On Efficient Fixed Parameter Algorithms for Weighted Vertex Cover

2000 ◽  
pp. 180-191 ◽  
Author(s):  
Rolf Niedermeier ◽  
Peter Rossmanith
Keyword(s):  
Vertex Cover ◽  
Fixed Parameter ◽  
Weighted Vertex

On efficient fixed-parameter algorithms for weighted vertex cover

2003 ◽  
Vol 47 (2) ◽  
pp. 63-77 ◽  
Author(s):  
Rolf Niedermeier ◽  
Peter Rossmanith
Keyword(s):  
Vertex Cover ◽  
Fixed Parameter ◽  
Weighted Vertex

Distributed Optimization for Weighted Vertex Cover via Heuristic Game Theoretic Learning

2020 ◽  
Author(s):  
Changhao Sun ◽  
Xiaochu Wang ◽  
Huaxin Qiu ◽  
Qian Chen ◽  
Qingrui Zhou
Keyword(s):  
Distributed Optimization ◽  
Vertex Cover ◽  
Weighted Vertex ◽  
Game Theoretic

Approximating Dynamic Weighted Vertex Cover with Soft Capacities

Algorithmica ◽  
2021 ◽  
Author(s):  
Hao-Ting Wei ◽  
Wing-Kai Hon ◽  
Paul Horn ◽  
Chung-Shou Liao ◽  
Kunihiko Sadakane
Keyword(s):  
Vertex Cover ◽  
Weighted Vertex

scholarly journals Parameterized Analysis of Multiobjective Evolutionary Algorithms and the Weighted Vertex Cover Problem

2019 ◽  
Vol 27 (4) ◽  
pp. 559-575
Author(s):  
Mojgan Pourhassan ◽  
Feng Shi ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithm ◽  
Complexity Analysis ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Optimal Solution ◽  
Population Based ◽  
Mutation Operator ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann ( 2013 ) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann ( 2013 ), we provide a fixed parameter evolutionary algorithm with respect to [Formula: see text], the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a [Formula: see text]-approximation in expected time [Formula: see text].

scholarly journals Generalized network dismantling

2019 ◽  
Vol 116 (14) ◽  
pp. 6554-6559 ◽  
Author(s):  
Xiao-Long Ren ◽  
Niels Gleinig ◽  
Dirk Helbing ◽  
Nino Antulov-Fantulin
Keyword(s):  
Large Scale ◽  
Vertex Cover ◽  
Criminal Organization ◽  
Fine Tuning ◽  
Laplacian Operator ◽  
Optimal Subset ◽  
Current State ◽  
Weighted Laplacian ◽  
Weighted Vertex ◽  
Large Scale Networks

Finding an optimal subset of nodes in a network that is able to efficiently disrupt the functioning of a corrupt or criminal organization or contain an epidemic or the spread of misinformation is a highly relevant problem of network science. In this paper, we address the generalized network-dismantling problem, which aims at finding a set of nodes whose removal from the network results in the fragmentation of the network into subcritical network components at minimal overall cost. Compared with previous formulations, we allow the costs of node removals to take arbitrary nonnegative real values, which may depend on topological properties such as node centrality or on nontopological features such as the price or protection level of a node. Interestingly, we show that nonunit costs imply a significantly different dismantling strategy. To solve this optimization problem, we propose a method which is based on the spectral properties of a node-weighted Laplacian operator and combine it with a fine-tuning mechanism related to the weighted vertex cover problem. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens more directions for understanding the vulnerability and robustness of complex systems.

scholarly journals Fixed-parameter algorithms for vertex cover P3

2016 ◽  
Vol 19 ◽  
pp. 12-22 ◽  
Author(s):  
Maw-Shang Chang ◽  
Li-Hsuan Chen ◽  
Ling-Ju Hung ◽  
Peter Rossmanith ◽  
Ping-Chen Su
Keyword(s):  
Vertex Cover ◽  
Fixed Parameter

scholarly journals Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem

Algorithmica ◽  
2012 ◽  
Vol 65 (4) ◽  
pp. 754-771 ◽  
Author(s):  
Stefan Kratsch ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithms ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Fixed Parameter ◽  
Cover Problem
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