Algorithm Research & Explore
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3307-3311

Backtracking algorithm with reduction for node-weighted Steiner tree problem

Hu Qin
Ning Aibing
Gou Haiwen
Zhang Huizhen
Business School, University of Shanghai for Science & Technology, Shanghai 200093, China

Abstract

The node-weighted Steiner tree problem is a classic NP-hard problem in the combinatorial optimization. The existing algorithms for studying the problem have the disadvantages of high time complexity and unavailability of the optimal solution. In view of the shortcomings of existing algorithms, this paper presented a backtracking algorithm based on reduced-order technique. Firstly, this paper studied the mathematical properties of the node-weighted Steiner tree problem and utilized its mathematical properties to reduce the scale of the problem. Then, it designed an upper bound sub-algorithm and a lower bound sub-algorithm and utilized such sub-algorithms to prune the solution space tree of the problem and improved the search efficiency. Finally, it designed a backtracking algorithm to solve the above-mentioned problem by utilizing the upper and lower bound sub-algorithms and mathematical properties. Example analysis and experimental results demonstrate that the algorithm is not only with lower time complexity, but also can obtain the optimal solution of the problem.

Foundation Support

国家自然科学基金资助项目(71401106)
上海市一流学科建设项目(S1201YLXK)

Publish Information

DOI: 10.19734/j.issn.1001-3695.2019.07.0262
Publish at: Application Research of Computers Printed Article, Vol. 37, 2020 No. 11
Section: Algorithm Research & Explore
Pages: 3307-3311
Serial Number: 1001-3695(2020)11-021-3307-05

Publish History

[2020-11-05] Printed Article

Cite This Article

胡沁, 宁爱兵, 苟海雯, 等. 节点加权的Steiner树问题的降阶回溯算法 [J]. 计算机应用研究, 2020, 37 (11): 3307-3311. (Hu Qin, Ning Aibing, Gou Haiwen, et al. Backtracking algorithm with reduction for node-weighted Steiner tree problem [J]. Application Research of Computers, 2020, 37 (11): 3307-3311. )

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Application Research of Computers, founded in 1984, is an academic journal of computing technology sponsored by Sichuan Institute of Computer Sciences under the Science and Technology Department of Sichuan Province.

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