5,288 research outputs found
Efficient algorithms for bipartite matching problems with preferences
Matching problems involve a set of participants, where each participant has a capacity and a subset of the participants rank a subset of the others in order of preference (strictly or with ties). Matching problems are motivated in practice by large-scale applications, such as automated matching schemes, which assign participants together based on their preferences over one another.
This thesis focuses on bipartite matching problems in which there are two disjoint sets of participants (such as medical students and hospitals). We present a range of efficient algorithms for finding various types of optimal matchings in the context of these problems. Our optimality criteria involve a diverse range of concepts that are alternatives to classical stability. Examples include so-called popular and Pareto optimal matchings, and also matchings that are optimal with respect to their profile (the number of participants obtaining their first choice, second choice and so on).
The first optimality criterion that we study is the notion of a Pareto optimal matching, a criterion that economists regard as a fundamental property to be satisfied by an optimal matching. We present the first algorithmic results on Pareto optimality for the Capacitated House Allocation problem (CHA), which is a many-to-one variant of the classical House Allocation problem, as well as for the Hospitals-Residents problem (HR), a generalisation of the classical Stable Marriage problem.
For each of these problems, we obtain a characterisation of Pareto optimal matchings, and then use this to obtain a polynomial-time algorithm for finding a maximum Pareto optimal matching.
The next optimality criterion that we study is the notion of a popular matching. We study popular matchings in CHA and present a polynomial-time algorithm for finding a maximum popular matching or reporting that none exists, given any instance of CHA. We extend our findings to the case in CHA where preferences may contain ties (CHAT) by proving the extension of a well-known result in matching theory to the capacitated bipartite graph case, and using this to obtain a polynomial-time algorithm for finding a maximum popular matching, or reporting that none exists.
We next study popular matchings in the Weighted Capacitated House Allocation problem (WCHA), which is a variant of CHA where the agents have weights assigned to them. We identify a structure in the underlying graph of the problem that singles out those edges that cannot belong to a popular matching. We then use this to construct a polynomial-time algorithm for finding a maximum popular matching or reporting that none exists, for the case where preferences are strict.
We then study popular matchings in a variant of the classical Stable Marriage problem with Ties and Incomplete preference lists (SMTI), where preference lists are symmetric. Here, we provide the first characterisation results on popular matchings in the bipartite setting where preferences are two-sided, which can either lead to a polynomial-time algorithm for solving the problem or help establish that it is NP-complete. We also provide the first algorithm for testing if a matching is popular in such a setting.
The remaining optimality criteria that we study involve profile-based optimal matchings. We define three versions of what it means for a matching to be optimal based on its profile, namely so-called greedy maximum, rank-maximal and generous maximum matchings. We study each of these in the context of CHAT and the Hospitals-Residents problem with Ties (HRT).
For each problem model, we give polynomial-time algorithms for finding a greedy maximum, a rank-maximal and a generous maximum matching
Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games
Additively separable hedonic games and fractional hedonic games have received
considerable attention. They are coalition forming games of selfish agents
based on their mutual preferences. Most of the work in the literature
characterizes the existence and structure of stable outcomes (i.e., partitions
in coalitions), assuming that preferences are given. However, there is little
discussion on this assumption. In fact, agents receive different utilities if
they belong to different partitions, and thus it is natural for them to declare
their preferences strategically in order to maximize their benefit. In this
paper we consider strategyproof mechanisms for additively separable hedonic
games and fractional hedonic games, that is, partitioning methods without
payments such that utility maximizing agents have no incentive to lie about
their true preferences. We focus on social welfare maximization and provide
several lower and upper bounds on the performance achievable by strategyproof
mechanisms for general and specific additive functions. In most of the cases we
provide tight or asymptotically tight results. All our mechanisms are simple
and can be computed in polynomial time. Moreover, all the lower bounds are
unconditional, that is, they do not rely on any computational or complexity
assumptions
Editorial: special issue on matching under preferences
This special issue of Algorithms is devoted to the study of matching problems
involving ordinal preferences from the standpoint of algorithms and complexit
Pareto Optimal Allocation under Uncertain Preferences
The assignment problem is one of the most well-studied settings in social
choice, matching, and discrete allocation. We consider the problem with the
additional feature that agents' preferences involve uncertainty. The setting
with uncertainty leads to a number of interesting questions including the
following ones. How to compute an assignment with the highest probability of
being Pareto optimal? What is the complexity of computing the probability that
a given assignment is Pareto optimal? Does there exist an assignment that is
Pareto optimal with probability one? We consider these problems under two
