相关论文: A Simple Yao-Yao-Based Spanner of Bounded Degree

A sparse graph that preserves an approximation of the shortest paths between all pairs of points in a plane is called a geometric spanner. Using range trees of sublinear size, we design an algorithm in massively parallel computation (MPC)…

Yao graphs are geometric spanners that connect each point of a given point set to its nearest neighbor in each of $k$ cones drawn around it. Yao graphs were introduced to construct minimum spanning trees in $d$ dimensional spaces. Moreover,…

We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G=(V,E) and any e > 0, a (1+e)-spanner for G of maximum degree O(1) and total weight O(w(MST)), where w(MST) denotes the weight of a minimum…

The unit disk graph (UDG) is a widely employed model for the study of wireless networks. In this model, wireless nodes are represented by points in the plane and there is an edge between two points if and only if their Euclidean distance is…

We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor $C_{del\approx 2.42$; however,…

It is an open problem whether Yao-Yao graphs $\mathsf{YY}_k$ (also known as sparse-Yao graphs) are all spanners when the integer parameter $k$ is large enough. In this paper we show that, for any integer $k\geq 42$, the Yao-Yao graph…

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs $(p,r)$ where $p$ is a point in the plane and $r$ is a real number. The distance between two points…

It is a long standing open problem whether Yao-Yao graphs $\mathsf{YY}_{k}$ are all spanners [li2002sparse]. Bauer and Damian [bauer2013infinite] showed that all $\mathsf{YY}_{6k}$ for $k \geq 6$ are spanners. Li and Zhan [li2016almost]…

In this paper, we introduce a variation of the well-studied Yao graphs. Given a set of points $S\subset \mathbb{R}^2$ and an angle $0 < \theta \leq 2\pi$, we define the continuous Yao graph $cY(\theta)$ with vertex set $S$ and angle…

We show that, for any integer k > 5, the Sparse-Yao graph YY_{6k} (also known as Yao-Yao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k > 7.

We prove that Y_6 is a spanner. Y_6 is the Yao graph on a set of planar points, which has an edge from each point x to a closest point y within each of the six angular cones of 60 deg surrounding x.

This paper presents a distributed algorithm on wireless ad-hoc networks that runs in polylogarithmic number of rounds in the size of the network and constructs a linear size, lightweight, (1+\epsilon)-spanner for any given \epsilon > 0. A…

Given a point set $P$ in the Euclidean space, a geometric $t$-spanner $G$ is a graph on $P$ such that for every pair of points, the shortest path in $G$ between those points is at most a factor $t$ longer than the Euclidean distance between…

This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in…

We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…

A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all…

The Yao graph for k=4, Y4, is naturally partitioned into four subgraphs, one per quadrant. We show that the subgraphs for one quadrant differ from the subgraphs for two adjacent quadrants in three properties: planarity, connectedness, and…

We present improved upper bounds on the spanning ratio of constrained $\theta$-graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points in the plane, a Yao-graph partitions the plane around…

Given a metric space $\mathcal{M}=(X,\delta)$, a weighted graph $G$ over $X$ is a metric $t$-spanner of $\mathcal{M}$ if for every $u,v \in X$, $\delta(u,v)\le d_G(u,v)\le t\cdot \delta(u,v)$, where $d_G$ is the shortest path metric in $G$.…

We show that the Yao graph Y4 in the L2 metric is a spanner with stretch factor 8(29+23sqrt(2)). Enroute to this, we also show that the Yao graph Y4 in the Linf metric is a planar spanner with stretch factor 8.