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Approximation Algorithms for Matroid and Knapsack Means Problems

Author

Listed:
  • Ao Zhao

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

  • Qian Liu

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

  • Yang Zhou

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

  • Min Li

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. China)

Abstract

In this paper, we concentrate on studying the k-means problem with a matroid or a knapsack constraint. In the matroid means problem, given an observation set and a matroid, the goal is to find a center set from the independent sets to minimize the cost. By using the linear programming (LP)-rounding technology, we obtain a constant approximation guarantee. For the knapsack means problem, we adopt a similar strategy to that of matroid means problem, whereas the difference is that we add a knapsack covering inequality to the relaxed LP in order to decrease the unbounded integrality gap.

Suggested Citation

  • Ao Zhao & Qian Liu & Yang Zhou & Min Li, 2023. "Approximation Algorithms for Matroid and Knapsack Means Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(01), pages 1-16, February.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:01:n:s0217595922400073
    DOI: 10.1142/S0217595922400073
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