Related papers: Greedy maximal independent sets via local limits
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…
This paper considers the optimal multi-agent persistent monitoring problem defined for a team of agents on a set of nodes (targets) interconnected according to a fixed network topology. The aim is to control this team so as to minimize a…
The greedy algorithm for approximating dominating sets is a simple method that is known to compute an $(\ln n+1)$-approximation of a minimum dominating set on any graph with $n$ vertices. We show that a small modification of the greedy…
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…
We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…
Let $G(n,c/n)$ and $G_r(n)$ be an $n$-node sparse random graph and a sparse random $r$-regular graph, respectively, and let ${\cal I}(n,r)$ and ${\cal I}(n,c)$ be the sizes of the largest independent set in $G(n,c/n)$ and $G_r(n)$. The…
We consider the algorithmic problem of finding large \textit{balanced} independent sets in sparse random bipartite graphs, and more generally the problem of finding independent sets with specified proportions of vertices on each side of the…
Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…
For the Erd\H{o}s-R\'enyi random graph G(n,p), we give a precise asymptotic formula for the size of a largest vertex subset in G(n,p) that induces a subgraph with average degree at most t, provided that p = p(n) is not too small and t =…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on $n$ vertices with maximum degree $d$, showing that an independent set drawn uniformly at random from such a graph has expected…
A simple greedy algorithm to find a maximal independent set (MIS) in a graph starts with the empty set and visits every vertex, adding it to the set if and only if none of its neighbours are already in the set. In this paper, we consider…
We examine the Maximum Independent Set Problem in an undirected graph. The main result is that this problem can be considered as the solving the same problem in a subclass of the weighted normal twin-orthogonal graphs. The problem is…
An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated…
We derive the distribution of the maximum number of common neighbours of a pair of vertices in a dense random regular graph.The proof involves two important steps. One step is to establish the extremal independence property: the asymptotic…
We consider the problem of identifying a subset of nodes in a network that will enable the fastest spread of information in a decentralized environment.In a model of communication based on a random walk on an undirected graph, the optimal…
Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise,…
In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set of disjoint edges one edge at a time; then we analyze the…
In this paper we introduce several extremal sequences of points on locally compact metric spaces and study their asymptotic properties. These sequences are defined through a greedy algorithm by minimizing a certain energy functional whose…
We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a computationally efficient asymptotic formula approximating the number of graphs within…