Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. Our algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting path is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. We provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number

Problemas de asignación de recursos humanos a través del problema de asignación multidimensional

149 páginas. Doctorado en Optimización.El problema de asignación de personal aparece en diversas industrias. La asignación eficiente de personal a trabajos, proyectos, herramientas, horarios, entre otros, tiene un impacto directo en términos monetarios para el negocio. El problema de asignación multidimensional (PAM) es la extensión natural del problema de asignación y puede ser utilizado en aplicaciones donde se requiere la asignación de personal. El caso más estudiado de PAM es el problema de asignación en tres dimensiones, sin embargo en años recientes han sido propuestas algunas heurísticas de búsqueda local y algoritmos meméticos para el caso general. En este trabajo de tesis se realiza un estudio profundo de PAM comenzando con un resumen del estado del arte de algoritmos, heurísticas y metaheurísticas para su resolución. Se describen algunos algoritmos y se propone uno nuevo que resuelve instancias de tamaño medio para PAM. Se propone la generalización de las conocidas heurísticas de variación de dimensión como una búsqueda local generalizada que proporciona un nuevo estado del arte de búsquedas locales para PAM. Adicionalmente, se propone un algoritmo memético con una estructura sencilla pero efectiva y que es competitivo con el mejor algoritmo memético conocido para PAM. Finalmente, se presenta un caso particular de problema de asignación de personal: el Problema de Asignación de Horarios (PAH). El PAH considera la asignación de personal a uno, dos o más conjuntos de objetos, por ejemplo puede ser requerida la asignación de profesores a cursos a periodos de tiempo a salones, para determinados grupos de estudiantes. Primero, se presenta el PAH así como una breve descripción de su estado del arte. Luego, se propone una nueva forma de modelar este problema a través de la resolución de PAM y se aplica sobre el PAH en la Universidad Autónoma Metropolitana, unidad Azcapotzalco (UAM-A). Se describen las consideraciones particulares del PAH en la UAM-A y proponemos una nueva solución para éste. Nuestra solución se basa en la resolución de múltiples PA3 a través de los algoritmos y heurísticas propuestos.Personnel assignment problems appear in several industries. The e cient assignment of personnel to jobs, projects, tools, time slots, etcetera, has a direct impact in terms monetary for the business. The Multidimensional Assignment Problem (MAP) is a natural extension of the well-known assignment problem and can be used on applications where the assignment of personnel is required. The most studied case of the MAP is the three dimensional assignment problem, though in recent years some local search heuristics and memetic algorithms have been proposed for the general case. Let X1; : : : ;Xs be a collection of s 3 disjoint sets, consider all combinations that belong to the Cartesian product X = X1 Xs such that each vector x 2 X, where x = (x1; : : : ; xs) with xi 2 Xi 8 1 i s, has associated a weight w(x). A feasible assignment is a collection A = (x1; : : : ; xn) of n vectors if xi k 6= xj k for each i 6= j and 1 k s. The weight of an assignment A is given by w(A) = Pn i=1 w(xi). A MAP in s dimensions is denoted as sAP. The objective of sAP is to nd an assignment of minimal weight. In this thesis we make an in depth study of MAP beginning with the state-ofthe- art algorithms, heuristics, and metaheuristics for solving it. We describe some algorithms and we propose a new one for solving optimally medium size instances of MAP. We propose the generalization of the called dimensionwise variation heuristics for MAP and a new generalized local search heuristic that provides new state-of-theart local searches for MAP. We also propose a new simple memetic algorithm that is competitive against the state-of-the-art memetic algorithm for MAP. In the last part of this thesis, we study a particular case of personnel assignment problem: the School Timetabling Problem (STP). The STP considers the assignment of personnel to other two or more sets, for example the assignment of professors to courses to time slots to rooms can be required. First, we provide a brief description of the state-of-the-art for STP. Then, we introduce a new approach for modeling this problem through the resolution of several MAP and we apply our solution on a real life case of study: STP at the Universidad Autonoma Metropolitana campus Azcapotzalco (UAM-A). We provide the particular aspects for STP at UAM-A and we provide a new solution for this problem. Our approach is based on solving several 3AP considering the introduced model and our proposed techniques.Consejo Mexiquense de Ciencia y Tecnología (Comecyt).Consejo Nacional de Ciencia y Tecnología (México

