Related papers: Eulerian Graph Sparsification by Effective Resista…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Let $V$ be a set of $n$ points in the plane. The unit-disk graph $G = (V, E)$ has vertex set $V$ and an edge $e_{uv} \in E$ between vertices $u, v \in V$ if the Euclidean distance between $u$ and $v$ is at most 1. The weight of each edge…
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
We consider the problem of reconstructing a rank-$k$ $n \times n$ matrix $M$ from a sampling of its entries. Under a certain incoherence assumption on $M$ and for the case when both the rank and the condition number of $M$ are bounded, it…
Cuts in graphs are a fundamental object of study, and play a central role in the study of graph algorithms. The problem of sparsifying a graph while approximately preserving its cut structure has been extensively studied and has many…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in $O^*(2^{3k})$ time given…
We give a randomized algorithm that finds a minimum cut in an undirected weighted $m$-edge $n$-vertex graph $G$ with high probability in $O(m \log^2 n)$ time. This is the first improvement to Karger's celebrated $O(m \log^3 n)$ time…
In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in undirected graphs. For unweighted graphs, we provide an algorithm for $2$-approximate APSP in $\tilde O(n^{2.5-r}+n^{\omega(r)})$ time, for any…
We give an algorithm that reduces the straight skeleton to the motorcycle graph in $O(n\log n)$ time for simple polygons and $O(n(\log n)\log m)$ time for a planar straight line graph (PSLG) with $m$ connected components. This improves on…
We show an $\widetilde{O}(m^{1.5} \epsilon^{-1})$ time algorithm that on a graph with $m$ edges and $n$ vertices outputs its spanning tree count up to a multiplicative $(1+\epsilon)$ factor with high probability, improving on the previous…
In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…
We present an algorithm for min-cost flow in graphs with $n$ vertices and $m$ edges, given a tree decomposition of width $\tau$ and size $S$, and polynomially bounded, integral edge capacities and costs, running in…
We provide a deterministic algorithm that finds, in $\epsilon^{-O(1)} n^2$ time, an $\epsilon$-regular Frieze-Kannan partition of a graph on $n$ vertices. The algorithm outputs an approximation of a given graph as a weighted sum of…
Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…
A classic result in graph theory, due to Batson, Spielman, and Srivastava (STOC 2009) shows that every graph admits a $(1 \pm \varepsilon)$ cut (or spectral) sparsifier which preserves only $O(n / \varepsilon^2)$ reweighted edges. However,…
In this paper we introduce a notion of spectral approximation for directed graphs. While there are many potential ways one might define approximation for directed graphs, most of them are too strong to allow sparse approximations in…
Whether or not the Sparsest Cut problem admits an efficient $O(1)$-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut,…
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…
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…