相关论文: Applying constraint programming to minimal lottery…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
This paper explores special arrangements of clues in $m \times n$ Numbrix puzzles. The maximum number of clues which fails to define an $m \times n$ puzzle is demonstrated for all $m$ and $n$. In addition, a small upper bound on the minimum…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
The recent lottery ticket hypothesis proposes that there is one sub-network that matches the accuracy of the original network when trained in isolation. We show that instead each network contains several winning tickets, even if the initial…
Consider the commonly known puzzle, given $k$ glass balls, find an optimal algorithm to determine the lowest floor of a building of $n$ floors from which a thrown glass ball will break. This puzzle was originally posed in its original form…
Patterned self-assembly tile set synthesis (PATS) aims at finding a minimum tile set to uniquely self-assemble a given rectangular color pattern. For $k \ge 1$, $k$-PATS is a variant of PATS that restricts input patterns to those with at…
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
We investigate the following version of the well-known R\'enyi-Ulam game. Two players - the Questioner and the Responder - play against each other. The Responder thinks of a number from the set $\{1,\ldots,n\}$, and the Questioner has to…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the…
Concentration bounds are given for throwing balls into bins independently according to a distribution $p$. The probability of a $k$-loaded bin after $m$ balls is shown to be controlled on both sides by $\rho_{m,k} := m \|p\|_k / k$. This…
We collect, survey and develop methods of (one-dimensional) stochastic approximation in a framework that seems suitable to handle fairly broad generalizations of Polya urns. To show the applicability of the results we determine the limiting…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
It is a long-standing open question to determine the minimum number of comparisons $S(n)$ that suffice to sort an array of $n$ elements. Indeed, before this work $S(n)$ has been known only for $n\leq 22$ with the exception for $n=16$, $17$,…
The minimum $k$-enclosing ball problem seeks the ball with smallest radius that contains at least~$k$ of~$m$ given points in a general $n$-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the…
The Lottery Ticket Hypothesis (LTH) states that for a reasonably sized neural network, a sub-network within the same network yields no less performance than the dense counterpart when trained from the same initialization. This work…
Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary…