Related papers: Better Streaming Algorithms for the Maximum Covera…
We study the problem of estimating the maximum matching size in graphs whose edges are revealed in a streaming manner. We consider both insertion-only streams and dynamic streams and present new upper and lower bound results for both…
Given an undirected graph $G$, the Densest $k$-subgraph problem (DkS) asks to compute a set $S \subset V$ of cardinality $\left\lvert S\right\rvert \leq k$ such that the weight of edges inside $S$ is maximized. This is a fundamental NP-hard…
In many emerging applications, data streams are monitored in a network environment. Due to limited communication bandwidth and other resource constraints, a critical and practical demand is to online compress data streams continuously with…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so…
Depth first search is a fundamental graph problem having a wide range of applications. For a graph $G=(V,E)$ having $n$ vertices and $m$ edges, the DFS tree can be computed in $O(m+n)$ using $O(m)$ space where $m=O(n^2)$. In the streaming…
We design a generic method for reducing the task of finding weighted matchings to that of finding short augmenting paths in unweighted graphs. This method enables us to provide efficient implementations for approximating weighted matchings…
Problems involving the efficient arrangement of simple objects, as captured by bin packing and makespan scheduling, are fundamental tasks in combinatorial optimization. These are well understood in the traditional online and offline cases,…
One of the oldest problems in the data stream model is to approximate the $p$-th moment $\|\mathcal{X}\|_p^p = \sum_{i=1}^n |\mathcal{X}_i|^p$ of an underlying vector $\mathcal{X} \in \mathbb{R}^n$, which is presented as a sequence of…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Attention computation takes both the time complexity of $O(n^2)$ and the space complexity of $O(n^2)$ simultaneously, which makes deploying Large Language Models (LLMs) in streaming applications that involve long contexts requiring…
In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy…
In Maximum $k$-Vertex Cover (Max $k$-VC), the input is an edge-weighted graph $G$ and an integer $k$, and the goal is to find a subset $S$ of $k$ vertices that maximizes the total weight of edges covered by $S$. Here we say that an edge is…
Parameterized complexity attempts to give a more fine-grained analysis of the complexity of problems: instead of measuring the running time as a function of only the input size, we analyze the running time with respect to additional…
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 consider the Maximum-weight Matching (MWM) problem in the streaming sliding window model of computation. In this model, the input consists of a sequence of weighted edges on a given vertex set $V$ of size $n$. The objective is to…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these…
We study the space complexity of solving the bias-regularized SVM problem in the streaming model. This is a classic supervised learning problem that has drawn lots of attention, including for developing fast algorithms for solving the…
Given an input acyclic digraph $G = (V,E)$ and a positive integer $k$, the problem of Maximum Coverage $k$-Antichains (resp., Chains) denoted as MA-$k$ (resp., MC-$k$) asks to find $k$ sets of pairwise unreachable vertices, known as…