Related papers: Optimally Sorting Evolving Data
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
In this paper we propose a novel method for learning how algorithms perform. Classically, algorithms are compared on a finite number of existing (or newly simulated) benchmark datasets based on some fixed metrics. The algorithm(s) with the…
Dynamic Time Warping (DTW) has become the pragmatic choice for measuring distance between time series. However, it suffers from unavoidable quadratic time complexity when the optimal alignment matrix needs to be computed exactly. This…
In the evolutionary computation community, it is widely believed that stagnation impedes convergence in evolutionary algorithms, and that convergence inherently indicates optimality. However, this perspective is misleading. In this study,…
We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant…
Evolutionary optimization algorithms are often derived from loose biological analogies and struggle to leverage information obtained during the sequential course of optimization. An alternative promising approach is to leverage data and…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different…
Online algorithm selection (OAS) aims to adapt the optimization process to changes in the fitness landscape and is expected to outperform any single algorithm from a given portfolio. Although this expectation is supported by numerous…
In the framework of convolutional neural networks, downsampling is often performed with an average-pooling, where all the activations are treated equally, or with a max-pooling operation that only retains an element with maximum activation…
Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it…
We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop…
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…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Given a text $T$ and a pattern $P$, the order-preserving matching problem is to find all substrings in $T$ which have the same relative orders as $P$. Order-preserving matching has been an active research area since it was introduced by…