Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm

The minimum dominating set (MDS) is the problem of finding the minimum number of nodes that have connections to all other nodes in a given graph. This problem belongs to the NP-complete complexity class that cannot be solved exactly in a polynomial time. Hence, we deployed a stochastic method to est...

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Main Authors: Abed, S.A., Rais, H.M.
Format: Article
Published: Springer 2020
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85077767130&doi=10.1007%2f978-3-030-33582-3_37&partnerID=40&md5=8fba0ba61fd9ae440848dd2b8598441c
http://eprints.utp.edu.my/24751/
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spelling my.utp.eprints.247512021-08-27T05:51:41Z Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm Abed, S.A. Rais, H.M. The minimum dominating set (MDS) is the problem of finding the minimum number of nodes that have connections to all other nodes in a given graph. This problem belongs to the NP-complete complexity class that cannot be solved exactly in a polynomial time. Hence, we deployed a stochastic method to estimate good solutions for the MDS in a reasonable time. However, the problem space of the MDS problem grows exponentially with respect to the graph size. Therefore, our proposed method partitions the given graph to sub-graphs that can be tackled independently, which reduces the computational time of finding the MDS solution. This paper investigates the swarm intelligence behaviour represented by a population-based approach called the bat algorithm (BA) to find the smallest set of nodes that dominate the graph. The BA explores a wide area of the search space; thus, it is capable of the diversification procedure. However, population-based algorithms are not good in exploiting the search space in comparison to single-solution based methods, therefore, we included the Simulated annealing (SA) algorithm to balance between exploitation and exploration in order to reach a best possible solution. To analyse the performance of the proposed partitioning scheme, we experimented with the hybrid algorithm on the graph, with and without partitioning. The gained results showed significant speed up when the partitioning scheme was applied. © Springer Nature Switzerland AG 2020. Springer 2020 Article NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85077767130&doi=10.1007%2f978-3-030-33582-3_37&partnerID=40&md5=8fba0ba61fd9ae440848dd2b8598441c Abed, S.A. and Rais, H.M. (2020) Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm. Advances in Intelligent Systems and Computing, 1073 . pp. 386-395. http://eprints.utp.edu.my/24751/
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description The minimum dominating set (MDS) is the problem of finding the minimum number of nodes that have connections to all other nodes in a given graph. This problem belongs to the NP-complete complexity class that cannot be solved exactly in a polynomial time. Hence, we deployed a stochastic method to estimate good solutions for the MDS in a reasonable time. However, the problem space of the MDS problem grows exponentially with respect to the graph size. Therefore, our proposed method partitions the given graph to sub-graphs that can be tackled independently, which reduces the computational time of finding the MDS solution. This paper investigates the swarm intelligence behaviour represented by a population-based approach called the bat algorithm (BA) to find the smallest set of nodes that dominate the graph. The BA explores a wide area of the search space; thus, it is capable of the diversification procedure. However, population-based algorithms are not good in exploiting the search space in comparison to single-solution based methods, therefore, we included the Simulated annealing (SA) algorithm to balance between exploitation and exploration in order to reach a best possible solution. To analyse the performance of the proposed partitioning scheme, we experimented with the hybrid algorithm on the graph, with and without partitioning. The gained results showed significant speed up when the partitioning scheme was applied. © Springer Nature Switzerland AG 2020.
format Article
author Abed, S.A.
Rais, H.M.
spellingShingle Abed, S.A.
Rais, H.M.
Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
author_facet Abed, S.A.
Rais, H.M.
author_sort Abed, S.A.
title Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
title_short Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
title_full Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
title_fullStr Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
title_full_unstemmed Solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
title_sort solving the minimum dominating set problem of partitioned graphs using a hybrid bat algorithm
publisher Springer
publishDate 2020
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85077767130&doi=10.1007%2f978-3-030-33582-3_37&partnerID=40&md5=8fba0ba61fd9ae440848dd2b8598441c
http://eprints.utp.edu.my/24751/
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