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An optimal time algorithm for finding a maximum weight independent set in a tree

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Abstract

The maximum weight independent set problem for a general graph is NP-hard. But for some special classes of graphs, polynomial time algorithms do exist for solving it. Based on the divide-and-conquer strategy, Pawagi has presented anO(|V|log|V|) time algorithm for solving this problem on a tree. In this paper, we propose anO(|V|) time algorithm to improve Pawagi's result. The proposed algorithm is based on the dynamic programming strategy and is time optimal within a constant factor.

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References

  1. M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA., 1979.

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  2. A. Frank,Some polynomial algorithms for certain graphs and hyper-graphs, in Proc. of the fifth British Combin. Conference, 1975, 211–226.

  3. S. Pawagi,Maximum weight independent set in trees, BIT 27, 2(1987), 170–180.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan, Republic of China

    G. H. Chen & M. T. Kuo

  2. Department of Electrical Engineering, National Central University, Chung-Li, Taiwan Republic of China

    J. P. Sheu

Authors
  1. G. H. Chen
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  2. M. T. Kuo
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  3. J. P. Sheu
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Chen, G.H., Kuo, M.T. & Sheu, J.P. An optimal time algorithm for finding a maximum weight independent set in a tree. BIT 28, 353–356 (1988). https://doi.org/10.1007/BF01934098

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  • DOI: https://doi.org/10.1007/BF01934098

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