We study the multistage K-facility reallocation problem on the real line, where we maintain K facility locations over T stages, based on the stage-dependent locations of n agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. K-facility reallocation problem was introduced by (B.D. Kaijzer and D. Wojtczak, IJCAI 2018), where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online K-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by stage fashion. By exploiting an interesting connection to the classical K-server problem, we present a constant-competitive algorithm for K = 2 facilities.

## Dettaglio pubblicazione

2019, IJCAI, Pages 273-279 (volume: 2019)

### Reallocating Multiple Facilities on the Line (*04c Atto di convegno in rivista*)

#### Fotakis Dimitris, Kavouras Loukas, Panagiotis Kostopanagiotis, LAZOS FILIPPOS, Skoulakis Stratis, Zarifis Nikolas

**ISBN:**978-0-9992411-4-1

**Gruppo di ricerca:**Algorithms and Data Science

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