Related papers: On the streaming complexity of fundamental geometr…
We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream. The cell probe model is a particularly strong computational model and subsumes, for example, the popular word RAM model.…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However…
Frequency estimation is one of the most fundamental problems in streaming algorithms. Given a stream $S$ of elements from some universe $U=\{1 \ldots n\}$, the goal is to compute, in a single pass, a short sketch of $S$ so that for any…
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known…
Many years ago John Tyrell a lecturer at King's college London challenged his Ph.D. students with the following puzzle: show that there is a unique triangle of minimal perimeter with exactly one vertex to lie on one of three given lines,…
We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to…
We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an…
In this work, we revisit the fundamental and well-studied problem of approximate pattern matching under edit distance. Given an integer $k$, a pattern $P$ of length $m$, and a text $T$ of length $n \ge m$, the task is to find substrings of…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
We introduce the problem of $k$-chasing of convex functions, a simultaneous generalization of both the famous k-server problem in $R^d$, and of the problem of chasing convex bodies and functions. Aside from fundamental interest in this…
We study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Data streaming, in which a large dataset is received as a "stream" of updates, is an important model in the study of space-bounded computation. Starting with the work of Le Gall [SPAA `06], it has been known that quantum streaming…
Friedman and Linial introduced the convex body chasing problem to explore the interplay between geometry and competitive ratio in metrical task systems. In convex body chasing, at each time step $t \in \mathbb{N}$, the online algorithm…
We address the unsupervised learning of several interconnected problems in low-level vision: single view depth prediction, camera motion estimation, optical flow, and segmentation of a video into the static scene and moving regions. Our key…
This article belongs to the area of geometric tomography, which is the study of geometric properties of solids based on data about their sections and projections. We describe a new direction in geometric tomography where different…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
We prove $n^{1+\Omega(1/p)}/p^{O(1)}$ lower bounds for the space complexity of $p$-pass streaming algorithms solving the following problems on $n$-vertex graphs: * testing if an undirected graph has a perfect matching (this implies lower…