87 research outputs found
Strategyproof Mechanisms For Group-Fair Facility Location Problems
We study the facility location problems where agents are located on a real
line and divided into groups based on criteria such as ethnicity or age. Our
aim is to design mechanisms to locate a facility to approximately minimize the
costs of groups of agents to the facility fairly while eliciting the agents'
locations truthfully. We first explore various well-motivated group fairness
cost objectives for the problems and show that many natural objectives have an
unbounded approximation ratio. We then consider minimizing the maximum total
group cost and minimizing the average group cost objectives. For these
objectives, we show that existing classical mechanisms (e.g., median) and new
group-based mechanisms provide bounded approximation ratios, where the
group-based mechanisms can achieve better ratios. We also provide lower bounds
for both objectives. To measure fairness between groups and within each group,
we study a new notion of intergroup and intragroup fairness (IIF) . We consider
two IIF objectives and provide mechanisms with tight approximation ratios
Intra-facility equity in discrete and continuous p-facility location problems
We consider facility location problems with a new form of equity criterion. Demand points have preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the envy felt by the demand points with respect to the rest of the demand points allocated to the same plant. After defining this new envy criterion and the general framework based on it, we provide formulations that model this approach in both the discrete and the continuous framework. The problems are illustrated with examples and the computational tests reported show the potential and limits of each formulation on several types of instances. Although this article is mainly focused on the introduction, modeling and formulation of this new concept of envy, some improvements for all the formulations presented are developed, obtaining in some cases better solution times.Project TED2021-130875B-I00, supported by MCIN/AEI/ 10.13039/
501100011033 and the European Union ‘‘NextGenerationEU/PRTR’’Research project PID2022-
137818OB-I00 (Ministerio de Ciencia e Innovación, Spain)Agencia
Estatal de Investigación (AEI), Spain: PID2020-114594GB-C2; Regional
Government of Andalusia, Spain P18-FR-1422 and B-FQM-322-UGR20
(ERDFIMAG-Maria
de Maeztu, Spain grant CEX2020-001105-M/AEI/10.13039/
501100011033Funding for open access charge: Universidad de
Granada / CBU
Making Decisions with Incomplete and Inaccurate Information
From assigning students to public schools to arriving at divorce settlements, there are many settings where preferences expressed by a set of stakeholders are used to make decisions that affect them. Due to its numerous applications, and thanks to the range of questions involved, such settings have received considerable attention in fields ranging from philosophy to political science, and particularly from economics and, more recently, computer science.
Although there exists a significant body of literature studying such settings, much of the work in this space make the assumption that stakeholders provide complete and accurate preference information to such decision-making procedures. However, due to, say, the high cognitive burden involved or privacy concerns, this may not always be feasible. The goal of this thesis is to explicitly address these limitations. We do so by building on previous work that looks at working with incomplete information, and by introducing solution concepts and notions that support the design of algorithms and mechanisms that can handle incomplete and inaccurate information in different settings.
We present our results in two parts. In Part I we look at decision-making in the presence of incomplete information. We focus on two broad themes, both from the perspective of an algorithm or mechanism designer. Informally, the first one studies the following question: Given incomplete preferences, how does one design algorithms that are `robust', i.e., ones that produce solutions that are ``good'' with respect to the underlying complete preferences? We look at this question in context of two well-studied problems, namely, i) (a version of) the two-sided matching problem and ii) (a version of) the facility location problem, and show how one can design approximately-robust algorithms in such settings. Following this, we look at the second theme, which considers the following question: Given incomplete preferences, how can one ask the agents for some more information in order to aid in the design of `robust' algorithms? We study this question in the context of the one-sided matching problem and show how even a very small amount of extra information can be used to get much better outcomes overall.
In Part II we turn our attention to decision-making in the presence of inaccurate information and look at the following question: How can one design `stable' algorithms, i.e., ones that do not produce vastly different outcomes as long as there are only small inaccuracies in a stakeholder's report of their preferences? We study this in the context of fair allocation of indivisible goods among two agents and show how, in contrast to popular fair allocation algorithms, there are alternative algorithms that are fair and approximately-stable
Fairness in maximal covering location problems
Acknowledgments
The authors thank the anonymous reviewers and the guest editors
of this issue for their detailed comments on this paper, which provided
significant insights for improving the previous versions of this
manuscript.
This research has been partially supported by Spanish Ministerio
de Ciencia e Innovación, AEI/FEDER grant number PID2020-114594GB
C21, AEI grant number RED2022-134149-T (Thematic Network: Location
Science and Related Problems), Junta de AndalucÃa projects P18-
FR-1422/2369 and projects FEDERUS-1256951, B-FQM-322-UGR20,
CEI-3-FQM331 and NetmeetData (Fundación BBVA 2019). The first
author was also partially supported by the IMAG-Maria de Maeztu
grant CEX2020-001105-M /AEI /10.13039/501100011033 and UENextGenerationEU
(ayudas de movilidad para la recualificación del
profesorado universitario. The second author was also partially supported
by the Research Program for Young Talented Researchers of the
University of Málaga under Project B1-2022_37, Spanish Ministry of
Education and Science grant number PEJ2018-002962-A, and the PhD
Program in Mathematics at the Universidad de Granada.This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) -fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.Spanish Ministerio
de Ciencia e InnovaciónAEI/FEDER grant number PID2020-114594GB
C21AEI grant number RED2022-134149-T (Thematic Network: Location
Science and Related Problems)Junta de AndalucÃa projects P18-
FR-1422/2369FEDERUS-1256951B-FQM-322-UGR20CEI-3-FQM331NetmeetData (Fundación BBVA 2019)IMAG-Maria de Maeztu
grant CEX2020-001105-M /AEI /10.13039/501100011033UE NextGenerationEUResearch Program for Young Talented Researchers of the
University of Málaga under Project B1-2022_37Spanish Ministry of
Education and Science grant number PEJ2018-002962-
Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation
We consider the following problem: There is a set of items (e.g., movies) and
a group of agents (e.g., passengers on a plane); each agent has some intrinsic
utility for each of the items. Our goal is to pick a set of items that
maximize the total derived utility of all the agents (i.e., in our example we
are to pick movies that we put on the plane's entertainment system).
However, the actual utility that an agent derives from a given item is only a
fraction of its intrinsic one, and this fraction depends on how the agent ranks
the item among the chosen, available, ones. We provide a formal specification
of the model and provide concrete examples and settings where it is applicable.
We show that the problem is hard in general, but we show a number of
tractability results for its natural special cases
A Semidefinite Programming approach for minimizing ordered weighted averages of rational functions
This paper considers the problem of minimizing the ordered weighted average
(or ordered median) function of finitely many rational functions over compact
semi-algebraic sets. Ordered weighted averages of rational functions are not,
in general, neither rational functions nor the supremum of rational functions
so that current results available for the minimization of rational functions
cannot be applied to handle these problems. We prove that the problem can be
transformed into a new problem embedded in a higher dimension space where it
admits a convenient representation. This reformulation admits a hierarchy of
SDP relaxations that approximates, up to any degree of accuracy, the optimal
value of those problems. We apply this general framework to a broad family of
continuous location problems showing that some difficult problems (convex and
non-convex) that up to date could only be solved on the plane and with
Euclidean distance, can be reasonably solved with different -norms and
in any finite dimension space. We illustrate this methodology with some
extensive computational results on location problems in the plane and the
3-dimension space.Comment: 27 pages, 1 figure, 7 table
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