46 research outputs found
On Truthful Constrained Heterogeneous Facility Location with Max-Variant Cost
We consider a problem where agents have private positions on a line, and
public approval preferences over two facilities, and their cost is the maximum
distance from their approved facilities. The goal is to decide the facility
locations to minimize the total and the max cost, while incentivizing the
agents to be truthful. We design a strategyproof mechanism that is
simultaneously - and -approximate for these two objective functions,
thus improving the previously best-known bounds of and
Heterogeneous Facility Location with Limited Resources
We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three different settings depending on the level of agent-related information that is public or private. For each setting, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results
Strategyproof Facility Location in Perturbation Stable Instances
We consider -Facility Location games, where strategic agents report
their locations on the real line, and a mechanism maps them to
facilities. Each agent seeks to minimize her distance to the nearest facility.
We are interested in (deterministic or randomized) strategyproof mechanisms
without payments that achieve a reasonable approximation ratio to the optimal
social cost of the agents. To circumvent the inapproximability of -Facility
Location by deterministic strategyproof mechanisms, we restrict our attention
to perturbation stable instances. An instance of -Facility Location on the
line is -perturbation stable (or simply, -stable), for some
, if the optimal agent clustering is not affected by moving any
subset of consecutive agent locations closer to each other by a factor at most
. We show that the optimal solution is strategyproof in
-stable instances whose optimal solution does not include any
singleton clusters, and that allocating the facility to the agent next to the
rightmost one in each optimal cluster (or to the unique agent, for singleton
clusters) is strategyproof and -approximate for -stable instances
(even if their optimal solution includes singleton clusters). On the negative
side, we show that for any and any , there is no
deterministic anonymous mechanism that achieves a bounded approximation ratio
and is strategyproof in -stable instances. We also prove
that allocating the facility to a random agent of each optimal cluster is
strategyproof and -approximate in -stable instances. To the best of our
knowledge, this is the first time that the existence of deterministic (resp.
randomized) strategyproof mechanisms with a bounded (resp. constant)
approximation ratio is shown for a large and natural class of -Facility
Location instances
Facility Location Games with Ordinal Preferences
We consider a new setting of facility location games with ordinal
preferences. In such a setting, we have a set of agents and a set of
facilities. Each agent is located on a line and has an ordinal preference over
the facilities. Our goal is to design strategyproof mechanisms that elicit
truthful information (preferences and/or locations) from the agents and locate
the facilities to minimize both maximum and total cost objectives as well as to
maximize both minimum and total utility objectives. For the four possible
objectives, we consider the 2-facility settings in which only preferences are
private, or locations are private. For each possible combination of the
objectives and settings, we provide lower and upper bounds on the approximation
ratios of strategyproof mechanisms, which are asymptotically tight up to a
constant. Finally, we discuss the generalization of our results beyond two
facilities and when the agents can misreport both locations and preferences
Heterogeneous Facility Location without Money
The study of the facility location problem in the presence of self-interested agents has recently emerged as the benchmark problem in the research on mechanism design without money. In the setting studied in the literature so far, agents are single-parameter in that their type is a single number encoding their position on a real line. We here initiate a more realistic model for several real-life scenarios. Specifically, we propose and analyze heterogeneous facility location without money, a novel model wherein: (i) we have multiple heterogeneous (i.e., serving different purposes) facilities, (ii) agents' locations are disclosed to the mechanism and (iii) agents bid for the set of facilities they are interested in (as opposed to bidding for their position on the network).
We study the heterogeneous facility location problem under two different objective functions, namely: social cost (i.e., sum of all agents' costs) and maximum cost. For either objective function, we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line. For the social cost objective function, we devise an (n-1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm. As regards the maximum cost objective function, we propose a 3-approximate deterministic strategyproof algorithm, and prove a 3/2 approximation lower bound for deterministic strategyproof mechanisms. Furthermore, we propose a 3/2-approximate randomized strategyproof algorithm and prove a 4/3 approximation lower bound for randomized strategyproof algorithms