Pareto optimality in house allocation problems

We study Pareto optimal matchings in the context of house allocation problems. We present an O(\sqrt{n}m) algorithm, based on Gales Top Trading Cycles Method, for finding a maximum cardinality Pareto optimal matching, where n is the number of agents and m is the total length of the preference lists. By contrast, we show that the problem of finding a minimum cardinality Pareto optimal matching is NP-hard, though approximable within a factor of 2. We then show that there exist Pareto optimal matchings of all sizes between a minimum and maximum cardinality Pareto optimal matching. Finally, we introduce the concept of a signature, which allows us to give a characterization, checkable in linear time, of instances that admit a unique Pareto optimal matching

Pareto optimality in many-to-many matching problems

Consider a many-to-many matching market that involves two finite disjoint sets, a set A of applicants and a set C of courses. Each applicant has preferences on the different sets of courses she can attend, while each course has a quota of applicants that it can admit. In this paper, we examine Pareto optimal matchings (briefly POM) in the context of such markets, that can also incorporate additional constraints, e.g., each course bearing some cost and each applicant having a limited budget available. We provide necessary and sufficient conditions for a many-to-many matching to be Pareto optimal and show that checking whether a given matching is Pareto optimal can be accomplished in 0(1 A 12 I C 12) time. Moreover, we provide a generalized version of serial dictatorship, which can be used to obtain any many-to-many POM. We also study some structural questions related to POM. We show that, unlike in the one-to-one case, finding a maximum cardinality POM is NP-hard for many-to-many markets. (C) 2014 Elsevier B.V. All rights reserved

Revealed preference tests of collectively rational consumption behavior: formulations and algorithms

This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are {\sc np}-complete. This makes the application of these tests problematic for (increasingly available) large(r) scale data sets. We then present two approaches to overcome this negative result. First, we introduce exact algorithms based on mixed-integer programming ({\sc mip}) formulations of the collective rationality tests, which can be usefully applied to medium sized data sets. Next, we propose simulated annealing heuristics, which allow for efficient testing of the collective model in the case of large data sets. We illustrate our methods by a number of computational experiments based on Dutch labor supply data.PAI COME

Kreativitat und Kommunikation bei Menschen mit Demenz

This book is a translation of Creativity and Communication in Persons with Dementia