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We study the repeated balls-into-bins process introduced by Becchetti, Clementi, Natale, Pasquale and Posta (2019). This process starts with $m$ balls arbitrarily distributed across $n$ bins. At each round $t=1,2,\ldots$, one ball is…
Previous work on tabulation hashing by Patrascu and Thorup from STOC'11 on simple tabulation and from SODA'13 on twisted tabulation offered Chernoff-style concentration bounds on hash based sums, e.g., the number of balls/keys hashing to a…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
We present an efficient parallel derandomization method for randomized algorithms that rely on concentrations such as the Chernoff bound. This settles a classic problem in parallel derandomization, which dates back to the 1980s. Consider…
In many experimental settings, one is tasked with obtaining information about certain relationships by applying perturbations to a set of independent variables and noting the changes in the set of dependent ones. While traditional…
We consider a generalization of the Bernoulli-Laplace model in which there are two urns and $n$ total balls, of which $r$ are red and $n - r$ white, and where the left urn holds $m$ balls. At each time increment, $k$ balls are chosen…
Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…
In this paper we develop algorithms for approximating matrix multiplication with respect to the spectral norm. Let A\in{\RR^{n\times m}} and B\in\RR^{n \times p} be two matrices and \eps>0. We approximate the product A^\top B using two…
Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This paper is concerned with developing scalable algorithms that under-approximate the backward reachable sets, for…
Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${\sim}\log n/\log\log n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29…
We introduce discrete time Markov chains that preserve uniform measures on boxed plane partitions. Elementary Markov steps change the size of the box from (a x b x c) to ((a-1) x (b+1) x c) or ((a+1) x (b-1) x c). Algorithmic realization of…
The Curveball algorithm is a variation on well-known switch-based Markov chain approaches for uniformly sampling binary matrices with fixed row and column sums. Instead of a switch, the Curveball algorithm performs a so-called binomial…
A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting depends on combinatorial data only. We show that any algorithm of this kind admits a tropical analogue which can be used to solve mean payoff…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
We study the long-term behavior of the two-thinning variant of the classical balls-and-bins model. In this model, an overseer is provided with uniform random allocation of $m$ balls into $n$ bins in an on-line fashion. For each ball, the…
In this text I present a couple of new principles and thereon based iterative methods for numerical solution of sequences of systems of linear equations with fixed system matrix and changing right-hand-sides. The use of the new methods is…
The classical Chernoff's theorem is a statement about discrete-time approximations of semigroups, where the approximations are consturcted as products of time-dependent contraction operators strongly differentiable at zero. We generalize…
The graphical balls-into-bins process is a generalization of the classical 2-choice balls-into-bins process, where the bins correspond to vertices of an arbitrary underlying graph $G$. At each time step an edge of $G$ is chosen uniformly at…
Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of…
We develop some new analytic bounds on transmission probabilities (and the related reflection probabilities and Bogoliubov coefficients) for generic one-dimensional scattering problems. To do so we rewrite the Schrodinger equation for some…