83,638 research outputs found
A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem
Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem. He proved that several other problems are complete for CC, including the stable marriage problem, and finding the lexicographical first maximal matching in a bipartite graph. We suggest alternative definitions of CC based on different reducibilities and introduce a two-sorted theory VCC* based on one of them. We sharpen and simplify Subramanian\u27s completeness proofs for the above two problems and formalize them in VCC*
Biomedical ontology alignment: An approach based on representation learning
While representation learning techniques have shown great promise in application to a number of different NLP tasks, they have had little impact on the problem of ontology matching. Unlike past work that has focused on feature engineering, we present a novel representation learning approach that is tailored to the ontology matching task. Our approach is based on embedding ontological terms in a high-dimensional Euclidean space. This embedding is derived on the basis of a novel phrase retrofitting strategy through which semantic similarity information becomes inscribed onto fields of pre-trained word vectors. The resulting framework also incorporates a novel outlier detection mechanism based on a denoising autoencoder that is shown to improve performance. An ontology matching system derived using the proposed framework achieved an F-score of 94% on an alignment scenario involving the Adult Mouse Anatomical Dictionary and the Foundational Model of Anatomy ontology (FMA) as targets. This compares favorably with the best performing systems on the Ontology Alignment Evaluation Initiative anatomy challenge. We performed additional experiments on aligning FMA to NCI Thesaurus and to SNOMED CT based on a reference alignment extracted from the UMLS Metathesaurus. Our system obtained overall F-scores of 93.2% and 89.2% for these experiments, thus achieving state-of-the-art results
Solving Hard Stable Matching Problems Involving Groups of Similar Agents
Many important stable matching problems are known to be NP-hard, even when
strong restrictions are placed on the input. In this paper we seek to identify
structural properties of instances of stable matching problems which will allow
us to design efficient algorithms using elementary techniques. We focus on the
setting in which all agents involved in some matching problem can be
partitioned into k different types, where the type of an agent determines his
or her preferences, and agents have preferences over types (which may be
refined by more detailed preferences within a single type). This situation
would arise in practice if agents form preferences solely based on some small
collection of agents' attributes. We also consider a generalisation in which
each agent may consider some small collection of other agents to be
exceptional, and rank these in a way that is not consistent with their types;
this could happen in practice if agents have prior contact with a small number
of candidates. We show that (for the case without exceptions), several
well-studied NP-hard stable matching problems including Max SMTI (that of
finding the maximum cardinality stable matching in an instance of stable
marriage with ties and incomplete lists) belong to the parameterised complexity
class FPT when parameterised by the number of different types of agents needed
to describe the instance. For Max SMTI this tractability result can be extended
to the setting in which each agent promotes at most one `exceptional' candidate
to the top of his/her list (when preferences within types are not refined), but
the problem remains NP-hard if preference lists can contain two or more
exceptions and the exceptional candidates can be placed anywhere in the
preference lists, even if the number of types is bounded by a constant.Comment: Results on SMTI appear in proceedings of WINE 2018; Section 6
contains work in progres
A Constraint Programming Approach to the Hospitals / Residents Problem
An instance I of the Hospitals / Residents problem (HR) involves a set of residents
(graduating medical students) and a set of hospitals, where each hospital has a given
capacity. The residents have preferences for the hospitals, as do hospitals for residents.
