We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-polynomial time on H-free graphs (graphs excluding a fixed graph H as an induced subgraph) for every H whose every connected component is a path or a subdivided claw (...

We introduce a new approach for designing Random-order Contention Resolution Schemes (RCRS’s) via exact solution in continuous time. Given a function c(y):[0,1] → [0,1], we show how to select each element which arrives at time y ∈ [0,1] with probability ...

We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression, p-norm regression (...

Most of the literature on online algorithms and sequential decision-making focuses on settings with “irrevocable decisions” where the algorithm’s decision upon arrival of the new input is set in stone and can never change in the future. One canonical ...

We study algorithms for estimating the size of maximum matching. This problem has been subject to extensive research. For n-vertex graphs, Bhattacharya, Kiss, and Saranurak [FOCS’23] (BKS) showed that an estimate that is within є n of the optimal ...

We design an almost linear-size sketching scheme for computing edit distance up to a given threshold k. The scheme consists of two algorithms, a sketching algorithm and a recovery algorithm. The sketching algorithm depends on the parameter k and takes as ...

A recent work by Christiansen, Nowicki, and Rotenberg [STOC’23] provides dynamic algorithms for coloring sparse graphs, concretely as a function of the graph’s arboricity α. They give two randomized algorithms: O(α logα) implicit coloring in poly(logn) ...

In a prophet inequality problem, n independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the worst-case ratio between ...

The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to satisfy an ε ...

We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in graphs undergoing edge insertions and/or deletions. In particular, we obtain the following results:

the first data structure to ...

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This setting ...

We give a strongly polynomial algorithm for minimum cost generalized flow, and hence for optimizing any linear program with at most two non-zero entries per row, or at most two non-zero entries per column. Primal and dual feasibility were shown by Végh ‍(...

In the semi-streaming model for processing massive graphs, an algorithm makes multiple passes over the edges of a given n-vertex graph and is tasked with computing the solution to a problem using O(n · log(n)) space. Semi-streaming algorithms for Maximal ...

A random m× n matrix S is an oblivious subspace embedding (OSE) with parameters є>0, δ∈(0,1/3) and d≤ m≤ n, if for any d-dimensional subspace W⊆ Rⁿ, P( ∀_{x∈ W} (1+є)⁻¹||x||≤ ||Sx||≤ (1+є)||x|| )≥ 1−δ. It is known that the embedding dimension of an OSE must ...

In the pinwheel scheduling problem, each task i is associated with a positive integer a_i called its period, and we want to (perpetually) schedule one task per day so that each task i is performed at least once every a_i days. An obvious necessary ...

We devise a polynomial-time algorithm for partitioning a simple polygon P into a minimum number of star-shaped polygons. The question of whether such an algorithm exists has been open for more than four decades [Avis and Toussaint, Pattern Recognit., ...

The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges. This includes ...

Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As different ...

The hypergraph unreliability problem asks for the probability that a hypergraph gets disconnected when every hyperedge fails independently with a given probability. For graphs, the unreliability problem has been studied over many decades, and multiple ...

In the classic Correlation Clustering problem introduced by Bansal, Blum, and Chawla ‍(FOCS 2002), the input is a complete graph where edges are labeled either + or −, and the goal is to find a partition of the vertices that minimizes the sum of the +...