An oracle chooses a function f from the set of n bits strings to itself, which is either a randomly chosen permutation or a randomly chosen function. When queried by an n-bit string w, the oracle computes f(w), truncates the m last bits, and returns only the first n −m bits of f(w). How many queries does a querying adversary need to submit in order to distinguish the truncated permutation from ...

We study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation (or rearranging) problems of arrays, and define the “presortedness” as a distance from the input array to t...

A permutation array (or code) of length n and distance d is a set G of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x; y [G is at least d. One motivation for coding with permutations is powerline communication. After summarizing known results, it is shown here that certain families of polynomials over finite fields give rise to permutation a...

A permutation array(permutation code, PA) of length n and distance d, denoted by (n, d) PA, is a set of permutations C from some fixed set of n elements such that the Hamming distance between distinct members x,y ∈ C is at least d. In this correspondence, we present two constructions of PA from fractional polynomials over finite field, and a construction of (n, d) PA from permutation group with...

Permutation is a fundamental operator for array data, with applications in, for example, changing matrix layouts and reorganizing data cubes. We consider the problem of permuting large quantities of data stored on secondary storage that supports fast random block accesses, such as solid state drives and distributed key-value stores. Faster random accesses open up interesting new opportunities f...

Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n, e.g., by padding the input array to a power of two. We show that this simplifying assumption is not necessarily correct since it may result in a bias (i.e., not all possible permutations are generated with equal likelihood)....

Every permutation of {1, 2, . . . , N} can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place using simultaneous swaps in two rounds of swaps. In the case where the permutation is the k-way perfect shuffle we develop two methods for efficiently computing the pair of involutions that accomplishes these swaps. The ...

This paper compares the type I error and power of the one- and two-sample t-tests, and the one- and two-sample permutation tests for detecting differences in gene expression between two microarray samples with replicates using Monte Carlo simulations. When data are generated from a normal distribution, type I errors and powers of the one-sample parametric t-test and one-sample permutation test ...

Every permutation of {1, 2, . . . , N} can be written as the product of two involutions. As a consequence, any permutation of the elements of an array can be performed in-place using simultaneous swaps in two rounds of swaps. In the case where the permutation is the k-way perfect shuffle we develop two methods for efficiently computing the pair of involutions that accomplishes these swaps. The ...