Joins are expensive, especially on large data and/or multiple relations. One promising approach in mitigating their high costs is to just return a simple random sample of the full join results, which is sufficient for many tasks. Indeed, in as early as 1999, Chaudhuri et al. posed the problem of sampling over joins as a fundamental challenge in large database systems. They also pointed out a fu...

This note extends a recent result of Kannan, Tetali and Vempala to completely solve, via a simple proof, the problem of random generation of a labeled tournament with a given score vector. The proof uses the method of path coupling applied to an appropriate Markov chain on the set of labeled tournaments with the same score vector. MRS: 65C05, 05C20.

A random balanced sample (RBS) is a multivariate distribution with n components Xk, each uniformly distributed on [−1, 1], such that the sum of these components is precisely 0. The corresponding vectors ~ X lie in an (n − 1)–dimensional polytope M(n). We present new methods for the construction of such RBS via densities over M(n) and these apply for arbitrary n. While simple densities had been ...

Many organizations such as the U.S. Census publicly release samples of data that they collect about private citizens. These datasets are first anonymized using various techniques and then a small sample is released so as to enable “do-it-yourself” calculations. This paper investigates the privacy of the second step of this process: sampling. We observe that rare values – values that occur with ...

Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose new random walk algorithm based on billiard trajectories. Numerical experiments demonstrate much faster convergence to uniform distribution.

We consider the problem of random sampling for bandlimited functions. When can a bandlimited function f be recovered from randomly chosen samples f(xj), j ∈ J ⊂ N? We estimate the probability that a sampling inequality of the form A‖f‖ 2 ≤ ∑ j∈J |f(xj)| ≤ B‖f‖2 hold uniformly for all functions f ∈ L(R) with supp f̂ ⊆ [−1/2, 1/2] or for some subset of bandlimited functions. In contrast to discret...

For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.

This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are slightly superlinear: the complexity is O(n(lnn)3) in approximate-size sampling and O(n4/3) in exact-size sampling (under a real-arithmetic computation mode...

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...

We show how to uniformly distribute data at random (not to be confounded with permutation routing) in two settings that are able to deal with massive data: coarse grained parallelism and external memory. In contrast to previously known work for parallel setups, our method is able to fulfill the three criteria of uniformity, work-optimality and balance among the processors simultaneously. To gua...