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Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling

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Abstract

In this paper, we propose to study a wide class of combinatorial optimization problems called combinatorial optimization problems with labelling. First, we give a combinatorial method to deal with the labelling version of some classical combinatorial optimization problems including minimum vertex cover, maximum independent set, minimum dominating set and minimum set cover, and convert the labelling problems into the original problems by polynomial-time reduction. We show that, although the labelling version of these problem seems more universal than their original counterparts, they are actually equivalent to the corresponding original problem from an algorithmic point of view. Moreover, we generalize the greedy approach for solving submodular cover problem to its labelling version, and as simple applications of our new method, we use it to solve the labelling versions of the minimum weighted spanning tree and connected vertex cover problem in a unified way.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 11971376. The authors are indebted to the anonymous reviewers for their careful reading of the manuscript of the paper and their valuable suggestions greatly improved the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China

    Zishen Yang, Wei Wang & Majun Shi

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  1. Zishen Yang
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  2. Wei Wang
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  3. Majun Shi
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Correspondence to Wei Wang.

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Communicated by Jörg Rambau.

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Yang, Z., Wang, W. & Shi, M. Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling. J Optim Theory Appl 188, 673–695 (2021). https://doi.org/10.1007/s10957-020-01802-x

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