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Further Study on Reverse 1-Center Problem on Trees

Author

Listed:
  • Ali Reza Sepasian

    (Faculty of Basic Science, Department of Mathematics, Fasa University, Fasa, Iran)

  • Javad Tayyebi

    (Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran)

Abstract

This paper studies two types of reverse 1-center problems under uniform linear cost function where edge lengths are allowed to reduce. In the first type, the aim is that the objective value is bounded by a prescribed fixed value p at minimum cost. The aim of the other is to improve the objective value as much as possible within a given budget. An algorithm based on dynamic programming is proposed to solve the first problem in linear time. Then, this algorithm is applied as a subroutine to design an algorithm to solve the second type of the problem in O(nlog(nK)) time in which K is a fixed number dependent on the problem parameters. Under the similarity assumption, this algorithm has a better complexity than the Nguyen algorithm (2013) with quadratic-time complexity. Some numerical experiments are conducted to validate this fact in practice.

Suggested Citation

  • Ali Reza Sepasian & Javad Tayyebi, 2020. "Further Study on Reverse 1-Center Problem on Trees," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(06), pages 1-18, December.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:06:n:s0217595920500347
    DOI: 10.1142/S0217595920500347
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