781 research outputs found
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
Approximability results for stable marriage problems with ties
We consider instances of the classical stable marriage problem in which persons may include ties in their preference lists. We show that, in such a setting, strong lower bounds hold for the approximability of each of the problems of finding an egalitarian, minimum regret and sex-equal stable matching. We also consider stable marriage instances in which persons may express unacceptable partners in addition to ties. In this setting, we prove that there are constants delta, delta' such that each of the problems of approximating a maximum and minimum cardinality stable matching within factors of delta, delta' (respectively) is NP-hard, under strong restrictions. We also give an approximation algorithm for both problems that has a performance guarantee expressible in terms of the number of lists with ties. This significantly improves on the best-known previous performance guarantee, for the case that the ties are sparse. Our results have applications to large-scale centralized matching schemes
Coherent resonant tunneling in ac fields
We have analyzed the tunneling transmission probability and electronic
current density through resonant heterostructures in the presence of an
external electromagnetic field. In this work, we compare two different models
for a double barrier : In the first case the effect of the external field is
taken into account by spatially dependent AC voltages and in the second one the
electromagnetic field is described in terms of a photon field that irradiates
homogeneously the whole sample. While in the first description the tunneling
takes place mainly through photo sidebands in the case of homogeneous
illumination the main effective tunneling channels correspond to the coupling
between different electronic states due to photon absorption and emission. The
difference of tunneling mechanisms between these configurations is strongly
reflected in the transmission and current density which present very different
features in both cases. In order to analyze these effects we have obtained,
within the Transfer Hamiltonian framework, a general expression for the
transition probability for coherent resonant tunneling in terms of the Green's
function of the system.Comment: 16 pages,Figures available upon request,to appear in Phys.Rev B (15
April 1996
An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure
The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for
the traveling salesman problem in an n-vertex graph with maximum degree 3. This
improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and
O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search
algorithm. The only branch rule is designed on a cut-circuit structure of a
graph induced by unprocessed edges. To improve a time bound by a simple
analysis on measure and conquer, we introduce an amortization scheme over the
cut-circuit structure by defining the measure of an instance to be the sum of
not only weights of vertices but also weights of connected components of the
induced graph.Comment: 24 pages and 4 figure
Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems
When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes
Profile-Based Optimal Matchings in the Student-Project Allocation Problem
In the Student/Project Allocation problem (spa) we seek to assign students to individual or group projects offered by lecturers. Students provide a list of projects they find acceptable in order of preference. Each student can be assigned to at most one project and there are constraints on the maximum number of students that can be assigned to each project and lecturer. We seek matchings of students to projects that are optimal with respect to profile, which is a vector whose rth component indicates how many students have their rth-choice project. We present an efficient algorithm for finding agreedy maximum matching in the spa context – this is a maximum matching whose profile is lexicographically maximum. We then show how to adapt this algorithm to find a generous maximum matching – this is a matching whose reverse profile is lexicographically minimum. Our algorithms involve finding optimal flows in networks. We demonstrate how this approach can allow for additional constraints, such as lecturer lower quotas, to be handled flexibly
An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects
The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 32 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the 32 -approximation algorithm finds stable matchings that are very close to having maximum cardinality
Stable marriage with general preferences
We propose a generalization of the classical stable marriage problem. In our
model, the preferences on one side of the partition are given in terms of
arbitrary binary relations, which need not be transitive nor acyclic. This
generalization is practically well-motivated, and as we show, encompasses the
well studied hard variant of stable marriage where preferences are allowed to
have ties and to be incomplete. As a result, we prove that deciding the
existence of a stable matching in our model is NP-complete. Complementing this
negative result we present a polynomial-time algorithm for the above decision
problem in a significant class of instances where the preferences are
asymmetric. We also present a linear programming formulation whose feasibility
fully characterizes the existence of stable matchings in this special case.
Finally, we use our model to study a long standing open problem regarding the
existence of cyclic 3D stable matchings. In particular, we prove that the
problem of deciding whether a fixed 2D perfect matching can be extended to a 3D
stable matching is NP-complete, showing this way that a natural attempt to
resolve the existence (or not) of 3D stable matchings is bound to fail.Comment: This is an extended version of a paper to appear at the The 7th
International Symposium on Algorithmic Game Theory (SAGT 2014
Riscos geotécnicos e vulnerabilidades: aplicação de grade regular para representação espacial da população na zona costeira.
Considerando o contexto de riscos e vulnerabilidades (UNISDR, 2004; 2013; BRASIL/PNPDC, 2012; IPCC, 2012) e de mudanças climáticas (BRASIL/PNMC, 2009; IPCC, 2007; 2014) no âmbito da gestão ou de políticas públicas, caracterizar as situações de riscos e vulnerabilidades nas zonas costeiras tem sido fundamental para as agendas científicas relacionadas à temática das dimensões humanas das mudanças climáticas e ambientais. Nesse sentido que esse trabalho buscou, mais do que caracterizar essas situações, identificar possíveis padrões no perfil socioeconômico da população que influenciam sua situação de vulnerabilidade, trazendo também ao debate uma reflexão sobre as limitações dos métodos propostos para a análise da vulnerabilidade, que muitas vezes (ou quase sempre), é apenas tangencial (MARANDOLA Jr., 2009). Por meio de uma análise geoespacial, buscou-se identificar quais são os principais elementos indicativos de vulnerabilidade na zona costeira de São Paulo, por meio da integração de dois conjuntos de dados organizados em um Sistema de Informações Geográficas (SIG): riscos geotécnicos sobrepostos em uma grade regular de células de tamanho de 250 m para as áreas urbanas e de 1000 m para áreas rurais (proposta por BUENO, 2014 ? em prep.; BUENO; DAGNINO, 2011). As variáveis do meio físico consistiram em: (a) riscos geotécnicos associados com processos geológicos e hidrológicos ? escorregamentos, inundação e recalques ou subsidência do solo; (b) declividade; (c) altitude e modelo digital de elevação e variáveis. As variáveis sociodemográficas foram: (d) número de pessoas (moradores); (e) gênero (pessoas responsáveis pelo domicílio de sexo masculino e feminino); (f) renda; (g) idade; (h) raça ou cor e (i) alfabetização, todas agregadas por grades regulares ou células como unidade de análise
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