Approximation algorithms for minimum weight connected 3-path vertex cover

2019 ◽  
Vol 347 ◽  
pp. 723-733 ◽  
Author(s):  
Yingli Ran ◽  
Zhao Zhang ◽  
Xiaohui Huang ◽  
Xiaosong Li ◽  
Ding-Zhu Du
Keyword(s):  
Approximation Algorithms ◽  
Minimum Weight ◽  
Vertex Cover

scholarly journals Approximation algorithms for minimum (weight) connected k-path vertex cover

2016 ◽  
Vol 205 ◽  
pp. 101-108 ◽  
Author(s):  
Xiaosong Li ◽  
Zhao Zhang ◽  
Xiaohui Huang
Keyword(s):  
Approximation Algorithms ◽  
Minimum Weight ◽  
Vertex Cover

Improved Approximation Algorithms for Minimum Weight Vertex Separators

2008 ◽  
Vol 38 (2) ◽  
pp. 629-657 ◽  
Author(s):  
Uriel Feige ◽  
MohammadTaghi Hajiaghayi ◽  
James R. Lee
Keyword(s):  
Approximation Algorithms ◽  
Minimum Weight ◽  
Vertex Separators

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].

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