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A combinatorial algorithm for the ordered 1-median problem on cactus graphs

  • Van Huy Pham
  • Nguyen Chi TamEmail author
Theoretical Article
  • 5 Downloads

Abstract

Cactus graph is a graph in which any two simple cycles has at most one vertex in common. In this paper we address the ordered 1-median location problem on cactus graphs, a generalization of some popular location models such as 1-median, 1-center, and 1-centdian problems. For the case with non-decreasing multipliers, we show that there exists a cycle or an edge that contains an ordered 1-median. Based on this property, we develop a combinatorial algorithm that finds an ordered 1-median on a cactus in \(O(n^2\log n)\) time, where n is the number of vertices in the underlying cactus.

Keywords

Location problem Ordered 1-median Cactus Convex 

Notes

Acknowledgements

The authors would like to acknowledge the anonymous referees for valuable comments which helped to improve the paper significantly.

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Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.AI Lab, Faculty of Information TechnologyTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Department of Mathematics, Teacher CollegeCan Tho UniversityCan ThoVietnam

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