Related papers: Efficiently Approximating Vertex Cover on Scale-Fr…
The densest subgraph problem has received significant attention, both in theory and in practice, due to its applications in problems such as community detection, social network analysis, and spam detection. Due to the high cost of obtaining…
Consider a graph with n nodes and m edges, independent edge weights and lengths, and arbitrary distance demands for node pairs. The spanner problem asks for a minimum-weight subgraph that satisfies these demands via sufficiently short paths…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…
This paper proposes a novel branch-and-bound(BMWVC) algorithm to exactly solve the minimum weight vertex cover problem (MWVC) in large graphs. The original contribution is several new graph reduction rules, allowing to reduce a graph G and…
To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of…
We study the vertex-cover problem which is an NP-hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, e.g., Erdoes-Renyi (ER) random graphs. These phase transitions coincide with changes of the…
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…
For many popular graph metric sparsifiers, such as spanners, emulators, and preservers, simple and elegant greedy algorithms are known that achieve state-of-the-art or existentially optimal tradeoffs between size and quality. The goal of…
Most optimization problems are notoriously hard. Considerable efforts must be spent in obtaining an optimal solution to certain instances that we encounter in the real world scenarios. Often it turns out that input instances get modified…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We give the first fully dynamic algorithm which maintains a $(1-\epsilon)$-approximate densest subgraph in worst-case time $\text{poly}(\log n, \epsilon^{-1})$ per update. Dense subgraph discovery is an important primitive for many…
Given a set $P$ of $n$ points in the plane, {\sc Covering Points by Lines} is the problem of finding a minimum-cardinality set $\L$ of lines such that every point $p \in P$ is incident to some line $\ell \in \L$. As a geometric variant of…
The greedy algorithm adapted from Kruskal's algorithm is an efficient and folklore way to produce a $k$-spanner with girth at least $k+2$. The greedy algorithm has shown to be `existentially optimal', while it's not `universally optimal'…
In the vertex connectivity problem, given an undirected $n$-vertex $m$-edge graph $G$, we need to compute the minimum number of vertices that can disconnect $G$ after removing them. This problem is one of the most well-studied graph…
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…
We consider the problem of maintaining an (approximately) minimum vertex cover in an $n$-node graph $G = (V, E)$ that is getting updated dynamically via a sequence of edge insertions/deletions. We show how to maintain a…
We study the generalized min sum set cover (GMSSC) problem, wherein given a collection of hyperedges $E$ with arbitrary covering requirements $k_e$, the goal is to find an ordering of the vertices to minimize the total cover time of the…
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…
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…
The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…