Related papers: Near-Optimal Space Lower Bounds for Streaming CSPs

For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…

The Parameterized Inapproximability Hypothesis (PIH), which is an analog of the PCP theorem in parameterized complexity, asserts that, there is a constant $\varepsilon> 0$ such that for any computable function $f:\mathbb{N}\to\mathbb{N}$,…

Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured…

This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…

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 construct and analyze a message-passing algorithm for random constraint satisfaction problems (CSPs) at large clause density, generalizing work of El Alaoui, Montanari, and Sellke for Maximum Cut [arXiv:2111.06813] through a connection…

We consider the problem of computing distance between a pattern of length $n$ and all $n$-length subwords of a text in the streaming model. In the streaming setting, only the Hamming distance ($L_0$) has been studied. It is known that…

We study the problem of graph and hypergraph sparsification in insertion-only data streams. The input is a hypergraph $H=(V, E, w)$ with $n$ nodes, $m$ hyperedges, and rank $r$, and the goal is to compute a hypergraph $\widehat{H}$ that…

Computing the approximate quantiles or ranks of a stream is a fundamental task in data monitoring. Given a stream of elements $x_1, x_2, \dots, x_n$ and a query $x$, a relative-error quantile estimation algorithm can estimate the rank of…

We identify a sharp separation in the streaming space complexity of Maximum Cut when the algorithm must output an approximate cut (rather than only the approximate value). For dense graphs, we show that $O(n/\varepsilon^2)$ space is…

We study the problem of partitioning integer sequences in the one-pass data streaming model. Given is an input stream of integers $X \in \{0, 1, \dots, m \}^n$ of length $n$ with maximum element $m$, and a parameter $p$. The goal is to…

We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of $m$ sets over $n$ elements in the query model, we show that sub-linear algorithms derived from existing techniques have…

In this paper we present improved bounds for approximating maximum matchings in bipartite graphs in the streaming model. First, we consider the question of how well maximum matching can be approximated in a single pass over the input using…

We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…

We prove that any two-pass graph streaming algorithm for the $s$-$t$ reachability problem in $n$-vertex directed graphs requires near-quadratic space of $n^{2-o(1)}$ bits. As a corollary, we also obtain near-quadratic space lower bounds for…

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a…

In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the…

We present an algorithm for the maximum matching problem in dynamic (insertion-deletions) streams with *asymptotically optimal* space complexity: for any $n$-vertex graph, our algorithm with high probability outputs an $\alpha$-approximate…

Space efficient algorithms play a central role in dealing with large amount of data. In such settings, one would like to analyse the large data using small amount of "working space". One of the key steps in many algorithms for analysing…

A Boolean maximum constraint satisfaction problem, Max-CSP($f$), is specified by a predicate $f:\{-1,1\}^k\to\{0,1\}$. An $n$-variable instance of Max-CSP($f$) consists of a list of constraints, each of which applies $f$ to $k$ distinct…