Related papers: A Subpolynomial Approximation Algorithm for Graph …
In this paper, we introduce the following new concept in graph drawing. Our task is to find a small collection of drawings such that they all together satisfy some property that is useful for graph visualization. We propose investigating a…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P's vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation…
Bundling crossings is a strategy which can enhance the readability of drawings. In this paper we consider good drawings, i.e., we require that any two edges have at most one common point which can be a common vertex or a crossing. Our main…
The goal in the stochastic vertex cover problem is to obtain an approximately minimum vertex cover for a graph $G^\star$ that is realized by sampling each edge independently with some probability $p\in (0, 1]$ in a base graph $G = (V, E)$.…
The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon $P$, is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
We consider the Minimum Dominating Set (MDS) problem on the intersection graphs of geometric objects. Even for simple and widely-used geometric objects such as rectangles, no sub-logarithmic approximation is known for the problem and…
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a…
Given a graph $G$ of degree $k$ over $n$ vertices, we consider the problem of computing a near maximum cut or a near minimum bisection in polynomial time. For graphs of girth $2L$, we develop a local message passing algorithm whose…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of…
Visualizing a graph $G$ in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masa\v{r}\'ik and Hlin\v{e}n\'y [GD 2023] recently asked for each edge of $G$ to be drawn without…
Given a simple graph $G = (V, E)$ and a constant integer $k \ge 2$, the $k$-path vertex cover problem ({\sc P$k$VC}) asks for a minimum subset $F \subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…