Related papers: Approximately Counting Subgraphs in Data Streams
Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
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…
A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph $G$, one can query the degree of a vertex, the existence of an edge between…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
We study the streaming complexity of $k$-counter approximate counting. In the $k$-counter approximate counting problem, we are given an input string in $[k]^n$, and we are required to approximate the number of each $j$'s ($j\in[k]$) in the…
We study the space complexity of four variants of the standard subgraph finding problem in the streaming model. Specifically, given an $n$-vertex input graph and a fixed-size pattern graph, we consider two settings: undirected simple…
Computing approximate shortest paths in the dynamic streaming setting is a fundamental challenge that has been intensively studied during the last decade. Currently existing solutions for this problem either build a sparse multiplicative…
This paper resolves one of the longest standing basic problems in the streaming computational model. Namely, optimal construction of quantile sketches. An $\varepsilon$ approximate quantile sketch receives a stream of items $x_1,\ldots,x_n$…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
We present a method for solving the transshipment problem - also known as uncapacitated minimum cost flow - up to a multiplicative error of $1 + \varepsilon$ in undirected graphs with non-negative edge weights using a tailored gradient…
We study streaming algorithms for the fundamental geometric problem of computing the cost of the Euclidean Minimum Spanning Tree (MST) on an $n$-point set $X \subset \mathbb{R}^d$. In the streaming model, the points in $X$ can be added and…
Graph streams, which refer to the graph with edges being updated sequentially in a form of a stream, have wide applications such as cyber security, social networks and transportation networks. This paper studies the problem of summarizing…
Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…
A $k$-truss is an edge-induced subgraph $H$ such that each of its edges belongs to at least $k-2$ triangles of $H$. This notion has been introduced around ten years ago in social network analysis and security, as a form of cohesive subgraph…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices…
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…
We consider the \textsf{Unit Interval Selection} problem in the one-pass random order streaming model. Here, an algorithm is presented a sequence of $n$ unit-length intervals on the line that arrive in uniform random order, and the…
Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of $n$ items from a data universe equipped with a total order, the task is to compute a sketch (data…