{"type":"ScholarlyArticle","title":"Reallocating Multiple Facilities on the Line","authors":[{"name":"Dimitris Fotakis","slug":"dimitris-fotakis","given":"Dimitris","family":"Fotakis","affiliation":"National Technical University of Athens"},{"name":"Loukas Kavouras","slug":"loukas-kavouras","given":"Loukas","family":"Kavouras","affiliation":"National Technical University of Athens"},{"name":"Panagiotis Kostopanagiotis","slug":"panagiotis-kostopanagiotis","given":"Panagiotis","family":"Kostopanagiotis","affiliation":"National Technical University of Athens"},{"name":"Philip Lazos","slug":"philip-lazos","given":"Philip","family":"Lazos","affiliation":"Sapienza University of Rome"},{"name":"Stratis Skoulakis","slug":"stratis-skoulakis","given":"Stratis","family":"Skoulakis","affiliation":"National Technical University of Athens"},{"name":"Nikos Zarifis","slug":"nikos-zarifis","given":"Nikos","family":"Zarifis","affiliation":"National Technical University of Athens"}],"abstract":"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.","doi":"10.24963/ijcai.2019/39","url":"https://ijcai.org/proceedings/2019/39","pdf":"https://ijcai.org/proceedings/2019/0039.pdf","markdown":"https://ijcai.org/proceedings/2019/39.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/39","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":39,"pages":{"first":273,"last":279},"keywords":["Machine Learning: Clustering","Agent-based and Multi-agent Systems: Agent Theories and Models","Agent-based and Multi-agent Systems: Resource Allocation"],"videos":[],"references":[{"position":1,"raw":"[An et al., 2017] Hyung-Chan An, Ashkan Norouzi-Fard, and Ola Svensson. 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