Lifting Linear Extension Complexity Bounds to the Mixed-Integer Setting

Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixed-integer program with few (even constantly many) integer variables. This is in stark contrast to linear formulations, where recent breakthroughs in the field of extended formulations have shown that many polytopes associated to classical combinatorial optimization problems do not even admit approximate extended formulations of sub-exponential size. We provide a general framework for lifting inapproximability results of extended formulations to the setting of mixed-integer extended formulations, and obtain almost tight lower bounds on the number of integer variables needed to describe a variety of classical combinatorial optimization problems. Among the implications we obtain, we show that any mixed-integer extended formulation of sub-exponential size for the matching polytope, cut polytope, traveling salesman polytope or dominant of the odd-cut polytope, needs $\Omega(n/\log n)$ many integer variables, where $n$ is the number of vertices of the underlying graph. Conversely, the above-mentioned polyhedra admit polynomial-size mixed-integer formulations with only $O(n)$ or $O(n \log n)$ (for the traveling salesman polytope) many integer variables. Our results build upon a new decomposition technique that, for any convex set $C$, allows for approximating any mixed-integer description of $C$ by the intersection of $C$ with the union of a small number of affine subspaces.Comment: A conference version of this paper will be presented at SODA 201

Max-sum diversity via convex programming

Diversity maximization is an important concept in information retrieval, computational geometry and operations research. Usually, it is a variant of the following problem: Given a ground set, constraints, and a function $f(\cdot)$ that measures diversity of a subset, the task is to select a feasible subset $S$ such that $f(S)$ is maximized. The \emph{sum-dispersion} function $f(S) = \sum_{x,y \in S} d(x,y)$, which is the sum of the pairwise distances in $S$, is in this context a prominent diversification measure. The corresponding diversity maximization is the \emph{max-sum} or \emph{sum-sum diversification}. Many recent results deal with the design of constant-factor approximation algorithms of diversification problems involving sum-dispersion function under a matroid constraint. In this paper, we present a PTAS for the max-sum diversification problem under a matroid constraint for distances $d(\cdot,\cdot)$ of \emph{negative type}. Distances of negative type are, for example, metric distances stemming from the $\ell_2$ and $\ell_1$ norm, as well as the cosine or spherical, or Jaccard distance which are popular similarity metrics in web and image search

Diversity Maximization in Doubling Metrics

Diversity maximization is an important geometric optimization problem with many applications in recommender systems, machine learning or search engines among others. A typical diversification problem is as follows: Given a finite metric space (X,d) and a parameter k in N, find a subset of k elements of X that has maximum diversity. There are many functions that measure diversity. One of the most popular measures, called remote-clique, is the sum of the pairwise distances of the chosen elements. In this paper, we present novel results on three widely used diversity measures: Remote-clique, remote-star and remote-bipartition. Our main result are polynomial time approximation schemes for these three diversification problems under the assumption that the metric space is doubling. This setting has been discussed in the recent literature. The existence of such a PTAS however was left open. Our results also hold in the setting where the distances are raised to a fixed power q >= 1, giving rise to more variants of diversity functions, similar in spirit to the variations of clustering problems depending on the power applied to the pairwise distances. Finally, we provide a proof of NP-hardness for remote-clique with squared distances in doubling metric spaces

Implementación de un prototipo-sistema para transporte de producto congelado, refrigerado a base de placas eutécticas recargables.

