Related papers: Power of $d$ Choices with Simple Tabulation
Let ${\mathcal D}(n)$ be the maximal determinant for $n \times n$ $\{\pm 1\}$-matrices, and $\mathcal R(n) = {\mathcal D}(n)/n^{n/2}$ be the ratio of ${\mathcal D}(n)$ to the Hadamard upper bound. Using the probabilistic method, we prove…
We study the $\textit{average-case deterministic query complexity}$ of boolean functions under a $\textit{uniform input distribution}$, denoted by $\mathrm{D}_\mathrm{ave}(f)$, the minimum average depth of zero-error decision trees that…
We analyze a new random algorithm for numerical integration of $d$-variate functions over $[0,1]^d$ from a weighted Sobolev space with dominating mixed smoothness $\alpha\ge 0$ and product weights $1\ge\gamma_1\ge\gamma_2\ge\cdots>0$, where…
We explore approximation algorithms for the $d$-dimensional geometric bin packing problem ($d$BP). Caprara (MOR 2008) gave a harmonic-based algorithm for $d$BP having an asymptotic approximation ratio (AAR) of $T_{\infty}^{d-1}$ (where…
We consider the following dynamic load-balancing process: given an underlying graph $G$ with $n$ nodes, in each step $t\geq 0$, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks…
Effective load balancing lies at the heart of many applications in operations. Frequently tackled via the balls-into-bins paradigm, seminal results established the power of two choices in load balancing: a limited amount of costly…
A subset of the Hamming cube over $n$-letter alphabet is said to be $d$-maximal if its diameter is $d$, and adding any point increases the diameter. Our main result shows that each $d$-maximal set is either of size at most $(n+o(n))^d$ or…
We consider the following load balancing process for $m$ tokens distributed arbitrarily among $n$ nodes connected by a complete graph: In each time step a pair of nodes is selected uniformly at random. Let $\ell_1$ and $\ell_2$ be their…
Cuckoo hashing with a stash is a robust multiple choice hashing scheme with high memory utilization that can be used in many network device applications. Unfortunately, for memory loads beyond 0.5, little is known on its performance. In…
Suppose $k$ balls are dropped into $n$ boxes independently with uniform probability, where $n, k$ are large with ratio approximately equal to some positive real $\lambda$. The maximum box count has a counterintuitive behavior: first of all,…
We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k >= 3 (distinct) associated buckets…
Most hash tables have an insertion time of $O(1)$, possibly qualified as expected and/or amortised. While insertions into cuckoo hash tables indeed seem to take $O(1)$ expected time in practice, only polylogarithmic guarantees are proven in…
Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used,…
We study the placement of n balls into n bins where balls and bins are represented as two vector spaces over Z 2 . The placement is done according to a linear transformation between the two vector spaces. We analyze the expected size of a…
When rows of an $n \times d$ matrix $A$ are given in a stream, we study algorithms for approximating the top eigenvector of the matrix ${A}^TA$ (equivalently, the top right singular vector of $A$). We consider worst case inputs $A$ but…
How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for…
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Writing the expected maximum as $\frac{r}{n}T+…
In this work, we examine a generic class of simple distributed balls-into-bins algorithms. Exploiting the strong concentration bounds that apply to balls-into-bins games, we provide an iterative method to compute accurate estimates of the…
In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting…