منابع مشابه
Random Sorting Networks
A sorting network is a shortest path from 12 · · · n to n · · · 21 in the Cayley graph of Sn generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n → ∞ the spacetime process of swaps converges to the product of semicircle law and Lebesgue measure. We conjecture that the trajectories of individual particles converge to random sine curves, while the permuta...
متن کاملRandom Subnetworks of Random Sorting Networks
A sorting network is a shortest path from 12 · · · n to n · · · 21 in the Cayley graph of Sn generated by nearest-neighbor swaps. For m ≤ n, consider the random m-particle sorting network obtained by choosing an n-particle sorting network uniformly at random and then observing only the relative order of m particles chosen uniformly at random. We prove that the expected number of swaps in locati...
متن کاملA pattern theorem for random sorting networks
A sorting network is a shortest path from 12 · · ·n to n · · · 21 in the Cayley graph of the symmetric group Sn generated by nearest-neighbor swaps. A pattern is a sequence of swaps that forms an initial segment of some sorting network. We prove that in a uniformly random n-element sorting network, any fixed pattern occurs in at least cn disjoint space-time locations, with probability tending t...
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Random sampling techniques have played a vital role in the design of sorting and selection algorithms for numerous models of computing. In this article we provide a summary of sorting and selection algorithms that have been devised using random sampling. Models of computations treated include the parallel comparison tree, the PRAM, the mesh, the mesh with fixed, reconfigurable, and optical buse...
متن کاملRandom roots and lineage sorting.
Lineage sorting has been suggested as a major force in generating incongruent phylogenetic signal when multiple gene partitions are examined. The degree of lineage sorting can be estimated using the coalescent process and simulation studies have also pointed to a major role for incomplete lineage sorting as a factor in phylogenetic inference. Some recent empirical studies point to an extreme ro...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2007.05.019