1,721,002 research outputs found
A monotone approximation algorithm for scheduling with precedence constraints
No full textWe provide a monotone -approximation algorithm for
scheduling related machines with precedence constraints
Approximation algorithms for scheduling and two-dimensional packing problems
Full text linkThis dissertation thesis is concerned with two topics of combinatorial optimization : scheduling and geometrical packing problems. Scheduling deals with the assignment of jobs to machines in a ‘good’ way, for suitable notions of good. Two particular problems are studied in depth : on the one hand, we consider the impact of machine failure on online scheduling, i.e. what are the consequences of the fact that in real life, machines do not work flawlessly around the clock, but need maintenance intervals or can break down? How do we need to adapt our algorithms to still obtain good overall schedules, and in what settings do we even have a chance to succeed? Our second problem is of a more static nature : in some settings, not every job is permitted on all the machines. A classical example would be that of workers which needs special qualification to execute some jobs, or a certain minimum requirement of memory size of computers, etc. The problem in general is notoriously hard to tackle; we present improved approximation ratios for several special cases. In particular, we derive a polynomial-time approximation scheme for nested interval restrictions, which occur naturally in many practical applications. Our final topic is two-dimensional geometric bin packing, the problem of packing rectangular objects into the minimum number of containers of identical size (figuratively speaking, we are arranging advertisements of fixed dimensions into the minimum number of print pages). It is known that no approximation ratio better than 2 is possible for this problem, unless P = NP; we present an algorithm that guarantees this ratio.Diese Promotionsschrift behandelt zwei Arten kombinatorischer Optimierungsprobleme : Ablaufplanungsprobleme und geometrische Packungsprobleme. Ablaufplanungsprobleme handeln davon, eine Menge von Aufgaben, die Jobs, auf eine Menge von ausführenden Maschinen oder Arbeitern zu verteilen, so dass
der entstehende Ablaufplan in geeignetem Sinne gut ist. Wir betrachten hier insbesondere folgende zwei Probleme der Ablaufplanung: einerseits untersuchen wir den Einfluß von Maschinenausfällen auf die Online-Ablaufplanung: im wirklichen Leben sind Maschinen nicht fehler- und
unterbrechungslos verfügbar. Wir geben eine teilweise Antwort auf die Frage, mit welchen Änderungen Algorithmen trotz unerwartet auftretender Maschinenausfälle gute Pläne erstellen können, und in welchen Fällen es prinzipiell nicht möglich ist, gute Ablaufpläne zu erstellen. Unser zweites Ablaufplanungsproblem ist von statischerer Natur: in der
praktischen Anwendung ist es häufig der Fall, dass nicht jede Maschine jeden Job ausführen kann. Ein einfaches Beispiel sind menschliche Arbeiter, die gewisse formale Qualifikationen für gewisse Jobs haben müssen. Diese Problem
erweist sich als in voller Allgemeinheit bekannt hartnäckig; wir stellen hier Algorithmen für einige Spezialfälle vor. Insbesondere präsentieren wir ein polynomielles Approximationsschema für den wichtigen Fall verschachtelter Restriktionen, der in der Mitarbeiterplanung auf natürliche
Weise auftritt. Schlussendlich untersuchen wir das zweidimensionale geometrische bin packing-Problem. Fragestellung dieses Problem ist es, rechteckige Objekte
in die minimale Anzahl von Containern gleicher Größe zu packen. Salopp gesprochen versuchen wir, eine vorgegebene Menge von Anzeigen mit vorgegebenen Abmessungen auf eine möglichst kleine Zahl von Druckseiten gleicher Größe zu platzieren. Es ist bekannt, dass dieses Problem keine
Algorithmus mit Approximationsgüte besser als 2 erlaubt, es sei denn, P = NP; wir stellen einen Algorithmus mit Güte 2 vor
A tale of two packing problems : improved algorithms and tighter bounds for online bin packing and the geometric knapsack problem
