17 research outputs found
Approximately Stable Matchings with Budget Constraints
This paper considers two-sided matching with budget constraints where one
side (firm or hospital) can make monetary transfers (offer wages) to the other
(worker or doctor). In a standard model, while multiple doctors can be matched
to a single hospital, a hospital has a maximum quota: the number of doctors
assigned to a hospital cannot exceed a certain limit. In our model, a hospital
instead has a fixed budget: the total amount of wages allocated by each
hospital to doctors is constrained. With budget constraints, stable matchings
may fail to exist and checking for the existence is hard. To deal with the
nonexistence of stable matchings, we extend the "matching with contracts" model
of Hatfield and Milgrom, so that it handles approximately stable matchings
where each of the hospitals' utilities after deviation can increase by factor
up to a certain amount. We then propose two novel mechanisms that efficiently
return such a stable matching that exactly satisfies the budget constraints. In
particular, by sacrificing strategy-proofness, our first mechanism achieves the
best possible bound. Furthermore, we find a special case such that a simple
mechanism is strategy-proof for doctors, keeping the best possible bound of the
general case.Comment: Accepted for the 32nd AAAI Conference on Artificial Intelligence
(AAAI2018). arXiv admin note: text overlap with arXiv:1705.0764
Preference Elicitation in Matching Markets Via Interviews: A Study of Offline Benchmarks
The stable marriage problem and its extensions have been
extensively studied, with much of the work in the literature
assuming that agents fully know their own preferences over
alternatives. This assumption however is not always practical
(especially in large markets) and agents usually need
to go through some costly deliberation process in order to
learn their preferences. In this paper we assume that such
deliberations are carried out via interviews, where an interview
involves a man and a woman, each of whom learns
information about the other as a consequence. If everybody
interviews everyone else, then clearly agents can fully learn
their preferences. But interviews are costly, and we may
wish to minimize their use. It is often the case, especially
in practical settings, that due to correlation between agents’
preferences, it is unnecessary for all potential interviews to
be carried out in order to obtain a stable matching. Thus
the problem is to find a good strategy for interviews to be
carried out in order to minimize their use, whilst leading to a
stable matching. One way to evaluate the performance of an
interview strategy is to compare it against a na¨ıve algorithm
that conducts all interviews. We argue however that a more
meaningful comparison would be against an optimal offline
algorithm that has access to agents’ preference orderings under
complete information. We show that, unless P=NP, no
offline algorithm can compute the optimal interview strategy
in polynomial time. If we are additionally aiming for a
particular stable matching (perhaps one with certain desirable
properties), we provide restricted settings under which
efficient optimal offline algorithms exist
Learning Desirable Matchings From Partial Preferences
We study the classic problem of matching agents to objects, where the
agents have ranked preferences over the objects. We focus on two popular
desiderata from the matching literature: Pareto optimality and rank-maximality.
Instead of asking the agents to report their complete preferences, our goal is
to learn a desirable matching from partial preferences, specifically a matching
that is necessarily Pareto optimal (NPO) or necessarily rank-maximal (NRM)
under any completion of the partial preferences. We focus on the top- model
in which agents reveal a prefix of their preference rankings. We design
efficient algorithms to check if a given matching is NPO or NRM, and to check
whether such a matching exists given top- partial preferences. We also study
online algorithms to elicit partial preferences adaptively, and prove bounds on
their competitive ratio
Scheduling under Uncertainty: A Query-based Approach
International audienceWe consider a single machine, a set of unit-time jobs, and a set of unit-time errors. We assume that the time-slot at which each error will occur is not known in advance but, for every error, there exists an uncertainty area during which the error will take place. In order to find if the error occurs in a specific time-slot, it is necessary to issue a query to it. In this work, we study two problems: (i) the error-query scheduling problem, whose aim is to reveal enough error-free slots with the minimum number of queries, and (ii) the lexicographic error-query scheduling problem where we seek the earliest error-free slots with the minimum number of queries. We consider both the off-line and the on-line versions of the above problems. In the former, the whole instance and its characteristics are known in advance and we give a polynomial-time algorithm for the error-query scheduling problem. In the latter, the adversary has the power to decide, in an on-line way, the time-slot of appearance for each error. We propose then both lower bounds and algorithms whose competitive ratios asymptotically match these lower bounds