Related papers: Local Routing in a Tree Metric 1-Spanner
Routing tables in ad hoc and wireless routing protocols can be represented using rooted trees. The constant need for communication and storage of these trees in routing protocols demands an efficient rooted tree coding algorithm. This…
Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO) for Euclidean space. A $(\tau,\rho)$-LSO is a collection $\Sigma$ of orderings such that for every $x,y\in\mathbb{R}^d$ there is an ordering…
Given an edge-weighted graph $G$ and $\epsilon>0$, a $(1+\epsilon)$-spanner is a spanning subgraph $G'$ whose shortest path distances approximate those of $G$ within a $(1+\epsilon)$ factor. If $G$ is from certain minor-closed graph…
We present a framework that unifies directed buy-at-bulk network design and directed spanner problems, namely, buy-at-bulk spanners. The goal is to find a minimum-cost routing solution for network design problems that capture economies at…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay…
An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…
This paper presents a distributed approach that scales up to segment tree crowns within a LiDAR point cloud representing an arbitrarily large forested area. The approach uses a single-processor tree segmentation algorithm as a building…
We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number $k$ of nodes are required to be connected in the solution. A prototypical example is…
In this article, we study the Euclidean minimum spanning tree problem in an imprecise setup. The problem is known as the \emph{Minimum Spanning Tree Problem with Neighborhoods} in the literature. We study the problem where the neighborhoods…
We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…
Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path…
We present an algorithm which computes a planar 2-spanner from an Unit Disk Graph when the node density is sufficient. The communication complexity in terms of number of node's identifier sent by the algorithm is $6n$, while the…
We give approximation schemes for Subset TSP and Steiner Tree on unit disk graphs, and more generally, on intersection graphs of similarly sized connected fat (not necessarily convex) polygons in the plane. As a first step towards this…
We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…
Efficient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is obtained using efficient partitioning of the space into hypercubes and solving…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has…
We study the local evolution of Prim's algorithm on large finite weighted graphs. When performed for $n$ steps, where $n$ is the size of the graph, Prim's algorithm will construct the minimal spanning tree (MST). We assume that our graphs…
While research on the geometry of planar graphs has been active in the past decades, many properties of planar metrics remain mysterious. This paper studies a fundamental aspect of the planar graph geometry: covering planar metrics by a…