Abstract
In this paper, we revisit the r-gathering problem. Given sets C and F of points on the plane and distance d(c, f) 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.
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First and second authors are partially supported through a grant from Pubali Bank Ltd.
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Sarker, A., Sung, Wk., Rahman, M.S. (2019). A Linear Time Algorithm for the r-Gathering Problem on the Line (Extended Abstract). In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_5
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DOI: https://doi.org/10.1007/978-3-030-10564-8_5
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