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APPROX
2015
Springer

Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees

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Reconstruction/Non-reconstruction Thresholds for Colourings of General Galton-Watson Trees
The broadcasting models on trees arise in many contexts such as discrete mathematics, biology, information theory, statistical physics and computer science. In this work, we consider the k-colouring model. A basic question here is whether the assignment at the root affects the distribution of the colourings at the vertices at distance h from the root. This is the so-called reconstruction problem. For the case where the underlying tree is d-ary it is well known that d/ ln d is the reconstruction threshold. That is, for k = (1 + )d/ ln d we have non-reconstruction while for k = (1 − )d/ ln d we have reconstruction. Here, we consider the largely unstudied case where the underlying tree is chosen according to a predefined distribution. In particular, we consider the well-known Galton-Watson trees. The corresponding model arises naturally in many contexts such as the theory of spin-glasses and its applications on random Constraint Satisfaction Problems (rCSP). The study on rCSP focuses...
Charilaos Efthymiou
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where APPROX
Authors Charilaos Efthymiou
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