Collision times in multicolor urn models and sequential graph coloring with applications to discrete logarithms

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Collision Times in Multicolor Urn Models and Sequential Graph Coloring With Applications to Discrete Logarithms

Consider an urn model where at each step one of q colors is sampled according to some probability distribution and a ball of that color is placed in an urn. The distribution of assigning balls to urns may depend on the color of the ball. Collisions occur when a ball is placed in an urn which already contains a ball of different color. Equivalently, this can be viewed as sequentially coloring a ...

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We study properties of graph colorings that minimize the quantity of color information with respect to a given probability distribution P on the vertices of the graph. The minimum entropy of any coloring of such a probabilistic graph (G,P ) is the chromatic entropy Hχ(G,P ). Applications of the chromatic entropy are found in data compression with side information at the receiver and digital ima...

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ژورنال

عنوان ژورنال: The Annals of Applied Probability

سال: 2016

ISSN: 1050-5164

DOI: 10.1214/16-aap1176