Related papers: Selection Algorithms with Small Groups
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may…
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…
We make progress on two important problems regarding attribute efficient learnability. First, we give an algorithm for learning decision lists of length $k$ over $n$ variables using $2^{\tilde{O}(k^{1/3})} \log n$ examples and time…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
For a finite group $G$, the size of a minimum generating set of $G$ is denoted by $d(G)$. Given a finite group $G$ and an integer $k$, deciding if $d(G)\leq k$ is known as the minimum generating set (MIN-GEN) problem. A group $G$ of order…
The n-way number partitioning problem, a fundamental challenge in combinatorial optimization, has significant implications for applications such as fair division and machine scheduling. Despite these problems being NP-hard, many…
Database query processing requires algorithms for duplicate removal, grouping, and aggregation. Three algorithms exist: in-stream aggregation is most efficient by far but requires sorted input; sort-based aggregation relies on external…
We address the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
In this paper, we describe randomized Shellsort--a simple, randomized, data-oblivious version of the Shellsort algorithm that always runs in O(n log n) time and, as we show, succeeds in sorting any given input permutation with very high…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…
Diversity is an important principle in data selection and summarization, facility location, and recommendation systems. Our work focuses on maximizing diversity in data selection, while offering fairness guarantees. In particular, we offer…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups, recently this has been relaxed in what is known as…
We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G cong H. For several decades, the n^(log_p n + O(1)) generator-enumeration bound (where p is the smallest prime…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
We study the collective schedules problem, which consists in computing a one machine schedule of a set of tasks, knowing that a set of individuals (also called voters) have preferences regarding the order of the execution of the tasks. Our…
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…