Related papers: Improving the dilation of a metric graph by adding…
The Planar Graph Metric Compression Problem is to compactly encode the distances among $k$ nodes in a planar graph of size $n$. Two na\"ive solutions are to store the graph using $O(n)$ bits, or to explicitly store the distance matrix with…
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…
Given a graph $G$ and a set of terminals $T$, a \emph{distance emulator} of $G$ is another graph $H$ (not necessarily a subgraph of $G$) containing $T$, such that all the pairwise distances in $G$ between vertices of $T$ are preserved in…
In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…
We present a simple greedy procedure to compute an $(\alpha,\beta)$-spanner for a graph $G$. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is…
We study the problem of estimating the edit distance between two $n$-character strings. While exact computation in the worst case is believed to require near-quadratic time, previous work showed that in certain regimes it is possible to…
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge…
Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…
Many real-world networks, such as transportation or trade networks, are dynamic in the sense that the edge set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has…
Seminal works on light spanners over the years provide spanners with optimal lightness in various graph classes, such as in general graphs, Euclidean spanners, and minor-free graphs. Three shortcomings of previous works on light spanners…
We give an algorithm for augmenting the edge connectivity of an undirected graph by using the isolating cuts framework (Li and Panigrahi, FOCS '20). Our algorithm uses poly-logarithmic calls to any max-flow algorithm, which yields a running…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
We consider the problem of constructing a graph of minimum degree $k\ge 1$ in the following controlled random graph process, introduced recently by Frieze, Krivelevich and Michaeli. Suppose the edges of the complete graph on $n$ vertices…
We design two incremental algorithms for computing an inclusion-minimal completion of an arbitrary graph into a cograph. The first one is able to do so while providing an additional property which is crucial in practice to obtain…
We give an embedding of the Poincar\'e halfspace $H^D$ into a discrete metric space based on a binary tiling of $H^D$, with additive distortion $O(\log D)$. It yields the following results. We show that any subset $P$ of $n$ points in $H^D$…
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 provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on $n$ vertices and a positive integer parameter $k$, find if there exist $k$ edges (arcs)…
Recent work has established that, for every positive integer $k$, every $n$-node graph has a $(2k-1)$-spanner on $O(f^{1-1/k} n^{1+1/k})$ edges that is resilient to $f$ edge or vertex faults. For vertex faults, this bound is tight. However,…