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We consider the problem of storing an ordered dictionary data structure over a distributed set of nodes. In contrast to traditional sequential data structures, distributed data structures should ideally have low congestion. We present a novel randomized data structure, called a <i>family tree</i>, to solve this problem. A family tree has optimal expected… (More)

While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special type of central extension, is widely believed to contain the essential hard cases. However, looking specifically at… (More)

Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using abelian hypergroups and an associated classical simulation theorem (a la Gottesman-Knill). Using these tools, we… (More)

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