En la presente investigación se desarrolló un prototipo-sistema para transportar producto congelado, refrigerado a base de placas con solución eutéctica el punto de congelación se establecería en -33 °C. Se empezó realizando un cálculo de potencia frigorífica con relación al aislamiento térmico seleccionado, las condiciones medioambientales, la carga térmica, las aperturas de puertas, el calor proporcionado por el ser humano y el volumen. Asimismo se realizó el diseño del prototipo sistema considerando factores energéticos, logísticos y frigoríficos con la finalidad de que el producto sea comercialmente competitivo, con el respaldo de información suministrada por un estudio de mercado realizado previamente por la empresa auspiciante. Con la finalidad de determinar la potencia frigorífica requerida se establecieron tres períodos de funcionamiento del prototipo sistema, el período de carga de la placa eutéctica es la base para la obtención de la potencia frigorífica requerida, mientras el período de introducción del producto congelado y el período de distribución de producto congelado entregaran la cantidad de calor que ingresaría al sistema y que sería almacenado por la placa eutéctica. El único período en el que se expulsaría calor al medio condensante sería en el período de carga de la placa eutéctica y este valor sería de 9100,85 kJ. El aislamiento seleccionado fue el poli isocianurato, con doble barrera antivapor de 100 mm de espesor con un coeficiente de conductividad térmica de 0,026 W/°C·m, la potencia frigorífica durante el período de carga fue de 590 W. Se documentó el procedimiento de fabricación del sistema con la finalidad de que pueda ser replicado en serie y se estableció un plan de mantenimiento semanal y mensual. El costo del proyecto fue de 6679,20 USD.In this research a prototype-system is developed to transport frozen product refrigerated based on plates with eutectic solution, where the freezing point, would be established at -33 °C. It began, performing a calculation of cooling power with respect to thermal insulation selected, environmental conditions, the thermal load, door openings, the heat provided by humans and volume. Also it took place, the design of the prototype system considering, energy, logistics and refrigerators factors in order to make the product commercially competitive, supported by information provided by market research previously conducted by the sponsoring company. In order to determine the required cooling capacity three periods of operation of the prototype system were established, the charging period of the eutectic plate would be the basis for obtaining the required cooling capacity, while the period of introduction of the frozen product and distribution period, of frozen product would deliver the amount of heat would enter into the system and would be stored by the eutectic plate. The only period in which the condensing heat medium would be ejected in the charging period of the eutectic plate and this value would be 9100.85 kJ. The selected insolation was poly-isocyanurate, dual vapor barrier, of 100 mm thickness with thermal conductivity coefficient of 0.026 W/°C·m, the cooling capacity during the charge was 590 W. It was documented, the manufacturing process system, in order that can be replicated in series and a plan weekly and monthly maintenance was established. The project cost was 6679.20 USD

Diretrizes para a gestão de empreendimentos de construção complexos do tipo comercial do mercado varejista com base nas abordagens Lean e Agile

Os empreendimentos de construção são cada vez mais complexos. A prática da gestão tradicional de empreendimentos no contexto da construção tem resultado em empreendimentos que demoram mais do planejado, custam mais do previsto e não atendem as expectativas de qualidade. A abordagem tradicional de gestão não considera todas as características de complexidade envolvidas em alguns empreendimentos, e os trata de forma similar, sem considerar o tipo de contexto. Esta pesquisa teve como ponto de partida um problema real identificado numa empresa varejista, que tem setores envolvidos no desenvolvimento de empreendimentos de construção para implantar ou reformar lojas. Estes empreendimentos são denominados nesta pesquisa como do tipo comercial do mercado varejista. Os processos de gestão de empreendimentos da empresa estão influenciados pela abordagem tradicional de gestão de empreendimentos, apesar das características de complexidade de seus empreendimentos. Neste contexto, existe a necessidade de desenvolver métodos e ferramentas de gestão que considerem todas as características de complexidade envolvidas nos empreendimentos, e o contexto específico no qual serão utilizados. As abordagens Lean e Agile são apontadas como duas alternativas para fundamentar tais desenvolvimentos. Esta pesquisa tem como objetivo principal desenvolver um conjunto de diretrizes para a gestão de empreendimentos de construção complexos do tipo comercial do mercado varejista, com base nas abordagens Lean e Agile. O método de pesquisa está fundamentado na design science research, sendo desenvolvido um artefato, que corresponde ao conjunto de diretrizes. A estratégia de pesquisa adotada foi a pesquisa-ação, de modo que as soluções foram construídas com a colaboração dos profissionais da empresa, sendo possível ter vários ciclos de aprendizagem durante a implementação das soluções, as mesmas que foram continuamente avaliadas e adaptadas. Como contribuição teórica, esta pesquisa discute como as abordagens Lean e Agile se sobrepõem e se complementam no contexto da gestão de empreendimentos.Construction projects are increasingly complex. Traditional project management practices in the context of construction has resulted in projects that take longer than planned, cost more than expected and do not meet quality expectations. The traditional project management approach does not consider all the complexity characteristics involved in some projects, and treats them in a similar way, without considering the type of context. The starting point for this research work was a real problem identified in a retail company, which has sectors involved in the development of construction projects to install or remodel stores. These projects are named in this investigation as retail market commercial projects. The company's existing project management processes were strongly based on the traditional project management approach, despite the complexity of its projects. In this context, there is a need to develop managerial methods and tools that take into account the complexity characteristics involved in construction projects, as well as the specific context in which these are used. The Lean and Agile approaches have been pointed as two alternatives to support such developments. The aim of this research work is to develop a set of guidelines for the management of complex retail market commercial projects, based on Lean and Agile approaches. The research method is based on design science research, which involves the development of an artifact, which corresponds to the set of guidelines. The research strategy adopted was action-research, so that the solutions were built in collaboration with the company's technical staff, along several learning cycles during the implementation of the solutions, which were continuously evaluated and adapted. As a theoretical contribution, this research study discusses how the Lean and Agile approaches overlap and complement each other in the context of project management

