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# A Novel Binary Firey Algorithm for the Minimum Labeling Spanning Tree Problem

Mugang Lin1,2,*, Fangju Liu3, Huihuang Zhao1,2, Jianzhen Chen1,2

1 College of Computer Science and Technology, Hengyang Normal University, Hengyang, 421002, China
2 Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, 421002, China
3 School of Computer Science, University of South China, Hengyang, 421001, China

* Corresponding Author: Mugang Lin. Email:

Computer Modeling in Engineering & Sciences 2020, 125(1), 197-214. https://doi.org/10.32604/cmes.2020.09502

## Abstract

Given a connected undirected graph G whose edges are labeled, the minimum labeling spanning tree (MLST) problem is to find a spanning tree of G with the smallest number of different labels. The MLST is an NP-hard combinatorial optimization problem, which is widely applied in communication networks, multimodal transportation networks, and data compression. Some approximation algorithms and heuristics algorithms have been proposed for the problem. Firey algorithm is a new meta-heuristic algorithm. Because of its simplicity and easy implementation, it has been successfully applied in various fields. However, the basic firefly algorithm for the MLST problem is proposed in this paper. A binary operation method to update firefly positions and a local feasible handling method are introduced, which correct unfeasible solutions, eliminate redundant labels, and make the algorithm more suitable for discrete problems. Computational results show that the algorithm has good performance. The algorithm can be extended to solve other discrete optimization problems.

## Keywords

APA Style
Lin, M., Liu, F., Zhao, H., Chen, J. (2020). A novel binary firey algorithm for the minimum labeling spanning tree problem. Computer Modeling in Engineering & Sciences, 125(1), 197-214. https://doi.org/10.32604/cmes.2020.09502
Vancouver Style
Lin M, Liu F, Zhao H, Chen J. A novel binary firey algorithm for the minimum labeling spanning tree problem. Comput Model Eng Sci. 2020;125(1):197-214 https://doi.org/10.32604/cmes.2020.09502
IEEE Style
M. Lin, F. Liu, H. Zhao, and J. Chen "A Novel Binary Firey Algorithm for the Minimum Labeling Spanning Tree Problem," Comput. Model. Eng. Sci., vol. 125, no. 1, pp. 197-214. 2020. https://doi.org/10.32604/cmes.2020.09502

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