SIAM Journal on Computing
Linked decompositions of networks and the power of choice in Polya urns
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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We establish some basic properties of a "Pólya choice" generalization of the standard Pólya urn process. From a set of kurns, the ith occupied by niballs, choose cdistinct urns i1,...,icwith probability proportional to $n_{i_1}^\gamma \times \cdots\times n_{i_c}^\gamma$, where 茂戮驴 0 is a constant parameter, and increment one with the smallest occupancy (breaking ties arbitrarily). We show that this model has a phase transition. If 0 茂戮驴茂戮驴 1, this still occurs with positive probability, but there is also positive probability that some urns get only finitely many balls while others get infinitely many.