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We give an $O(n^{1.5} \log n)$ algorithm that, given a directed planar graph with arc capacities, a set of source nodes and a single sink node, finds a maximum flow from the sources to the sink . This is the first subquadratic-time strongly…
A semi-streaming algorithm in dynamic graph streams processes any $n$-vertex graph by making one or multiple passes over a stream of insertions and deletions to edges of the graph and using $O(n \cdot \mbox{polylog}(n))$ space.…
We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and…
This paper presents a new deterministic algorithm for single-source shortest paths (SSSP) on real non-negative edge-weighted directed graphs, with running time $O(m\sqrt{\log n}+\sqrt{mn\log n\log \log n})$, which is $O(m\sqrt{\log n\log…
We present a randomized parallel algorithm in the {\sf PRAM} model for $k$-vertex connectivity. Given an undirected simple graph, our algorithm either finds a set of fewer than $k$ vertices whose removal disconnects the graph or reports…
We improve the running times of $O(1)$-approximation algorithms for the set cover problem in geometric settings, specifically, covering points by disks in the plane, or covering points by halfspaces in three dimensions. In the unweighted…
In this paper, we design efficient algorithms to approximately count the number of edges of a given $k$-hypergraph, and to sample an approximately uniform random edge. The hypergraph is not given explicitly, and can be accessed only through…
We present a randomized approximation algorithm for computing traveling salesperson tours in undirected regular graphs. Given an $n$-vertex, $k$-regular graph, the algorithm computes a tour of length at most $\left(1+\frac{7}{\ln…
Let ${\mathcal C}$ be a proper minor-closed family of graphs. We present a randomized algorithm that given a graph $G \in {\mathcal C}$ with $n$ vertices, finds a simple cycle of size $k$ in $G$ (if exists) in $2^{O(k)}n$ time. The…
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…
In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\in\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1…
Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…
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…
In recent years, the problem of computing the frequencies of the induced $k$-vertex subgraphs of a graph, or \emph{$k$-graphlets}, has become central. One approach for this problem is to sample $k$-graphlets randomly. Classic algorithms for…
Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang…
We study graph orientations that minimize the entropy of the in-degree sequence. The problem of finding such an orientation is an interesting special case of the minimum entropy set cover problem previously studied by Halperin and Karp…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time $O(m\sqrt{\log n \cdot \log\log n})$ in the comparison-addition model. This is the…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…