~ is
the minimum number~ such that there exist positive semidefinite -matrices , such that S(k,\ell) =
\mbox{tr}(A_k^* B_\ell).
The most important, lower bound technique for nonnegative rank is solely
based on the support of the matrix S, i.e., its zero/non-zero pattern. In this
paper, we characterize the power of lower bounds on positive semidefinite rank
based on solely on the support.Comment: 9 page
BROJA-2PID: A robust estimator for bivariate partial information decomposition
Makkeh, Theis, and Vicente found in [8] that Cone Programming model is the
most robust to compute the Bertschinger et al. partial information decompostion
(BROJA PID) measure [1]. We developed a production-quality robust software that
computes the BROJA PID measure based on the Cone Programming model. In this
paper, we prove the important property of strong duality for the Cone Program
and prove an equivalence between the Cone Program and the original Convex
problem. Then describe in detail our software and how to use it.\newline\inden
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