Related papers: Nearly-Optimal Mergesorts: Fast, Practical Sorting…
The maximum coverage problem is to select $k$ sets from a collection of sets such that the cardinality of the union of the selected sets is maximized. We consider $(1-1/e-\epsilon)$-approximation algorithms for this NP-hard problem in three…
Motivated by settings such as medical treatments or aircraft maintenance, we consider a scheduling problem with jobs that consist of two operations, a test and a processing part. The time required to execute the test is known in advance…
Inspired by a common technique for shuffling a deck of cards on a table without riffling, we formalize the pile shuffle and investigate its capabilities as a sorting device. Our study is novel in that we consider pile shuffle in three…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
We study a class of robust assortment optimization problems that was proposed by Farias, Jagabathula, and Shah (2013). The goal in these problems is to find an assortment that maximizes a firm's worst-case expected revenue under all…
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the…
In this manuscript, we address continuous unconstrained multi-objective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we analyze the class of Front Descent methods, which…
This report investigates three fundamental search algorithms: Linear Search, Binary Search, and Two Pointer Search. Linear Search checks each element sequentially, Binary Search divides the search space in half, and Two Pointer Search uses…
Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…
Sorting is one of the most fundamental problems in the field of computer science. With the rapid development of manycore processors, it shows great importance to design efficient parallel sort algorithm on manycore architecture. This paper…
Linear combination is a potent data fusion method in information retrieval tasks, thanks to its ability to adjust weights for diverse scenarios. However, achieving optimal weight training has traditionally required manual relevance…
We study sorting of permutations by random swaps if each comparison gives the wrong result with some fixed probability $p<1/2$. We use this process as prototype for the behaviour of randomized, comparison-based optimization heuristics in…
We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients.…
Shellsort is a sorting method that is attractive due to its simplicity, yet it takes effort to analyze its efficiency. The heart of the algorithm is the gap sequence chosen a priori and used during sorting. The selection of this gap…
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…
Sorting is an essential operation in computer science with direct consequences on the performance of large scale data systems, real-time systems, and embedded computation. However, no sorting algorithm is optimal under all distributions of…