Related papers: Selection Algorithms with Small Groups
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying…
In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
We show that several versions of Floyd and Rivest's improved algorithm Select for finding the $k$th smallest of $n$ elements require at most $n+\min\{k,n-k\}+O(n^{1/2}\ln^{1/2}n)$ comparisons on average and with high probability. This…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
Tiering is an essential technique for building large-scale information retrieval systems. While the selection of documents for high priority tiers critically impacts the efficiency of tiering, past work focuses on optimizing it with respect…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. That is why a lot of effort has been put into finding sorting algorithms that sort large sets as fast as possible. But the…
The authors recently gave an $n^{O(\log\log n)}$ time membership query algorithm for properly learning decision trees under the uniform distribution (Blanc et al., 2021). The previous fastest algorithm for this problem ran in $n^{O(\log…
Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. The more sophisticated and fast sorting algorithms become asymptotically, the less efficient they are for small sets of items…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
Unsupervised learning, and more specifically clustering, suffers from the need for expertise in the field to be of use. Researchers must make careful and informed decisions on which algorithm to use with which set of hyperparameters for a…
We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be…
Various decision support systems are available that implement Data Mining and Data Warehousing techniques for diving into the sea of data for getting useful patterns of knowledge (pearls). Classification, regression, clustering, and many…
While a broad range of techniques have been proposed to tackle distribution shift, the simple baseline of training on an $\textit{undersampled}$ balanced dataset often achieves close to state-of-the-art-accuracy across several popular…
An important subcase of the hidden subgroup problem is equivalent to the shift problem over abelian groups. An efficient solution to the latter problem would serve as a building block of quantum hidden subgroup algorithms over solvable…
In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a_1,\ldots,a_n} over \Sigma^m, where \Sigma is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median…
We investigate deterministic and randomized streaming algorithms for word problems in finitely generated groups and semigroups. For this we introduce the notion of a distinguisher: a randomized streaming algorithm that processes two input…
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…