Related papers: Dynamic and Streaming Algorithms for Union Volume …
Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this…
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than $2$. Specifically, we obtain a…
The Memory Reallocation problem asks to dynamically maintain an assignment of given objects of various sizes to non-overlapping contiguous chunks of memory, while supporting updates (insertions/deletions) in an online fashion. The total…
Given a set of vectors $X = \{ x_1,\dots, x_n \} \subset \mathbb{R}^d$, the Euclidean max-cut problem asks to partition the vectors into two parts so as to maximize the sum of Euclidean distances which cross the partition. We design new…
Max-Cut is a fundamental combinatorial optimization problem that has been studied in various computational settings. We initiate the study of its streaming complexity in \emph{general metric spaces} with access to distance oracles. We give…
We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…
We construct a quasi-polynomial time deterministic approximation algorithm for computing the volume of an independent set polytope with restrictions. Randomized polynomial time approximation algorithms for computing the volume of a convex…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…
Depth estimation is an important step in many computer vision problems such as 3D reconstruction, novel view synthesis, and computational photography. Most existing work focuses on depth estimation from single frames. When applied to…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
We present efficient dynamic data structures for maintaining the union of unit discs and the lower envelope of pseudo-lines in the plane. More precisely, we present three main results in this paper: (i) We present a linear-size data…
We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting. For $(k, z)$-clustering in the streaming model, we achieve a number of words…
Penetration depth (PD) is essential for robotics due to its extensive applications in dynamic simulation, motion planning, haptic rendering, etc. The Expanding Polytope Algorithm (EPA) is the de facto standard for this problem, which…
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we developed an incremental approach to compute the proper orthogonal decomposition (POD) of PDE simulation data. Specifically, we developed an…
This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic…
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
Let $P$ be a set of points in the plane and let $m$ be an integer. The goal of Max Cover by Unit Disks problem is to place $m$ unit disks whose union covers the maximum number of points from~$P$. We are interested in the dynamic version of…