Finding large stable matchings

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 article, we present two new heuristics for finding large stable matchings in variants of these problems in which ties are on one side only. We describe an empirical study involving these heuristics and the best existing approximation algorithm for this problem. Our results indicate that all three of these algorithms perform significantly better than naive tie-breaking algorithms when applied to real-world and randomly-generated data sets and that one of the new heuristics fares slightly better than the other algorithms, in most cases. This study, and these particular problem variants, are motivated by important applications in 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

Technological and environmental risks in the context of climate change.

Considering the importance of the debate on the topic of disasters related to landslides, flooding and technological risks, under international and more recently in Brazil, this work analyzes the situations of vulnerability risk areas on the Northern Coast of São Paulo. The situation analyzed refers to the effects of the implementation of large infrastructure projects related to oil and gas on the occupation of risk areas to landslides and flooding, besides considering the technological risks inherent in these megaprojects. Figure 1 show the technological and environmental risks in three regions of Brazilian Southeast coast ? detailed to Northern coast of São Paulo

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 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

Multiscale approaches to analyse risks and vulnerabilities in the coastal zone (Brazil).

The objectives of this work were: (i) identified the risk areas of landslides, flooding and sea level rise and social vulnerabilities in different scales of analysis; (ii) analyse the risk perception of people living in this risk areas; (iii) found a common dialogues between sciences and communities to inform policy and decision-making in the different socioeconomic sectors

Unbounded-Error Classical and Quantum Communication Complexity

Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently, \cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum} communication complexity in the {\em one-way communication} model can also be investigated using the arrangement, and showed that it is exactly (without a difference of even one qubit) half of the classical one-way communication complexity. In this paper, we extend the arrangement argument to the {\em two-way} and {\em simultaneous message passing} (SMP) models. As a result, we show similarly tight bounds of the unbounded-error two-way/one-way/SMP quantum/classical communication complexities for {\em any} partial/total Boolean function, implying that all of them are equivalent up to a multiplicative constant of four. Moreover, the arrangement argument is also used to show that the gap between {\em weakly} unbounded-error quantum and classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200

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

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