Experimental Comparison of Five Approximation Algorithms for Minimum Vertex Cover

Khan, Imran; Khan, Sangeen

doi:10.14257/ijunesst.2014.7.6.07

Cited by 5 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There exist other vertex cover algorithms, such as nearly optimal vertex cover NOVAC-1 [33], advanced vertex support algorithm AVSA [34] and modified vertex support algorithm MVSA [35], and heuristic algorithms ListLeft and ListRight [36]. Some studies performed comparisons [37] of existing minimum vertex cover algorithms. Pseudo code for minimum vertex cover algorithms can be found in the article [38].…”

Section: Prior and Related Workmentioning

confidence: 99%

Defining the Minimum Security Baseline in a Multiple Security Standards Environment by Graph Theory Techniques

et al. 2019

View full text Add to dashboard Cite

One of the best ways to protect an organization’s assets is to implement security requirements defined by different standards or best practices. However, such an approach is complicated and requires specific skills and knowledge. In case an organization applies multiple security standards, several problems can arise related to overlapping or conflicting security requirements, increased expenses on security requirement implementation, and convenience of security requirement monitoring. To solve these issues, we propose using graph theory techniques. Graphs allow the presentation of security requirements of a standard as graph vertexes and edges between vertexes, and would show the relations between different requirements. A vertex cover algorithm is proposed for minimum security requirement identification, while graph isomorphism is proposed for comparing existing organization controls against a set of minimum requirements identified in the previous step.

show abstract

Section: Prior and Related Workmentioning

confidence: 99%

Defining the Minimum Security Baseline in a Multiple Security Standards Environment by Graph Theory Techniques

et al. 2019

View full text Add to dashboard Cite

show abstract

“…They proposed algorithm called vertex support algorithm (VSA). [6,13] A modification of the VAS is called MVAS where the selection of the vertex does not depend only on the vertex that have the maximum the support value but it finds all the vertices with minimum support value and then it selects the vertex with minimum support from the list of all neighbors of the selected vertices. MVAS shows better results in some benchmarks comparing to original VAS.…”

Section: Related Workmentioning

confidence: 99%

“…MVAS shows better results in some benchmarks comparing to original VAS. [6,13] Some other solutions depend on genetic algorithms such as (HVX). Xu and Ma presented solution that uses annealing algorithms to find the minimum vertex cover.…”

Section: Related Workmentioning

confidence: 99%

NMVSA Greedy Solution for Vertex Cover Problem

Eshtay¹,

Sleit²,

Sharieh³

2016

ijacsa

View full text Add to dashboard Cite

Abstract-Minimum vertex cover (MVC) is a well-known NPComplete optimization problem. The importance of MVC in theory and practical comes from the wide range of its applications. This paper describes a polynomial time greedy algorithm to find near optimal solutions for MVC. The new algorithm NMVAS is a modification of already existed algorithm called MVAS which uses the same principle of selecting candidate from the neighborhood of the vertex with a modification in the selection procedure. A comparative study is conducted between the NMVAS and MVAS which shows that the proposed algorithm NMVSA provides better or equal results in the most cases of the underlying data sets which leads to a better average approximation ratio of NMVAS. NMVAS inherits the simplicity of the original algorithm.

show abstract

“…To solve the MVCP, distinct kinds of algorithms were developed to introduce worthy solutions. Several exact [19,20], heuristic [21][22][23], and metaheuristic [10][11][12][13][14]24] algorithms were presented to achieve the purpose of solving the MVCP. The exact algorithms always find the optimal solution to the optimization problems if the problem size is comparatively small.…”

mentioning

confidence: 99%

“…Both of these types of algorithms can find a solution as close as possible to the optimal solution. Maximum Degree Greedy (MDG), Vertex Support Algorithm (VSA), and New Modified Vertex Support Algorithm (NMVSA) [21,22] are some of the heuristic algorithms that were introduced specifically for the MVCP.…”

mentioning

confidence: 99%

Most Valuable Player Algorithm for Solving Minimum Vertex Cover Problem

Khattab¹,

Sharieh²,

Mahafzah³

2019

IJACSA

View full text Add to dashboard Cite

Minimum Vertex Cover Problem (MVCP) is a combinatorial optimization problem that is utilized to formulate multiple real-life applications. Owing to this fact, abundant research has been undertaken to discover valuable MVCP solutions. Most Valuable Player Algorithm (MVPA) is a recently developed metaheuristic algorithm that inspires its idea from team-based sports. In this paper, the MVPA_MVCP algorithm is introduced as an adaptation of the MVPA for the MVCP. The MVPA_MVCP algorithm is implemented using Java programming language and tested on a Microsoft Azure virtual machine. The performance of the MVPA_MVCP algorithm is evaluated analytically in terms of run time complexity. Its average-case run time complexity is ceased to , where I is the size of the initial population, |V| is the number of vertices and |E| is the number of edges of the tested graph. The MVPA_MVCP algorithm is evaluated experimentally in terms of the quality of gained solutions and the run time. The experimental results over 15 instances of DIMACS benchmark revealed that the MVPA_MVCP algorithm could, in the best case, get the best known optimal solution for seven data instances. Also, the experimental findings exposed that there is a direct relation between the number of edges of the graph under test and the run time.

show abstract

Experimental Comparison of Five Approximation Algorithms for Minimum Vertex Cover

Abstract: Abstract

Cited by 5 publications

References 16 publications

Defining the Minimum Security Baseline in a Multiple Security Standards Environment by Graph Theory Techniques

Defining the Minimum Security Baseline in a Multiple Security Standards Environment by Graph Theory Techniques

NMVSA Greedy Solution for Vertex Cover Problem

Most Valuable Player Algorithm for Solving Minimum Vertex Cover Problem

Contact Info

Product

Resources

About