A solution of I is a stable matching, which is an assignment of residents to hospitals
that respects the capacity conditions and preference lists in a precise way. In this
paper we present constraint encodings for HR that give rise to important structural
properties. We also present a computational study using both randomly-generated
and real-world instances. Our study suggests that Constraint Programming is indeed
an applicable technology for solving this problem, in terms of both theory and practice
Demography in a new key
The widespread opinion that demography is lacking in theory is based in part on a particular view of the nature of scientific theory, generally known as logical empiricism [or positivism]. A newer school of philosophy of science, the model-based view, provides a different perspective on demography, one that enhances its status as a scientific discipline. From this perspective, much of formal demography can be seen as a collection of substantive models of population dynamics [how populations and cohorts behave], in short, theoretical knowledge. And many theories in behavioural demography - often discarded as too old or too simplistic - can be seen as perfectly good scientific theory, useful for many purposes, although often in need of more rigorous statement.demographic models, demographic theory, methodology, philosophy of science, population theory, the structure of demographic knowledge
The Complexity of Approximately Counting Stable Roommate Assignments
We investigate the complexity of approximately counting stable roommate
assignments in two models: (i) the -attribute model, in which the preference
lists are determined by dot products of "preference vectors" with "attribute
vectors" and (ii) the -Euclidean model, in which the preference lists are
determined by the closeness of the "positions" of the people to their
"preferred positions". Exactly counting the number of assignments is
#P-complete, since Irving and Leather demonstrated #P-completeness for the
special case of the stable marriage problem. We show that counting the number
of stable roommate assignments in the -attribute model () and the
3-Euclidean model() is interreducible, in an approximation-preserving
sense, with counting independent sets (of all sizes) (#IS) in a graph, or
counting the number of satisfying assignments of a Boolean formula (#SAT). This
means that there can be no FPRAS for any of these problems unless NP=RP. As a
consequence, we infer that there is no FPRAS for counting stable roommate
assignments (#SR) unless NP=RP. Utilizing previous results by the authors, we
give an approximation-preserving reduction from counting the number of
independent sets in a bipartite graph (#BIS) to counting the number of stable
roommate assignments both in the 3-attribute model and in the 2-Euclidean
model. #BIS is complete with respect to approximation-preserving reductions in
the logically-defined complexity class #RH\Pi_1. Hence, our result shows that
an FPRAS for counting stable roommate assignments in the 3-attribute model
would give an FPRAS for all of #RH\Pi_1. We also show that the 1-attribute
stable roommate problem always has either one or two stable roommate
assignments, so the number of assignments can be determined exactly in
polynomial time
Differences in mental health between adults in stepfamilies and 'first families'
This study used longitudinal data from the UK National Child Development Study (N = 5844) to examine whether mental health measured at age 42 was associated with living in a stepfamily. Accounting for the potential selection of those with mental health problems at the onset of family formation (at age 23) into, or out of, stepfamilies we show that stepparents, their partners and particularly those in dual stepparent families all had worse mental health than parents in âfirst familiesâ. It was also found that the mental health of men was worse if they were a stepparent than if they were the partner of a stepparent, while the reverse was the case for women
Solving stable matching problems using answer set programming
Since the introduction of the stable marriage problem (SMP) by Gale and
Shapley (1962), several variants and extensions have been investigated. While
this variety is useful to widen the application potential, each variant
requires a new algorithm for finding the stable matchings. To address this
issue, we propose an encoding of the SMP using answer set programming (ASP),
which can straightforwardly be adapted and extended to suit the needs of
specific applications. The use of ASP also means that we can take advantage of
highly efficient off-the-shelf solvers. To illustrate the flexibility of our
approach, we show how our ASP encoding naturally allows us to select optimal
stable matchings, i.e. matchings that are optimal according to some
user-specified criterion. To the best of our knowledge, our encoding offers the
first exact implementation to find sex-equal, minimum regret, egalitarian or
maximum cardinality stable matchings for SMP instances in which individuals may
designate unacceptable partners and ties between preferences are allowed.
This paper is under consideration in Theory and Practice of Logic Programming
(TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725
The Complexity of Approximately Counting Stable Matchings
We investigate the complexity of approximately counting stable matchings in
the -attribute model, where the preference lists are determined by dot
products of "preference vectors" with "attribute vectors", or by Euclidean
distances between "preference points" and "attribute points". Irving and
Leather proved that counting the number of stable matchings in the general case
is #P-complete. Counting the number of stable matchings is reducible to
counting the number of downsets in a (related) partial order and is
interreducible, in an approximation-preserving sense, to a class of problems
that includes counting the number of independent sets in a bipartite graph
(#BIS). It is conjectured that no FPRAS exists for this class of problems. We
show this approximation-preserving interreducibilty remains even in the
restricted -attribute setting when (dot products) or
(Euclidean distances). Finally, we show it is easy to count the number of
stable matchings in the 1-attribute dot-product setting.Comment: Fixed typos, small revisions for clarification, et
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