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Strategyproof Approximation of the Minimax on Networks Michal Feldman

Summary: Strategyproof Approximation of the Minimax on Networks
Noga Alon
Michal Feldman
Ariel D. Procaccia
Moshe Tennenholtz
We consider the problem of locating a facility on a network, represented by a graph. A set of
strategic agents have different ideal locations for the facility; the cost of an agent is the distance
between its ideal location and the facility. A mechanism maps the locations reported by the
agents to the location of the facility. We wish to design mechanisms that are strategyproof, in
the sense that agents can never benefit by lying, and at the same time provide a small approxi-
mation ratio with respect to the minimax measure. We design a novel "hybrid" strategyproof
randomized mechanism that provides a tight approximation ratio of 3/2 when the network is
a circle (known as a ring in the case of computer networks). Furthermore, we show that no
randomized SP mechanism can provide an approximation ratio better than 2 - o(1) even when
the network is a tree, thereby matching a trivial upper bound of two.
1 Introduction
In facility location problems one must locate a facility so as to serve a set of agents. Each choice
of location for the facility has a cost (also known as effect) with respect to each agent. In this
context, a mechanism (or social choice function, or location rule) receives the locations of the


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics