Related papers: Streaming Algorithms for Planar Convex Hulls
With the dawn of the Big Data era, data sets are growing rapidly. Data is streaming from everywhere - from cameras, mobile phones, cars, and other electronic devices. Clustering streaming data is a very challenging problem. Unlike the…
The Hierarchical Clustering (HC) problem consists of building a hierarchy of clusters to represent a given dataset. Motivated by the modern large-scale applications, we study the problem in the \streaming model, in which the memory is…
We propose two one-pass streaming algorithms for the $\mathcal{NP}$-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an…
In this paper, we present Ray-shooting Quickhull, which is a simple, randomized, outputsensitive version of the Quickhull algorithm for constructing the convex hull of a set of n points in the plane. We show that the randomized Ray-shooting…
Motivated by the trend to outsource work to commercial cloud computing services, we consider a variation of the streaming paradigm where a streaming algorithm can be assisted by a powerful helper that can provide annotations to the data…
Cosmological $N$-body simulations play a vital role in studying models for the evolution of the Universe. To compare to observations and make a scientific inference, statistic analysis on large simulation datasets, e.g., finding halos,…
In this work, we present data stream algorithms to compute optimal splits for decision tree learning. In particular, given a data stream of observations \(x_i\) and their corresponding labels \(y_i\), without the i.i.d. assumption, the…
Vector-based algorithms are novel algorithms in optimal any-angle path planning that are motivated by bug algorithms, bypassing free space by directly conducting line-of-sight checks between two queried points, and searching along obstacle…
We study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a $(\delta,\epsilon)$-stationary point from…
The Hierarchical Heavy Hitters problem extends the notion of frequent items to data arranged in a hierarchy. This problem has applications to network traffic monitoring, anomaly detection, and DDoS detection. We present a new streaming…
Seeking the convex hull of an object is a very fundamental problem arising from various tasks. In this work, we propose two variational convex hull models using level set representation for 2-dimensional data. The first one is an exact…
We study learning-augmented streaming algorithms for estimating the value of MAX-CUT in a graph. In the classical streaming model, while a $1/2$-approximation for estimating the value of MAX-CUT can be trivially achieved with $O(1)$ words…
In this paper we propose a new algorithm for streaming principal component analysis. With limited memory, small devices cannot store all the samples in the high-dimensional regime. Streaming principal component analysis aims to find the…
We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…
In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly…
In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points…
Processing data streams arriving at high speed requires the development of models that can provide fast and accurate predictions. Although deep neural networks are the state-of-the-art for many machine learning tasks, their performance in…
This paper proposes and evaluates a novel algorithm for streaming video over HTTP. The problem is formulated as a non-convex optimization problem which is constrained by the predicted available bandwidth, chunk deadlines, available video…
This article reviews recent advances in convex optimization algorithms for Big Data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary…