Facility Reallocation on the Line
Bart de Keijzer, Dominik Wojtczak

TL;DR
This paper studies multi-stage facility reallocation on a line, deriving optimal algorithms for offline and online cases, and proposing strategy-proof mechanisms with competitive ratios, including extensions to multiple facilities and weighted agents.
Contribution
It introduces optimal algorithms for both offline and online facility reallocation problems, and proposes strategy-proof mechanisms with competitive ratios, extending to multiple facilities and weighted agents.
Findings
Optimal offline and online algorithms derived.
Online algorithm has competitive ratio of (n+2)/(n+1).
Strategy-proof mechanism with competitive ratios of (n+3)/(n+1) and (n+4)/n.
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 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 . As neither of these algorithms turns out to yield a strategy-proof mechanism,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAuction Theory and Applications · Optimization and Search Problems · Transportation and Mobility Innovations
