Facility Reallocation on the Line

Keijzer, Bart de and Wojtczak, Dominik ORCID: 0000-0001-5560-0546 (2021) Facility Reallocation on the Line. In: Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}, 2018-7-13 - 2018-7-19.

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Abstract

We consider a multi-stage facility reallocation problems on the real line, where a facility is being moved between time stages based on the locations reported by $n$ agents. The aim of the reallocation algorithm is to minimise the social cost, i.e., the sum over the total distance between the facility and all agents at all stages, plus the cost incurred for moving the facility. We study this problem both in the offline setting and online setting. In the offline case the algorithm has full knowledge of the agent locations in all future stages, and in the online setting the algorithm does not know these future locations and must decide the location of the facility on a stage-per-stage basis. We derive the optimal algorithm in both cases. For the online setting we show that its competitive ratio is $(n+2)/(n+1)$. As neither of these algorithms turns out to yield a strategy-proof mechanism, we propose another strategy-proof mechanism which has a competitive ratio of $(n+3)/(n+1)$ for odd $n$ and $(n+4)/n$ for even $n$, which we conjecture to be the best possible. We also consider a generalisation with multiple facilities and weighted agents, for which we show that the optimum can be computed in polynomial time for a fixed number of facilities.

Item Type:	Conference or Workshop Item (Unspecified)
Additional Information:	28 Pages, 5 Figures. A prelimininary version of the paper, with most proofs omitted, has appeared at IJCAI 2018
Uncontrolled Keywords:	cs.GT, cs.GT, cs.AI, cs.DS
Depositing User:	Symplectic Admin
Date Deposited:	31 May 2018 07:43
Last Modified:	19 Jan 2023 06:33
DOI:	10.24963/ijcai.2018/26
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3021365