Related papers: Constant Query Time $(1 + \epsilon)$-Approximate D…
We study sublinear time algorithms for estimating the size of maximum matching. After a long line of research, the problem was finally settled by Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation factor of $2$.…
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…
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $poly(\log{\log{n}})$ rounds in the near-linear memory MPC model. Our results are for…
The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph $G$, we examine the problem of assigning directions to each edge of $G$…
We consider the following graph reconstruction problem: given an unweighted connected graph $G = (V,E)$ with visible vertex set $V$ and an oracle which takes two vertices $u,v \in V$ and returns the shortest path distance between $u$ and…
Consider a set $P$ of $n$ points in $\mathbb{R}^d$. In the discrete median line segment problem, the objective is to find a line segment bounded by a pair of points in $P$ such that the sum of the Euclidean distances from $P$ to the line…
In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the…
Let $P \subset \mathbb{R}^d$ be a set of $n$ points in $d$ dimensions such that each point $p \in P$ has an associated radius $r_p > 0$. The transmission graph $G$ for $P$ is the directed graph with vertex set $P$ such that there is an edge…
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph $G$ such that we may support insertions and deletions of edges in $G$ as well as distance queries between any two nodes $u,v$ subject to the constraint…
We maintain a $(1+\varepsilon)$-spanner over the disk intersection graph of a dynamic set of disks. We restrict all disks to have their diameter in $[4,\Psi]$ for some fixed and known $\Psi$. The resulting $(1+\varepsilon)$-spanner has size…
Nguyen and Onak constructed the first constant-time algorithm for the approximation of the size of the maximum matching in bounded degree graphs. The Borel oracle machinery is a tool that can be used to convert some statements in Borel…
The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…
We present a simple and faster algorithm for computing fair cuts on undirected graphs, a concept introduced in recent work of Li et al. (SODA 2023). Informally, for any parameter $\epsilon>0$, a $(1+\epsilon)$-fair $(s,t)$-cut is an…
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…
Given a set of n disjoint balls b1, . . ., bn in IRd, we provide a data structure, of near linear size, that can answer (1 \pm \epsilon)-approximate kth-nearest neighbor queries in O(log n + 1/\epsilon^d) time, where k and \epsilon are…
We present an $(1+\varepsilon)$-approximation algorithm with quasi-polynomial running time for computing the maximum weight independent set of polygons out of a given set of polygons in the plane (specifically, the running time is $n^{O(…
Let $G=(V,E)$ be an unweighted undirected graph with $n$ vertices and $m$ edges. Let $g$ be the girth of $G$, that is, the length of a shortest cycle in $G$. We present a randomized algorithm with a running time of $\tilde{O}\big(\ell \cdot…
Let $G$ be an $n$-node and $m$-edge positively real-weighted undirected graph. For any given integer $f \ge 1$, we study the problem of designing a sparse \emph{f-edge-fault-tolerant} ($f$-EFT) $\sigma${\em -approximate single-source…
The distance sensitivity oracle (DSO) problem asks us to preprocess a given graph $G=(V,E)$ in order to answer queries of the form $d(x,y,e)$, which denotes the shortest path distance in $G$ from vertex $x$ to vertex $y$ when edge $e$ is…
An orientable sequence of order $n$ is a cyclic binary sequence such that each length-$n$ substring appears at most once \emph{in either direction}. Maximal length orientable sequences are known only for $n\leq 7$, and a trivial upper bound…