Related papers: QuickLexSort: An efficient algorithm for lexicogra…

This paper proposes a framework of L-BFGS based on the (approximate) second-order information with stochastic batches, as a novel approach to the finite-sum minimization problems. Different from the classical L-BFGS where stochastic batches…

Given a sequence of $n$ numbers and $k$ parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that $k$ queues suffice to sort the sequence if the Longest Decreasing Subsequence (LDS) of…

The blessing of ubiquitous data also comes with a curse: the communication, storage, and labeling of massive, mostly redundant datasets. We seek to solve this problem at its core, collecting only valuable data and throwing out the rest via…

First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…

We focus on sorting, which is the building block of many machine learning algorithms, and propose a novel distributed sorting algorithm, named Coded TeraSort, which substantially improves the execution time of the TeraSort benchmark in…

Sorting is a tedious but simple task for human intelligence and can be solved fairly easily algorithmically. However, for Large Language Models (LLMs) this task is surprisingly hard, as some properties of sorting are among known weaknesses…

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…

A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…

Subset selection for the rank $k$ approximation of an $n\times d$ matrix $A$ offers improvements in the interpretability of matrices, as well as a variety of computational savings. This problem is well-understood when the error measure is…

A simple and fast analysis method to sort large data sets into groups with shared distinguishing characteristics is described, and applied to single molecular break junction conductance versus electrode displacement data. The method, based…

The Beeping Network (BN) model captures important properties of biological processes. Paradoxically, the extremely limited communication capabilities of such nodes has helped BN become one of the fundamental models for networks. Since in…

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

One of the greatest algorithms of all time is Quicksort. Its average running time is famously O(nlog(n)), and its variance, less famously, is O(n^2) (hence its standard deviation is O(n)). But what about higher moments? Here we find…

Many previous works in spike sorting study spike classification and compression independently. In this paper, a novel algorithm is proposed called MetaSort to address these two problems. To deal with compression, a novel adaptive level…

The problem of relevance ranking consists of sorting a set of objects with respect to a given criterion. Since users may prefer different relevance criteria, the ranking algorithms should be adaptable to the user needs. Two main approaches…

Spike sorting is a fundamental preprocessing step for many neuroscience studies which rely on the analysis of spike trains. In this paper, we present two unsupervised spike sorting algorithms based on discriminative subspace learning. The…

The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…

The amount of information stored in the form of documents on the internet has been increasing rapidly. Thus it has become a necessity to organize and maintain these documents in an optimum manner. Text classification algorithms study the…

We introduce XiSort, a deterministic and reproducible sorting algorithm for floating-point sequences based on IEEE-754 total ordering and entropy minimization. XiSort guarantees bit-for-bit stability across runs and platforms by resolving…

Most previous studies of the sorting algorithm QuickSort have used the number of key comparisons as a measure of the cost of executing the algorithm. Here we suppose that the n independent and identically distributed (i.i.d.) keys are each…