Privatization of the pension scheme in Korea

Thesis(Master) --KDI School:Master of Economic Policy,1999INTRODUCTION 1. OVERVIEW OF THE WORLD STATUS AND RETIREMENT 2. A CONCEPTUAL FRAMEWORK OF PENSION SYSTEMS 3. DEPICTING THE KOREAN PENSION SCHEME 4. COSTS AND BENEFITS OF PRIVATIZATION 5. BREAKING INTO NEW PLANS 6. CONCLUSIONS AND RECOMMENDATIONSOutstandingmasterpublishedby Jorge Alfonso Cevallos Carrera

Approximation algorithms for geometric dispersion

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with wide applications in web search and information retrieval, where one needs to find a small and diverse representative subset of a large dataset. The problem has recently received a great deal of attention in the computational geometry and operations research communities; and since it is NP-hard, research has focused on efficient heuristics and approximation algorithms. Several classes of distance functions have been considered in the literature. Many of the most common distances used in applications are induced by a norm in a real vector space. The focus of this thesis is on MSD over these geometric instances. We provide for it simple and fast polynomial-time approximation schemes (PTASs), as well as improved constant-factor approximation algorithms. We pay special attention to the class of negative-type distances, a class that includes Euclidean and Manhattan distances, among many others. In order to exploit the properties of this class, we apply several techniques and results from the theory of isometric embeddings. We explore the following variations of the MSD problem: matroid and matroid-intersection constraints, knapsack constraints, and the mixed-objective problem that maximizes a combination of the sum of pairwise distances with a submodular monotone function. In addition to approximation algorithms, we present a core-set for geometric instances of low dimension, and we discuss the efficient implementation of some of our algorithms for massive datasets, using the streaming and distributed models of computation

Estudio de factibilidad para el establecimiento de una hostería comunitaria en la comunidad de Cube – Quininde

Ecuador es uno de los 17 países mega diversos del mundo, es decir, de los más ricos en biodiversidad y endemismo. Con tan sólo 256.370 km2, o el 0.17% de la superficie terrestre del planeta, Ecuador posee más del 11 % de todas las especies de vertebrados terrestres; 16.087 especies de plantas vasculares; y, alrededor de 600 especies de peces marinos. Por su extensión continental y entre todos los países mega diversos, Ecuador es el número uno en biodiversidad de vertebrados terrestres por unidad de superficie: casi 11 especies por cada 1.000 km2.1 Ecuador tiene asimismo una gran diversidad cultural que se manifiesta en la existencia de nacionalidades indígenas, comunidades afro ecuatorianas y diferentes grupos humanos que interactúan, dependen de su entorno natural y reconocen la importancia del uso adecuado de la biodiversidad para garantizar el desarrollo sostenible y el mantenimiento de la riqueza cultural del país

Overview of Polkadot and its Design Considerations

In this paper we describe the design components of the heterogenous multi-chain protocol Polkadot and explain how these components help Polkadot address some of the existing shortcomings of blockchain technologies. At present, a vast number of blockchain projects have been introduced and employed with various features that are not necessarily designed to work with each other. This makes it difficult for users to utilise a large number of applications on different blockchain projects. Moreover, with the increase in number of projects the security that each one is providing individually becomes weaker. Polkadot aims to provide a scalable and interoperable framework for multiple chains with pooled security that is achieved by the collection of components described in this paper