Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatoria...Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-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.Firefly 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 is not suitable for discrete problems.To this end,a novel discrete 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.展开更多
This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree. The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually. Although there e...This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree. The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually. Although there exist linear time algorithms for Prufer-like codes [1,2,3], the algorithms utilize the integer sorting algorithms. The special range of the integers to be sorted is utilized to obtain a linear time integer sorting algorithm. The Prufer code problem is reduced to integer sorting. In this paper we consider the Prufer code problem in a different angle and a more direct manner. We start from a naïve algorithm, then improved it gradually and finally we obtain a very practical linear time algorithm. The techniques we used in this paper are of interest in their own right.展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant 61772179the Hunan Provincial Natural Science Foundation of China under Grant 2019JJ40005+3 种基金the Science and Technology Plan Project of Hunan Province under Grant 2016TP1020the Double First-Class University Project of Hunan Province under Grant Xiangjiaotong[2018]469the Open Fund Project of Hunan Provincial Key Laboratory of Intelligent Information Processing and Application for Hengyang Normal University under Grant IIPA19K02the Science Foundation of Hengyang Normal University under Grant 19QD13.
文摘Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-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.Firefly 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 is not suitable for discrete problems.To this end,a novel discrete 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.
文摘This paper studies the algorithms for coding and decoding Prufer codes of a labeled tree. The algorithms for coding and decoding Prufer codes of a labeled tree in the literatures require time usually. Although there exist linear time algorithms for Prufer-like codes [1,2,3], the algorithms utilize the integer sorting algorithms. The special range of the integers to be sorted is utilized to obtain a linear time integer sorting algorithm. The Prufer code problem is reduced to integer sorting. In this paper we consider the Prufer code problem in a different angle and a more direct manner. We start from a naïve algorithm, then improved it gradually and finally we obtain a very practical linear time algorithm. The techniques we used in this paper are of interest in their own right.
