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Given an unordered array of $N$ elements drawn from a totally ordered set and an integer $k$ in the range from $1$ to $N$, in the classic selection problem the task is to find the $k$-th smallest element in the array. We study the…

This paper introduces a novel method, referred to as "hashing", which involves masking potentially bias-inducing words in large language models (LLMs) with hash-like meaningless identifiers to reduce cognitive biases and reliance on…

Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns. We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters…

We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…

Let $X$ be a set of items of size $n$ , which may contain some defective items denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The test outcome is $1$ (positive) if $Q$…

A mobile agent equipped with a compass and a measure of length has to find an inert treasure in the Euclidean plane. Both the agent and the treasure are modeled as points. In the beginning, the agent is at a distance at most $D>0$ from the…

The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…

In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on…

By periodically returning a search process to a known or random state, random resetting possesses the potential to unveil new trajectories, sidestep potential obstacles, and consequently enhance the efficiency of locating desired targets.…

Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…

Permutation matrices play a key role in matching and assignment problems across the fields, especially in computer vision and robotics. However, memory for explicitly representing permutation matrices grows quadratically with the size of…

Large Language Models (LLMs) have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical…

We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the…

The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity…

This work presents a content-based recommender system for machine learning classifier algorithms. Given a new data set, a recommendation of what classifier is likely to perform best is made based on classifier performance over similar known…

In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix…

The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…

Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…

Given $n$ real numbers $0\leq x_1,...,x_n<1$ and a permutation~$\sigma$ of $\{1,...,n\}$, we can always find $\xbar_1,...,\xbar_n\in\{0,1\}$ so that the partial sums $\xbar_1+... +\xbar_k$ and $\xbar_{\sigma 1}+... +\xbar_{\sigma k}$ differ…