696 research outputs found
Popular matchings: structure and algorithms
An instance of the popular matching problem (POP-M) consists of a set of applicants and a set of posts. Each applicant has a preference list that strictly ranks a subset of the posts. A matching M of applicants to posts is popular if there is no other matching M' such that more applicants prefer M' to M than prefer M to M'. This paper provides a characterization of the set of popular matchings for an arbitrary POP-M instance in terms of a structure called the switching graph, a directed graph computable in linear time from the preference lists. We show that the switching graph can be exploited to yield efficient algorithms for a range of associated problems, including
the counting and enumeration of the set of popular matchings and computing popular matchings that satisfy various additional optimality criteria. Our algorithms for computing such optimal popular matchings improve those described in a recent paper by Kavitha and Nasre
An integer programming Model for the Hospitals/Residents Problem with Couples
The Hospitals/Residents problem with Couples (hrc) is a generalisation of the classical Hospitals/Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc. Further, we present an Integer Programming (IP) model for hrc and extend it the case where preference lists can include ties. Further, we describe an empirical study of an IP model for HRC and its extension to the case where preference lists can include ties. This model was applied to randomly generated instances and also real-world instances arising from previous matching runs of the Scottish Foundation Allocation Scheme, used to allocate junior doctors to hospitals in Scotland
Local search for stable marriage problems with ties and incomplete lists
The stable marriage problem has a wide variety of practical applications,
ranging from matching resident doctors to hospitals, to matching students to
schools, or more generally to any two-sided market. We consider a useful
variation of the stable marriage problem, where the men and women express their
preferences using a preference list with ties over a subset of the members of
the other sex. Matchings are permitted only with people who appear in these
preference lists. In this setting, we study the problem of finding a stable
matching that marries as many people as possible. Stability is an envy-free
notion: no man and woman who are not married to each other would both prefer
each other to their partners or to being single. This problem is NP-hard. We
tackle this problem using local search, exploiting properties of the problem to
reduce the size of the neighborhood and to make local moves efficiently.
Experimental results show that this approach is able to solve large problems,
quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International
Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun
eds., Springer LNA
How does star formation proceed in the circumnuclear starburst ring of NGC 6951?
Gas inflowing along stellar bars is often stalled at the location of
circumnuclear rings, that form an effective reservoir for massive star
formation and thus shape the central regions of galaxies. However, how exactly
star formation is proceeding within these circumnuclear starburst rings is
subject of debate. Two main scenarios for this process have been put forward:
In the first the onset of star formation is regulated by the total amount of
gas present in the ring with star forming starting once a mass threshold has
reached in a `random' position within the ring like `popcorn'. In the second
star formation preferentially takes place near the locations where the gas
enters the ring. This scenario has been dubbed `pearls-on-a-string'. Here we
combine new optical IFU data covering the full stellar bar with existing
multi-wavelength data to study in detail the 580 pc radius circumnuclear
starburst ring in the nearby spiral galaxy NGC 6951. Using HST archival data
together with Sauron and Oasis IFU data, we derive the ages and stellar masses
of star clusters as well as the total stellar content of the central region.
Adding information on the molecular gas distribution, stellar and gaseous
dynamics and extinction, we find that the circumnuclear ring in NGC 6951 is
~1-1.5 Gyr old and has been forming stars for most of that time. We see
evidence for preferred sites of star formation within the ring, consistent with
the `pearls-on-a-string' scenario, when focusing on the youngest stellar
populations. Due to the ring's longevity this signature is washed out when
older stellar populations are included in the analysis.Comment: accepted for publication in A&A, 15 page
Socially stable matchings in the hospitals / residents problem
In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings.
In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for three special cases of the problem
Counting Popular Matchings in House Allocation Problems
We study the problem of counting the number of popular matchings in a given
instance. A popular matching instance consists of agents A and houses H, where
each agent ranks a subset of houses according to their preferences. A matching
is an assignment of agents to houses. A matching M is more popular than
matching M' if the number of agents that prefer M to M' is more than the number
of people that prefer M' to M. A matching M is called popular if there exists
no matching more popular than M. McDermid and Irving gave a poly-time algorithm
for counting the number of popular matchings when the preference lists are
strictly ordered.
