Related papers: Dynamic Geometric Set Cover, Revisited
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use…
Large volumes of spatiotemporal data, characterized by high spatial and temporal variability, may experience structural changes over time. Unlike traditional change-point problems, each sequence in this context consists of function-valued…
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
We revisit the classic problem of simplex range searching and related problems in computational geometry. We present a collection of new results which improve previous bounds by multiple logarithmic factors that were caused by the use of…
Recently, Cygan, Kowalik, and Wykurz [IPL 2009] gave sub-exponential-time approximation algorithms for the Set-Cover problem with approximation ratios better than ln(n). In light of this result, it is natural to ask whether such…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…
Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide…
Algebraic data structures are the main subroutine for maintaining distances in fully dynamic graphs in subquadratic time. However, these dynamic algebraic algorithms generally cannot maintain the shortest paths, especially against adaptive…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
We study parameterized and approximation algorithms for a variant of Set Cover, where the universe of elements to be covered consists of points in the plane and the sets with which the points should be covered are segments. We call this…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…
We study the time complexity of the discrete $k$-center problem and related (exact) geometric set cover problems when $k$ or the size of the cover is small. We obtain a plethora of new results: - We give the first subquadratic algorithm for…
Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object. In recent years, they have found significant applications in solvers for symmetric diagonally…
We consider the directed minimum weight cycle problem in the fully dynamic setting. To the best of our knowledge, so far no fully dynamic algorithms have been designed specifically for the minimum weight cycle problem in general digraphs.…