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A Linear Time Algorithm for the r-Gathering Problem on the Line (Extended Abstract)

  • Anik SarkerEmail author
  • Wing-kin SungEmail author
  • M. Sohel RahmanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)

Abstract

In this paper, we revisit the r-gathering problem. Given sets C and F of points on the plane and distance d(cf) for each \(c \in C\) and \(f\in F\), an r-gathering of C to F is an assignment A of C to open facilities \(F' \subseteq F\) such that r or more members of C are assigned to each open facility. The cost of an r-gathering is \(\max _{c \in C}{d(c, A(c))}\). The r-gathering problem computes the r-gathering minimizing the cost. In this paper we study the r-gathering problem when C and F are on a line and present a \(O(|C| + |F|)\)-time algorithm to solve the problem. Our solution is optimal since any algorithm needs to read C and F at least once.

Notes

Acknowledgement

First and second authors are partially supported through a grant from Pubali Bank Ltd.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of CSEBUETDhakaBangladesh
  2. 2.School of ComputingNational University of SingaporeSingaporeSingapore
  3. 3.Genome Institute of SingaporeSingaporeSingapore

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