Facility Reallocation on the Line

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