Related papers: Optimally Sorting Evolving Data
We examine sorting algorithms for $n$ elements whose basic operation is comparing $t$ elements simultaneously (a $t$-comparator). We focus on algorithms that use only a single round or two rounds -- comparisons performed in the second round…
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…
We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
The investigation of input-output systems often requires a sophisticated choice of test inputs to make best use of limited experimental time. Here we present an iterative algorithm that continuously adjusts an ensemble of test inputs…
Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small…
The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population…
Aggregating multiple input rankings into a consensus ranking is essential in various fields such as social choice theory, hiring, college admissions, web search, and databases. A major challenge is that the optimal consensus ranking might…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…