Information flows, graphs and their guessing numbers
S Riis - 2006 4th International Symposium on Modeling and …, 2006 - ieeexplore.ieee.org
2006 4th International Symposium on Modeling and Optimization in …, 2006•ieeexplore.ieee.org
We provide a counter example to a conjecture by Leslie Valiant. Most interestingly the
counter example was found by introducing guessing numbers-a new graph theoretical
concept. We show that solvability of information flow problems of a quite general type is
closely related to problems concerning guessing numbers. We reduce a few other
conjectures by Valiant, to a general problem about guessing numbers. Valiant's conjectures
have been shown to be linked to the long standing open question of proving non-linear size …
counter example was found by introducing guessing numbers-a new graph theoretical
concept. We show that solvability of information flow problems of a quite general type is
closely related to problems concerning guessing numbers. We reduce a few other
conjectures by Valiant, to a general problem about guessing numbers. Valiant's conjectures
have been shown to be linked to the long standing open question of proving non-linear size …
We provide a counter example to a conjecture by Leslie Valiant. Most interestingly the counter example was found by introducing guessing numbers - a new graph theoretical concept. We show that solvability of information flow problems of a quite general type is closely related to problems concerning guessing numbers. We reduce a few other conjectures by Valiant, to a general problem about guessing numbers. Valiant’s conjectures have been shown to be linked to the long standing open question of proving non-linear size, non-logarithmic depth lower bounds on unrestricted circuits in Circuit Complexity. As a by-product we establish (by use of results by Valiant) an interesting link between Circuit Complexity and Network Coding, a new direction of research in multiuser information theory.
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