433 research outputs found
Popular Matchings in the Capacitated House Allocation Problem
We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matching MⲠsuch that the number of agents who prefer their allocation in MⲠto that in M exceeds the number of agents who prefer their allocation in M to that in Mâ˛. Here, we give an O(âC+n1m) algorithm to determine if an instance of CHA admits a popular matching, and if so, to find a largest such matching, where C is the total capacity of the houses, n1 is the number of agents and m is the total length of the agentsâ preference lists. For the case where preference lists may contain ties, we give an O(âCn1+m) algorithm for the analogous problem
Popular matchings
We consider the problem of matching a set of applicants to a set of posts, where each applicant has a preference list, ranking a non-empty subset of posts in order of preference, possibly involving ties. We say that a matching M is popular if there is no matching M' such that the number of applicants preferring M' to M exceeds the number of applicants preferring M to M'. In this paper, we give the first polynomial-time algorithms to determine if an instance admits a popular matching, and to find a largest such matching, if one exists. For the special case in which every preference list is strictly ordered (i.e. contains no ties), we give an O(n+m) time algorithm, where n is the total number of applicants and posts, and m is the total length of all the preference lists. For the general case in which preference lists may contain ties, we give an O(ânm) time algorithm, and show that the problem has equivalent time complexity to the maximum-cardinality bipartite matching problem
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
The stable roommates problem with globally-ranked pairs
We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, they can be found in polynomial time. However, it is still the case that strongly stable matchings may not exist, and so we consider the complexity of finding weakly stable matchings with various desirable properties. In particular, we present a polynomial-time algorithm to find a rank-maximal (weakly stable) matching. This is the first generalization of an algorithm due to [Irving et al. 06] to a nonbipartite setting. Also, we describe several hardness results in an even more restricted setting for each of the problems of finding weakly stable matchings that are of maximum size, are egalitarian, have minimum regret, and admit the minimum number of weakly blocking pairs
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
Quaternionic and Hyper-K\"ahler Metrics from Generalized Sigma Models
The problem of finding new metrics of interest, in the context of SUGRA, is
reduced to two stages: first, solving a generalized BPS sigma model with full
quaternionic structure proposed by the authors and, second, constructing the
hyper-K\"{a}hler metric, or suitable deformations of this condition, taking
advantage of the correspondence between the quaternionic left-regular potential
and the hyper-K\"{a}hler metric of the target space. As illustration, new
solutions are obtained using generalized Q-sigma model for Wess-Zumino type
superpotentials. Explicit solutions analog to the Berger's sphere and
Abraham-Townsend type are given and generalizations of 4-dimensional
quaternionic metrics, product of complex ones, are shown and discussed.Comment: 8 pages, two column, no figure
Universal Self Force from an Extended-Object Approach
We present a consistent extended-object approach for determining the self
force acting on an accelerating charged particle. In this approach one
considers an extended charged object of finite size , and calculates
the overall contribution of the mutual electromagnetic forces. Previous
implementations of this approach yielded divergent terms
that could not be cured by mass-renormalization. Here we explain the origin of
this problem and fix it. We obtain a consistent, universal, expression for the
extended-object self force, which conforms with Dirac's well known formula.Comment: Latex, one postscript figure, 4 page
Popular matchings in the marriage and roommates problems
Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching MⲠwith the property that more applicants prefer their allocation in MⲠto their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases
Qac genes and biocide tolerance in clinical veterinary methicillin-resistant and methicillin-susceptible Staphylococcus aureus and Staphylococcus pseudintermedius
Qac genes are associated with increased tolerance to quaternary ammonium compounds and other cationic biocides such as chlorhexidine. This study aimed to determine whether qac genes and increased biocide tolerance were present in 125 clinical methicillin-resistant and susceptible veterinary staphylococci. A total of 125 methicillin-resistant Staphylococcus aureus (MRSA) and methicillin-resistant and -susceptible Staphylococcus pseudintermedius (MRSP and MSSP) from three archived Australian veterinary staphylococci collections underwent whole genome sequencing, multilocus sequence typing and qac gene screening. Two MRSA isolates (12%) harboured qacA/B genes; both isolates were ST8 from horses. QacJ, qacG and smr genes were identified in 28/90 (31%) MRSP and 1/18 (6%) MSSP isolates. ST71 MRSP was significantly more likely to harbour qac genes than other MRSP clones (pâŻ<âŻ0.05). A random subset of 31 isolates underwent minimum bactericidal concentration (MBC) testing against F10SCTM (benzalkonium chloride and biguanide), and HexaconTM (chlorhexidine gluconate), with and without the addition of bovine serum albumin (BSA) as an in vitro substitute for organic matter contamination. Qac genes were not associated with increased phenotypic biocide tolerance but biocide efficacy was significantly affected by the presence of BSA. In the absence of BSA, all MBC values were well below the recommended usage concentration. When BSA was present, regardless of qac gene presence, 50% of MRSA and 43% of MRSP had an F10SCTM MBC above the recommended concentration for general disinfection. Qac genes did not confer increased in vitro biocide tolerance to veterinary staphylococci. Organic matter contamination must be minimized to ensure the efficacy of biocides against MRSA and MRSP
The Hospitals/Residents Problem with Couples: complexity and integer programming models
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, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc
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