Related papers: Self-Improving Algorithms
Ailon et al. [SICOMP'11] proposed self-improving algorithms for sorting and Delaunay triangulation (DT) when the input instances $x_1,\cdots,x_n$ follow some unknown \emph{product distribution}. That is, $x_i$ comes from a fixed unknown…
Computing the coordinate-wise maxima of a planar point set is a classic and well-studied problem in computational geometry. We give an algorithm for this problem in the \emph{self-improving setting}. We have $n$ (unknown) independent…
Ailon et al. (SICOMP 2011) proposed a self-improving sorter that tunes its performance to an unknown input distribution in a training phase. The input numbers $x_1,x_2,\ldots,x_n$ come from a product distribution, that is, each $x_i$ is…
Finding the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry. We consider these problems in the self-improving setting. Here, we have $n$ distributions…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes $O(n \log n + m)$ time, where $n$ is the input size and $m$ is the output size. This is the first…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
The expected improvement (EI) algorithm is a popular strategy for information collection in optimization under uncertainty. The algorithm is widely known to be too greedy, but nevertheless enjoys wide use due to its simplicity and ability…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems,…
We consider stochastic optimization with delayed gradients where, at each time step $t$, the algorithm makes an update using a stale stochastic gradient from step $t - d_t$ for some arbitrary delay $d_t$. This setting abstracts asynchronous…
We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The $n$ input points are drawn from a hidden mixture of product distributions; we are only…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We explore the fundamental problem of sorting through the lens of learning-augmented algorithms, where algorithms can leverage possibly erroneous predictions to improve their efficiency. We consider two different settings: In the first…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…