相关论文: Randomization yields simple O(n log star n) algori…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
An $s$-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses $O(s)$ additional words of space. We present a randomized $s$-workspace algorithm for…
A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
The dilation of a Euclidean graph is defined as the ratio of distance in the graph divided by distance in R^d. In this paper we consider the problem of positioning the root of a star such that the dilation of the resulting star is minimal.…
We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input…
We study smoothed analysis of distributed graph algorithms, focusing on the fundamental minimum spanning tree (MST) problem. With the goal of studying the time complexity of distributed MST as a function of the "perturbation" of the input…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We provide an algorithm that, given an $n$-vertex $m$-edge Eulerian graph with polynomially bounded weights, computes an $\breve{O}(n\log^{2} n \cdot \varepsilon^{-2})$-edge $\varepsilon$-approximate Eulerian sparsifier with high…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
Given an undirected edge-weighted graph $G=(V,E)$ with $m$ edges and $n$ vertices, the minimum cut problem asks to find a subset of vertices $S$ such that the total weight of all edges between $S$ and $V \setminus S$ is minimized. Karger's…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…
With the recent popularity of graphical clustering methods, there has been an increased focus on the information between samples. We show how learning cluster structure using edge features naturally and simultaneously determines the most…
Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding {\em rectangular layouts} is a key problem. We…
We provide a simple new randomized contraction approach to the global minimum cut problem for simple undirected graphs. The contractions exploit 2-out edge sampling from each vertex rather than the standard uniform edge sampling. We…