Evolutionary algorithms and the Vertex Cover problem

Oliveto, Pietro S.; He, Jifeng; Yao, Xin

doi:10.1109/cec.2007.4424701

Cited by 29 publications

(23 citation statements)

References 15 publications

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“…The first runtime results concerning EAs for vertex cover, which have recently appeared, are those of Friedrich et al [27] and Oliveto et al [1]. The latter work is presented and extended in this paper.…”

Section: B Related Workmentioning

confidence: 66%

Analysis of the $(1+1)$-EA for Finding Approximate Solutions to Vertex Cover Problems

Oliveto¹,

He²,

Yao³

2009

IEEE Trans. Evol. Computat.

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Abstract-Vertex cover is one of the best known NP-Hard combinatorial optimization problems. Experimental work has claimed that evolutionary algorithms (EAs) perform fairly well for the problem and can compete with problem-specific ones. A theoretical analysis that explains these empirical results is presented concerning the random local search algorithm and the (1 + 1)-EA. Since it is not expected that an algorithm can solve the vertex cover problem in polynomial time, a worst case approximation analysis is carried out for the two considered algorithms and comparisons with the best known problemspecific ones are presented. By studying instance classes of the problem, general results are derived. Although arbitrarily bad approximation ratios of the (1 + 1)-EA can be proved for a bipartite instance class, the same algorithm can quickly find the minimum cover of the graph when a restart strategy is used. Instance classes where multiple runs cannot considerably improve the performance of the (1 + 1)-EA are considered and the characteristics of the graphs that make the optimization task hard for the algorithm are investigated and highlighted. An instance class is designed to prove that the (1 + 1)-EA cannot guarantee better solutions than the state-of-the-art algorithm for vertex cover if worst cases are considered. In particular, a lower bound for the worst case approximation ratio, slightly less than two, is proved. Nevertheless, there are subclasses of the vertex cover problem for which the (1 + 1)-EA is efficient. It is proved that if the vertex degree is at most two, then the algorithm can solve the problem in polynomial time.Index Terms-Combinatorial optimization, computational complexity, evolutionary algorithms, vertex cover, worst-case approximation.

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Section: B Related Workmentioning

confidence: 66%

Analysis of the $(1+1)$-EA for Finding Approximate Solutions to Vertex Cover Problems

Oliveto¹,

He²,

Yao³

2009

IEEE Trans. Evol. Computat.

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“…Moreover, current pre-deployment AAP solutions are adhoc, inadequate and inefficient. Furthermore, because AAP has close resemblance with the vertex cover problem [2], we suspect that AAP belongs to the class of NP problems. Therefore, to analyze the AAP is timely, and we must design efficient and effective heuristics that can identify good quality solutions.…”

Section: Motivationmentioning

confidence: 99%

Antenna Arrangements in a Telecommunication Network

Karami

Khan

2012

2012 10th International Conference on Frontiers of Information Technology

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Abstract-In this paper, we discuss the approach to efficiently place antennas to cover users within a telecommunication network. The main goal is to lower the power and utilities cost while covering all of the users within the telecommunication network. Four heuristics are proposed and compared. I. MOTIVATIONThe main objective for telecommunication networks are to provide end-to-end quality of service (QoS) and coverage to every client in the system. Antenna Arrangement Problem (AAP) is often considered an optimization problem in the predeployment stage of a telecommunication network. Such an assumption may be valid when we consider a static population density. However, increasing population, telecommunication advancement, and construction constraints, makes the mentioned assumption infeasible [1]. Therefore, we must approach the AAP as an evolving after deployment optimization problem. Moreover, current pre-deployment AAP solutions are adhoc, inadequate and inefficient. Furthermore, because AAP has close resemblance with the vertex cover problem [2], we suspect that AAP belongs to the class of NP problems. Therefore, to analyze the AAP is timely, and we must design efficient and effective heuristics that can identify good quality solutions. II. RELATED WORKThe antenna arrangements in a telecommunication network has been studied extensively in the literature. Ref.[3] has utilized a model called Master-Slave model with Local Cultivation model (MSLC) to solve an antenna arrangement problem of mobile telecommunication. A new intruder detection method using Multiple Input Multiple Output (MIMO) channel is discussed in [4]. Authors have utilized the time correlation function for channel matrix of MIMO channel as the cost function, and have clarified which antenna arrangement is suitable for MIMO sensor by using the measured propagation channels in an indoor environment. Ref. [5] have proposed a method to estimate the number of partial discharge sources in multipath environment using the multichannel blind deconvolution method called the super-exponential deflation method. Authors have also presented a performance comparison of antenna arrangements for estimating the number of partial discharge sources. In [6] authors have focused on the errors originated from the theoretical basis of the Standard Antenna Method. They have presented a fundamental formula for the calibration method with intensive discussion on the associated errors. They have also shown that the most important error sources are the non-uniformity of the field in which an antenna under calibration is immersed, and that the serious errors are caused by the close coupling between a transmit antenna and a standard tuned dipole antenna. The fundamental monopole antenna array arrangement for actual mobile terminals that satisfies the requirements for beam-steering, diversity and MIMO transmission is discussed in [7]. In [8] two branch vertical space diversity (V-SD) and horizontal space diversity (H-SD) antenna arrangements mounted on a metal pole to illumin...

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“…Al. compared evolutionary algorithms to approximation algorithms [5]. In the work the theoretical proofs of time complexity and the Vertex Cover size have been explored and enhanced.…”

Section: Literature Reviewmentioning

confidence: 99%

The Applicability of Genetic algorithm to Vertex Cover

Bhasin¹,

Amini²

2015

IJCA

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The Vertex Cover Problem calls for the selection of a set of vertices(V) in a way that all the edges of the graph, connected to those vertices constitute the set E of the given graph G= (V, E). The problem finds applications in various fields and is therefore, one of the most widely researched topics in NP Complete Problems. The problem is an NP Complete problem this work proposes a Genetic Algorithm based solution to handle the problem. The proposed algorithm has been implemented and tested for various graphs. These instances vary in the number of vertices and connectivity. The results are encouraging. This paper also explores the available techniques in order to put the things in the perspective. The future scope of this work intends to apply Diploid Genetic Algorithms to the problem to incorporate robustness into the proposed algorithm.

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Evolutionary algorithms and the Vertex Cover problem

Cited by 29 publications

References 15 publications

Analysis of the $(1+1)$-EA for Finding Approximate Solutions to Vertex Cover Problems

Analysis of the $(1+1)$-EA for Finding Approximate Solutions to Vertex Cover Problems

Antenna Arrangements in a Telecommunication Network

The Applicability of Genetic algorithm to Vertex Cover

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