Approximating Spanning Trees with Few Branches

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• 作者：Markus Chimani (1)
  Joachim Spoerhase (2)
  
  1. Institute of Computer Science ; Friedrich-Schiller-University ; Jena ; Germany
  2. Institute of Computer Science ; University of W眉rzburg ; W眉rzburg ; Germany
  
• 关键词：Theory of computation ; Design and analysis of algorithms ; Approximation algorithms analysis ; Routing and network design problems
• 刊名：Theory of Computing Systems
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：56
• 期：1
• 页码：181-196
• 全文大小：522 KB
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  5. F眉rer, M., Raghavachari, B.: Approximating the minimum degree spanning tree to within one from the optimal degree. In: Proceedings of the Third Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms (SODA鈥?2), pp. 317鈥?24 (1992)
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  11. Knauer, M., Spoerhase, J.: Better approximation algorithms for the maximum internal spanning tree problem. In: Proceedings of the 11th Algorithms and Data Structures Symposium (WADS鈥?9), Lecture Notes in Computer Science, vol. 5664, pp. 459鈥?70 (2009)
  12. Lu, H.I., Ravi, R.: The power of local optimization: approximation algorithms for maximum-leaf spanning tree. In: Proceedings of the Thirtieth Annual Allerton Conference on Communication, Control and computing, pp. 533鈥?42 (1992)
  13. Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Math. Oper. Res. 18 (1), 1鈥?1 (1993) CrossRef
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• 刊物类别：Computer Science
• 刊物主题：Theory of Computation
  Computational Mathematics and Numerical Analysis
  
• 出版者：Springer New York
• ISSN：1433-0490

文摘

Given an undirected, connected graph, the aim of the minimum branch-node spanning tree problem is to find a spanning tree with the minimum number of nodes of degree larger than 2. The problem is motivated by network design problems where junctions are significantly more expensive than simple end- or through-nodes, and are thus to be avoided. Unfortunately, it is NP-hard to recognize instances that admit an objective value of zero, rendering the search for guaranteed approximation ratios futile. We suggest to investigate a complementary formulation, called maximum path-node spanning tree, where the goal is to find a spanning tree that maximizes the number of nodes with degree at most two. While the optimal solutions (and the practical applications) of both formulations coincide, our formulation proves more suitable for approximation. In fact, it admits a trivial 1/2-approximation algorithm. Our main contribution is a local search algorithm that guarantees a ratio of 6/11, as well as showing that the problem is APX-hard, i.e., it does not allow a PTAS.