# Common Information and Unique Disjointness

@article{Braun2013CommonIA, title={Common Information and Unique Disjointness}, author={G{\'a}bor Braun and Sebastian Pokutta}, journal={Algorithmica}, year={2013}, volume={76}, pages={597-629} }

We provide an information-theoretic framework for establishing strong lower bounds on the nonnegative rank of matrices by means of common information, a notion previously introduced in Wyner (IEEE Trans Inf Theory 21(2):163–179, 1975). The framework is a generalization of the one in Braverman and Moitra (Proceedings of the forty-fifth annual ACM symposium on theory of computing, pp 161–170, 2013) for the shifted uniqe disjointness (UDISJ) matrix to arbitrary nonnegative matrices. Common…

## 46 Citations

### Information-theoretic approximations of the nonnegative rank

- Computer Science, Mathematicscomputational complexity
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A systematic study of common information extending the dual characterization of Witsenhausen, which characterizes the minimal nonnegative rank under tensoring and small perturbations of a matrix and provides new insights into its information-theoretic structure.

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The study of SDP lifts over Cartesian product of fixed-size positive semidefinite cones is motivated mainly from practical considerations where it is well known that such SDPs can be solved more efficiently than general SSPs.

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This work relates the communication complexity of generalizations of quantum theory to questions of mainstream interest in the area of combinatorial optimization with recent exponential lower bounds on the linear extension complexity of polytopes.

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The first explicit example of a function that incurs a higher communication cost than the input length in the secure computation model of Feige, Kilian and Naor (1994), who had shown that such functions exist are obtained.

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This work defines a consistent reduction mechanism that degrades approximation factors in a controlled fashion and which, at the same time, is compatible with approximate linear and semidefinite programming formulations.

### An Almost Optimal Algorithm for Computing Nonnegative

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