Fair Multi-Agent Bandits

In this paper, we study the problem of fair multi-agent multi-arm bandit learning when agents do not communicate with each other, except collision information, provided to agents accessing the same arm simultaneously. We provide an algorithm with regret $O\left(N^3 \log \frac{B}{\Delta} f(\log T) \log T \right)$ (assuming bounded rewards, with unknown bound), where $f(t)$ is any function diverging to infinity with $t$. This significantly improves previous results which had the same upper bound on the regret of order $O(f(\log T) \log T )$ but an exponential dependence on the number of agents. The result is attained by using a distributed auction algorithm to learn the sample-optimal matching and a novel order-statistics-based regret analysis. Simulation results present the dependence of the regret on $\log T$.Comment: 17 pages, 3 figure

New Auction Algorithms for the Assignment Problem and Extensions

We consider the classical linear assignment problem, and we introduce new auction algorithms for its optimal and suboptimal solution. The algorithms are founded on duality theory, and are related to ideas of competitive bidding by persons for objects and the attendant market equilibrium, which underlie real-life auction processes. We distinguish between two fundamentally different types of bidding mechanisms: aggressive and cooperative. Mathematically, aggressive bidding relies on a notion of approximate coordinate descent in dual space, an epsilon-complementary slackness condition to regulate the amount of descent approximation, and the idea of epsilon-scaling to resolve efficiently the price wars that occur naturally as multiple bidders compete for a smaller number of valuable objects. Cooperative bidding avoids price wars through detection and cooperative resolution of any competitive impasse that involves a group of persons. We discuss the relations between the aggressive and the cooperative bidding approaches, we derive new algorithms and variations that combine ideas from both of them, and we also make connections with other primal-dual methods, including the Hungarian method. Furthermore, our discussion points the way to algorithmic extensions that apply more broadly to network optimization, including shortest path, max-flow, transportation, and minimum cost flow problems with both linear and convex cost functions

Methods to Improve Applicability and Efficiency of Distributed Data-Centric Compute Frameworks

The success of modern applications depends on the insights they collect from their data repositories. Data repositories for such applications currently exceed exabytes and are rapidly increasing in size, as they collect data from varied sources - web applications, mobile phones, sensors and other connected devices. Distributed storage and data-centric compute frameworks have been invented to store and analyze these large datasets. This dissertation focuses on extending the applicability and improving the efficiency of distributed data-centric compute frameworks

Occlusion reasoning for multiple object visual tracking

Thesis (Ph.D.)--Boston UniversityOcclusion reasoning for visual object tracking in uncontrolled environments is a challenging problem. It becomes significantly more difficult when dense groups of indistinguishable objects are present in the scene that cause frequent inter-object interactions and occlusions. We present several practical solutions that tackle the inter-object occlusions for video surveillance applications. In particular, this thesis proposes three methods. First, we propose "reconstruction-tracking," an online multi-camera spatial-temporal data association method for tracking large groups of objects imaged with low resolution. As a variant of the well-known Multiple-Hypothesis-Tracker, our approach localizes the positions of objects in 3D space with possibly occluded observations from multiple camera views and performs temporal data association in 3D. Second, we develop "track linking," a class of offline batch processing algorithms for long-term occlusions, where the decision has to be made based on the observations from the entire tracking sequence. We construct a graph representation to characterize occlusion events and propose an efficient graph-based/combinatorial algorithm to resolve occlusions. Third, we propose a novel Bayesian framework where detection and data association are combined into a single module and solved jointly. Almost all traditional tracking systems address the detection and data association tasks separately in sequential order. Such a design implies that the output of the detector has to be reliable in order to make the data association work. Our framework takes advantage of the often complementary nature of the two subproblems, which not only avoids the error propagation issue from which traditional "detection-tracking approaches" suffer but also eschews common heuristics such as "nonmaximum suppression" of hypotheses by modeling the likelihood of the entire image. The thesis describes a substantial number of experiments, involving challenging, notably distinct simulated and real data, including infrared and visible-light data sets recorded ourselves or taken from data sets publicly available. In these videos, the number of objects ranges from a dozen to a hundred per frame in both monocular and multiple views. The experiments demonstrate that our approaches achieve results comparable to those of state-of-the-art approaches