Approximation Algorithms for Problems in Makespan Minimization on Unrelated Parallel Machines

A fundamental problem in scheduling is makespan minimization on unrelated parallel machines (R||Cmax). Let there be a set J of jobs and a set M of parallel machines, where every job Jj ∈ J has processing time or length pi,j ∈ ℚ+ on machine Mi ∈ M. The goal in R||Cmax is to schedule the jobs non-preemptively on the machines so as to minimize the length of the schedule, the makespan. A ρ-approximation algorithm produces in polynomial time a feasible solution such that its objective value is within a multiplicative factor ρ of the optimum, where ρ is called its approximation ratio. The best-known approximation algorithms for R||Cmax have approximation ratio 2, but there is no ρ-approximation algorithm with ρ \u3c 3/2 for R||Cmax unless P=NP. A longstanding open problem in approximation algorithms is to reconcile this hardness gap. We take a two-pronged approach to learn more about the hardness gap of R||Cmax: (1) find approximation algorithms for special cases of R||Cmax whose approximation ratios are tight (unless P=NP); (2) identify special cases of R||Cmax that have the same 3/2-hardness bound of R||Cmax, but where the approximation barrier of 2 can be broken. This thesis is divided into four parts. The first two parts investigate a special case of R||Cmax called the graph balancing problem when every job has one of two lengths and the machines may have one of two speeds. First, we present 3/2-approximation algorithms for the graph balancing problem with one speed and two job lengths. In the second part of this thesis we give an approximation algorithm for the graph balancing problem with two speeds and two job lengths with approximation ratio (√65+7)/8 ≈ 1.88278. In the third part of the thesis we present approximation algorithms and hardness of approximation results for two problems called R||Cmax with simple job-intersection structure and R||Cmax with bounded job assignments. We conclude this thesis by presenting algorithmic and computational complexity results for a generalization of R||Cmax where J is partitioned into sets called bags, and it must be that no two jobs belonging to the same bag are scheduled on the same machine

Mobile Ad-Hoc Networks

Being infrastructure-less and without central administration control, wireless ad-hoc networking is playing a more and more important role in extending the coverage of traditional wireless infrastructure (cellular networks, wireless LAN, etc). This book includes state-of-the-art techniques and solutions for wireless ad-hoc networks. It focuses on the following topics in ad-hoc networks: quality-of-service and video communication, routing protocol and cross-layer design. A few interesting problems about security and delay-tolerant networks are also discussed. This book is targeted to provide network engineers and researchers with design guidelines for large scale wireless ad hoc networks

Developing Advanced Academic Degree Educational Profiles for Career Fields

This research develops a career field\u27s educational profile through use of the decision analysis approach of value-focused thinking (VFT). VFT is used to solicit the capabilities that the career field manager (CFM) desires its officers obtain from an advanced academic program. This process generates a value hierarchy and a focused set of alternatives (degree programs). The academic programs\u27 content are evaluated against the hierarchy to determine how well it meets the values of the functional area. A rankordered list of degrees is produced and a portfolio of degrees is selected through the use of CFM-approved goal-setting criteria. The specific breakdown of the portfolio into percentages of the force that should attain each degree is then determined through the CFM\u27s specified relative value increments of the goal-setting criteria. The resulting effort creates a guide for CFMs to communicate to their corps on the types of degrees to earn and provides justification for fully-funded degree slots

Journal of Telecommunications and Information Technology, 2011, nr 3

kwartalni

2012-2013 Louisiana Tech University Catalog

The Louisiana University Catalog includes announcements and course descriptions for courses offered at Louisiana Tech University for the academic year of 2012-2013.https://digitalcommons.latech.edu/university-catalogs/1003/thumbnail.jp

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Programmation dynamique avec approximation de la fonction valeur

L'utilisation d'outils pour l'approximation de la fonction de valeur est essentielle pour pouvoir traiter des problèmes de prise de décisions séquentielles de grande taille. Les méthodes de programmation dynamique (PD) et d'apprentissage par renforcement (A/R) introduites aux chapitres 1 et 2 supposent que la fonction de valeur peut être représentée (mémorisée) en attribuant une valeur à chaque état (dont le nombre est supposé fini), par exemple sous la forme d'un tableau. Ces méthodes de résolution, dites exactes, permettent de déterminer la solution optimale du problème considéré (ou tout au moins de converger vers cette solution optimale). Cependant, elles ne s'appliquent souvent qu'à des problèmes jouets, car pour la plupart des applications intéressantes, le nombre d'états possibles est si grand (voire infini dans le cas d'espaces continus) qu'une représentation exacte de la fonction ne peut être parfaitement mémorisée. Il devient alors nécessaire de représenter la fonction de valeur, de manière approchée, à l'aide d'un nombre modéré de coefficients, et de redéfinir et analyser des méthodes de résolution, dites approchées pour la PD et l'A/R, afin de prendre en compte les conséquences de l'utilisation de telles approximations dans les problèmes de prise de décisions séquentielles

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp