Related papers: Revisiting Maximum Satisfiability and Related Prob…
We consider the maximum matching problem in the semi-streaming model formalized by Feigenbaum, Kannan, McGregor, Suri, and Zhang that is inspired by giant graphs of today. As our main result, we give a two-pass $(1/2 + 1/16)$-approximation…
We initiate the study of the Interval Selection problem in the (streaming) sliding window model of computation. In this problem, an algorithm receives a potentially infinite stream of intervals on the line, and the objective is to maintain…
Given a collection of $m$ sets from a universe $\mathcal{U}$, the Maximum Set Coverage problem consists of finding $k$ sets whose union has largest cardinality. This problem is NP-Hard, but the solution can be approximated by a polynomial…
Many real-world applications pose challenges in incorporating fairness constraints into the $k$-center clustering problem, where the dataset consists of $m$ demographic groups, each with a specified upper bound on the number of centers to…
We explore a novel problem in streaming submodular maximization, inspired by the dynamics of news-recommendation platforms. We consider a setting where users can visit a news website at any time, and upon each visit, the website must…
This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F \subseteq E$…
We study the maximum weight matching problem in the random-order semi-streaming model and in the robust communication model. Unlike many other sublinear models, in these two frameworks, there is a large gap between the guarantees of the…
We consider the streaming complexity of a fundamental task in approximate pattern matching: the $k$-mismatch problem. It asks to compute Hamming distances between a pattern of length $n$ and all length-$n$ substrings of a text for which the…
Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…
In the $k$-mismatch problem we are given a pattern of length $n$ and a text and must find all locations where the Hamming distance between the pattern and the text is at most $k$. A series of recent breakthroughs have resulted in an…
The remarkable achievements of machine learning techniques in analyzing discrete structures have drawn significant attention towards their integration into combinatorial optimization algorithms. Typically, these methodologies improve…
Given a set of vectors $X = \{ x_1,\dots, x_n \} \subset \mathbb{R}^d$, the Euclidean max-cut problem asks to partition the vectors into two parts so as to maximize the sum of Euclidean distances which cross the partition. We design new…
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…
We present a streaming algorithm for the vertex connectivity problem in dynamic streams with a (nearly) optimal space bound: for any $n$-vertex graph $G$ and any integer $k \geq 1$, our algorithm with high probability outputs whether or not…
We provide $\widetilde{O}(\epsilon^{-1})$-pass semi-streaming algorithms for computing $(1-\epsilon)$-approximate maximum cardinality matchings in bipartite graphs. Our most efficient methods are deterministic and use optimal, $O(n)$,…
In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly…
Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural…
Given a 2-SAT formula $F$ consisting of $n$ variables and $\cn$ random clauses, what is the largest number of clauses $\max F$ satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of…
We present a deterministic $(1+\varepsilon)$-approximate maximum matching algorithm in $\mathsf{poly} 1/\varepsilon$ passes in the semi-streaming model, solving the long-standing open problem of breaking the exponential barrier in the…
We show that both clustering and subspace embeddings can be performed in the streaming model with the same asymptotic efficiency as in the central/offline setting. For $(k, z)$-clustering in the streaming model, we achieve a number of words…