natural uncertainty models: (1) the lottery model in which each agent has an
independent probability distribution over linear orders and (2) the joint
probability model that involves a joint probability distribution over
preference profiles. For both of the models, we present a number of algorithmic
and complexity results.Comment: Preliminary Draft; new results & new author
Efficient algorithms for bipartite matching problems with preferences
Matching problems involve a set of participants, where each participant has a capacity and a subset of the participants rank a subset of the others in order of preference (strictly or with ties). Matching problems are motivated in practice by large-scale applications, such as automated matching schemes, which assign participants together based on their preferences over one another. This thesis focuses on bipartite matching problems in which there are two disjoint sets of participants (such as medical students and hospitals). We present a range of efficient algorithms for finding various types of optimal matchings in the context of these problems. Our optimality criteria involve a diverse range of concepts that are alternatives to classical stability. Examples include so-called popular and Pareto optimal matchings, and also matchings that are optimal with respect to their profile (the number of participants obtaining their first choice, second choice and so on). The first optimality criterion that we study is the notion of a Pareto optimal matching, a criterion that economists regard as a fundamental property to be satisfied by an optimal matching. We present the first algorithmic results on Pareto optimality for the Capacitated House Allocation problem (CHA), which is a many-to-one variant of the classical House Allocation problem, as well as for the Hospitals-Residents problem (HR), a generalisation of the classical Stable Marriage problem. For each of these problems, we obtain a characterisation of Pareto optimal matchings, and then use this to obtain a polynomial-time algorithm for finding a maximum Pareto optimal matching. The next optimality criterion that we study is the notion of a popular matching. We study popular matchings in CHA and present a polynomial-time algorithm for finding a maximum popular matching or reporting that none exists, given any instance of CHA. We extend our findings to the case in CHA where preferences may contain ties (CHAT) by proving the extension of a well-known result in matching theory to the capacitated bipartite graph case, and using this to obtain a polynomial-time algorithm for finding a maximum popular matching, or reporting that none exists. We next study popular matchings in the Weighted Capacitated House Allocation problem (WCHA), which is a variant of CHA where the agents have weights assigned to them. We identify a structure in the underlying graph of the problem that singles out those edges that cannot belong to a popular matching. We then use this to construct a polynomial-time algorithm for finding a maximum popular matching or reporting that none exists, for the case where preferences are strict. We then study popular matchings in a variant of the classical Stable Marriage problem with Ties and Incomplete preference lists (SMTI), where preference lists are symmetric. Here, we provide the first characterisation results on popular matchings in the bipartite setting where preferences are two-sided, which can either lead to a polynomial-time algorithm for solving the problem or help establish that it is NP-complete. We also provide the first algorithm for testing if a matching is popular in such a setting. The remaining optimality criteria that we study involve profile-based optimal matchings. We define three versions of what it means for a matching to be optimal based on its profile, namely so-called greedy maximum, rank-maximal and generous maximum matchings. We study each of these in the context of CHAT and the Hospitals-Residents problem with Ties (HRT). For each problem model, we give polynomial-time algorithms for finding a greedy maximum, a rank-maximal and a generous maximum matching.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Sub-channel Assignment, Power Allocation and User Scheduling for Non-Orthogonal Multiple Access Networks
In this paper, we study the resource allocation and user scheduling problem
for a downlink nonorthogonal multiple access network where the base station
allocates spectrum and power resources to a set of users. We aim to jointly
optimize the sub-channel assignment and power allocation to maximize the
weighted total sum-rate while taking into account user fairness. We formulate
the sub-channel allocation problem as equivalent to a many-to-many two-sided
user-subchannel matching game in which the set of users and sub-channels are
considered as two sets of players pursuing their own interests. We then propose
a matching algorithm which converges to a two-side exchange stable matching
after a limited number of iterations. A joint solution is thus provided to
solve the sub-channel assignment and power allocation problems iteratively.
Simulation results show that the proposed algorithm greatly outperforms the
orthogonal multiple access scheme and a previous non-orthogonal multiple access
scheme.Comment: Accepted as a regular paper by IEEE Transactions on Wireless
Communication
Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game
We study the variant of the stable marriage problem in which the preferences
of the agents are allowed to include indifferences. We present a mechanism for
producing Pareto-stable matchings in stable marriage markets with indifferences
that is group strategyproof for one side of the market. Our key technique
involves modeling the stable marriage market as a generalized assignment game.
We also show that our mechanism can be implemented efficiently. These results
can be extended to the college admissions problem with indifferences
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