Related papers: Simpler, faster and shorter labels for distances i…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
Time-series generated by end-users, edge devices, and different wearables are mostly unlabelled. We propose a method to auto-generate labels of un-labelled time-series, exploiting very few representative labelled time-series. Our method is…
We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous…
Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…
We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of $\log n + O(\log \log)$ labeling schemes supporting each of these functions…
We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs $\cF$ labels…
Answering the shortest-path distance between two arbitrary locations is a fundamental problem in road networks. Labelling-based solutions are the current state-of-the-arts to render fast response time, which can generally be categorised…
An {\em ancestry labeling scheme} labels the nodes of any tree in such a way that ancestry queries between any two nodes in a tree can be answered just by looking at their corresponding labels. The common measure to evaluate the quality of…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
We study the fully dynamic All-Pairs Shortest Paths (APSP) problem in undirected edge-weighted graphs. Given an $n$-vertex graph $G$ with non-negative edge lengths, that undergoes an online sequence of edge insertions and deletions, the…
We present succinct labeling schemes for answering connectivity queries in graphs subject to a specified number of vertex failures. An $f$-vertex/edge fault tolerant ($f$-V/EFT) connectivity labeling is a scheme that produces succinct…
We consider the problem of computing compact routing tables for a (weighted) planar graph $G:= (V, E,w)$ in the PRAM, CONGEST, and the novel HYBRID communication model. We present algorithms with polylogarithmic work and communication that…
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…
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…
In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of…
In a series of papers, Avraham, Filtser, Kaplan, Katz, and Sharir (SoCG'14), Kaplan, Katz, Saban, and Sharir (ESA'23), and Katz, Saban, and Sharir (ESA'24) studied a class of geometric optimization problems -- including reverse shortest…
There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…
(Directed) graphs with node attributes are a common type of data in various applications and there is a vast literature on developing metrics and efficient algorithms for comparing them. Recently, in the graph learning and optimization…
A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such a labeling, the vertices are labeled with unique values…
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…