Related papers: Linear Hashing Is Optimal
We consider $(\epsilon,\delta)$-PAC maximum-selection and ranking for general probabilistic models whose comparisons probabilities satisfy strong stochastic transitivity and stochastic triangle inequality. Modifying the popular knockout…
Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails…
We consider the problem of scattering $n$ robots in a two dimensional continuous space. As this problem is impossible to solve in a deterministic manner, all solutions must be probabilistic. We investigate the amount of randomness (that is,…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For…
In the online hitting set problem, sets arrive over time, and the algorithm has to maintain a subset of elements that hit all the sets seen so far. Alon, Awerbuch, Azar, Buchbinder, and Naor (SICOMP 2009) gave an algorithm with competitive…
Recent studies have suggested that Large Language Models (LLMs) could provide interesting ideas contributing to mathematical discovery. This claim was motivated by reports that LLM-based genetic algorithms produced heuristics offering new…
The problem of fast items retrieval from a fixed collection is often encountered in most computer science areas, from operating system components to databases and user interfaces. We present an approach based on hash tables that focuses on…
Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…
In the parameterized problem \textsc{MaxLin2-AA}[$k$], we are given a system with variables $x_1,...,x_n$ consisting of equations of the form $\prod_{i \in I}x_i = b$, where $x_i,b \in \{-1, 1\}$ and $I\subseteq [n],$ each equation has a…
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that…
This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated…
A run in a string is a maximal periodic substring. For example, the string $\texttt{bananatree}$ contains the runs $\texttt{anana} = (\texttt{an})^{3/2}$ and $\texttt{ee} = \texttt{e}^2$. There are less than $n$ runs in any length-$n$…
Let $U_N$ denote a Haar Unitary matrix of dimension N, and consider the field \[ {\bf U}(z) = \log |\det(1-zU_N)| \] for z in the unit disk. Then, \[ \frac{\max_{|z|=1} {\bf U}(z) -\log N + \frac{3}{4} \log\log N} {\log\log N} \to 0 \] in…
Double hashing has recently found more common usage in schemes that use multiple hash functions. In double hashing, for an item $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +k g(x)) \bmod n$ for…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
For the problem of maximizing a monotone, submodular function with respect to a cardinality constraint $k$ on a ground set of size $n$, we provide an algorithm that achieves the state-of-the-art in both its empirical performance and its…
With the growth of image on the web, research on hashing which enables high-speed image retrieval has been actively studied. In recent years, various hashing methods based on deep neural networks have been proposed and achieved higher…
Let R_n be the radius of the largest disk covered after n steps of a simple random walk. We prove that almost surely limsup_{n \to \infty}(log R_n)^2/(log n log_3 n) = 1/4, where log_3 denotes 3 iterations of the log function. This is…
In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…