The view size estimation plays an important role in query optimization. It has been observed that many data follow a power law distribution. In this paper, we consider the balls in bins problem where we place balls into N bins when the bin selection probabilities follow a power law distribution. As a generalization to the coupon collector’s problem, we address the problem of determining the exp...

We answer a question of David Larman, by proving the following result. Any four unit balls in 3-dimensional space, whose centers are not collinear, have at most twelve common tangent lines. This bound is tight.

We provide a lower bound construction showing that the union of unit balls in R has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir.

We investigate the distribution, mean value, variance and some limiting properties of an urn model of white and red balls under random multiple drawing (either with or without replacement) when the number of white and red balls added follows a schedule that depends on the number of white balls chosen in each drawing.

Suppose an urn contains M balls, of different types, which are removed from the urn in a uniform random manner. In the hypergeometric coupon collection problem, we are interested in the set of balls that have been removed at the moment when at least one ball of each type has been removed. In its dual, we are interested in the set of removed balls at the first moment that this set contains all o...

We prove that projective spaces of Lorentzian and real stable polynomials are homeomorphic to closed Euclidean balls. This solves a conjecture June Huh the author. The proof utilizes refines connection between symmetric exclusion process in Interacting Particle Systems geometry polynomials.

For every tuple $d_1,\dots, d_l\geq 2,$ let $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}$ denote the tensor product of $\mathbb{R}^{d_i},$ $i=1,\dots,l.$ Let us by $\mathcal{B}(d)$ hyperspace centrally symmetric convex bodies in $\mathbb{R}^d,$ $d=d_1\cdots d_l,$ endowed with Hausdorff distance, and $\mathcal{B}_\otimes(d_1,\dots,d_l)$ subset consisting that are closed unit balls reaso...

The construction of the formal ball model for metric spaces due to Edalat and Heckmann was generalized Q-categories by Kostanek Waszkiewicz, where Q is a commutative unital quantale. This paper concerns influence structure quantale on connection between Yoneda completeness directed their sets balls. In case that unit interval [0, 1] equipped with continuous t-norm &, it shown in order each Q-ca...

Inspired by Bondarenko’s counter-example to Borsuk’s conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions. In particular, from generalized quadrangles we obtain unit ball packings in dimension q3 − q2 + q with chromatic number q3 + 1, where q is a prime power. This improves the previous low...