We first consider the case of ties in preference lists. Nasre proved that the
problem of counting the number of popular matching is #P-hard when there are
ties. We give an FPRAS for this problem.
We then consider the popular matching problem where preference lists are
strictly ordered but each house has a capacity associated with it. We give a
switching graph characterization of popular matchings in this case. Such
characterizations were studied earlier for the case of strictly ordered
preference lists (McDermid and Irving) and for preference lists with ties
(Nasre). We use our characterization to prove that counting popular matchings
in capacitated case is #P-hard
Therapeutic and educational objectives in robot assisted play for children with autism
âThis material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." âCopyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.â DOI: 10.1109/ROMAN.2009.5326251This article is a methodological paper that describes the therapeutic and educational objectives that were identified during the design process of a robot aimed at robot assisted play. The work described in this paper is part of the IROMEC project (Interactive Robotic Social Mediators as Companions) that recognizes the important role of play in child development and targets children who are prevented from or inhibited in playing. The project investigates the role of an interactive, autonomous robotic toy in therapy and education for children with special needs. This paper specifically addresses the therapeutic and educational objectives related to children with autism. In recent years, robots have already been used to teach basic social interaction skills to children with autism. The added value of the IROMEC robot is that play scenarios have been developed taking children's specific strengths and needs into consideration and covering a wide range of objectives in children's development areas (sensory, communicational and interaction, motor, cognitive and social and emotional). The paper describes children's developmental areas and illustrates how different experiences and interactions with the IROMEC robot are designed to target objectives in these areas.Final Published versio
Late-type galaxies observed with SAURON. Two-dimensional stellar and emission-line kinematics of 18 spirals
We present the stellar and gas kinematics of a sample of 18 nearby late-type
spiral galaxies (Hubble types ranging from Sb to Sd), observed with the
integral-field spectrograph SAURON at the 4.2-m William Herschel Telescope.
SAURON covers the spectral range 4800-5380 A, allowing us to measure the Hbeta,
Fe, Mgb absorption features and the emission in the Hbeta line and the [OIII],
and [NI] doublets over a 33x41 arcsec field of view. The maps cover the nuclear
region of these late-type galaxies and in all cases include the entire bulge.
In many cases the stellar kinematics suggests the presence of a cold inner
region, as visible from a central drop in the stellar velocity dispersion. The
ionised gas is almost ubiquitous and behaves in a complicated fashion: the gas
velocity fields often display more features than the stellar ones, including
wiggles in the zero-velocity lines, irregular distributions, ring-like
structures. The line ratio [OIII]/Hbeta often takes on low values over most of
the field, probably indicating a wide-spread star formation.Comment: 34 pages, 24 figures. Accepted for publication in MNRAS. A version
with full resolution figures is available at
http://www.strw.leidenuniv.nl/sauron/papers/ganda2005_late_types.pd
Popular matchings with two-sided preferences and one-sided ties
We are given a bipartite graph where each vertex has a
preference list ranking its neighbors: in particular, every ranks its
neighbors in a strict order of preference, whereas the preference lists of may contain ties. A matching is popular if there is no matching
such that the number of vertices that prefer to exceeds the number of
vertices that prefer to~. We show that the problem of deciding whether
admits a popular matching or not is NP-hard. This is the case even when
every either has a strict preference list or puts all its neighbors
into a single tie. In contrast, we show that the problem becomes polynomially
solvable in the case when each puts all its neighbors into a single
tie. That is, all neighbors of are tied in 's list and desires to be
matched to any of them. Our main result is an algorithm (where ) for the popular matching problem in this model. Note that this model
is quite different from the model where vertices in have no preferences and
do not care whether they are matched or not.Comment: A shortened version of this paper has appeared at ICALP 201
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