Abstract
We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer \(c_i\) to facility \(f_j\) before the next customer \(c_{i+1}\) arrives. The cost of this assignment is the distance between \(c_i\) and \(f_j\). The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.
Work on this project was funded in part by NSF grant CCF-AF 1712119.
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Ahmed, A.R., Rahman, M.S., Kobourov, S. (2018). Online Facility Assignment. In: Rahman, M., Sung, WK., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2018. Lecture Notes in Computer Science(), vol 10755. Springer, Cham. https://doi.org/10.1007/978-3-319-75172-6_14
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DOI: https://doi.org/10.1007/978-3-319-75172-6_14
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