Full text linkIn this thesis, we deal with two packing problems: the online bin packing and the geometric knapsack problem. In online bin packing, the aim is to pack a given number of items of different size into a minimal number of containers. The items need to be packed one by one without knowing future items. For online bin packing in one dimension, we present a new family of algorithms that constitutes the first improvement over the previously best algorithm in almost 15 years. While the algorithmic ideas are intuitive, an elaborate analysis is required to prove its competitive ratio. We also give a lower bound for the competitive ratio of this family of algorithms. For online bin packing in higher dimensions, we discuss lower bounds for the competitive ratio and show that the ideas from the one-dimensional case cannot be easily transferred to obtain better two-dimensional algorithms. In the geometric knapsack problem, one aims to pack a maximum weight subset of given rectangles into one square container. For this problem, we consider online approximation algorithms. For geometric knapsack with square items, we improve the running time of the best known PTAS and obtain an EPTAS. This shows that large running times caused by some standard techniques for geometric packing problems are not always necessary and can be improved. Finally, we show how to use resource augmentation to compute optimal solutions in EPTAS-time, thereby improving upon the known PTAS for this case.In dieser Arbeit betrachten wir zwei Packungsprobleme: Online Bin Packing und das geometrische Rucksackproblem. Bei Online Bin Packing versucht man, eine gegebene Menge an Objekten verschiedener Größe in die kleinstmögliche Anzahl an Behältern zu packen. Die Objekte müssen eins nach dem anderen gepackt werden, ohne zukünftige Objekte zu kennen. Für eindimensionales Online Bin Packing beschreiben wir einen neuen Algorithmus, der die erste Verbesserung gegenüber dem bisher besten Algorithmus seit fast 15 Jahren darstellt. Während die algorithmischen Ideen intuitiv sind, ist eine ausgefeilte Analyse notwendig um das Kompetitivitätsverhältnis zu beweisen. Für Online Bin Packing in mehreren Dimensionen geben wir untere Schranken für das Kompetitivitätsverhältnis an und zeigen, dass die Ideen aus dem eindimensionalen Fall nicht direkt zu einer Verbesserung führen. Beim geometrischen Rucksackproblem ist es das Ziel, eine größtmögliche Teilmenge gegebener Rechtecke in einen einzelnen quadratischen Behälter zu packen. Für dieses Problem betrachten wir Approximationsalgorithmen. Für das Problem mit quadratischen Objekten verbessern wir die Laufzeit des bekannten PTAS zu einem EPTAS. Die langen Laufzeiten vieler Standardtechniken für geometrische Probleme können also vermieden werden. Schließlich zeigen wir, wie Ressourcenvergrößerung genutzt werden kann, um eine optimale Lösung in EPTAS-Zeit zu berechnen, was das bisherige PTAS verbessert.Google PhD Fellowshi
Approximation and Online Algorithms
No full textThis thesis presents results of our research in the area of optimization problems with incomplete information-our research is focused on the online scheduling problems. Our research is based on the worst-case analysis of studied problems and algorithms; thus we use methods of the competitive analysis during our research. Althrough there are many "real-world" industrial and theoretical applications of the online scheduling problems there are still so many open problems with so simple description. Therefore it is important, interesting and also challenging to study the online scheduling problems and their simplified variants as well. In this thesis we have shown the following our results of our research on the online scheduling problems: A 1.58-competitive online algorithm for the problem of randomized scheduling of unit jobs on a single processor, where the jobs are arriving over time and the total weight of processed jobs ismaximized. A lower bound 1.172 on the competitive ratio for the problem of randomized scheduling of 2-uniform unit jobs on a single processor, where the jobs are arriving over time andthe totalweight of processed jobs is maximized. A lower bound 1.25 on the competitive ratio for the problem of randomized scheduling of s-uniform unit jobs on a single processor where s is tending to..
Aproximační a online algoritmy
Full text linkThis thesis presents results of our research in the area of optimization problems with incomplete information-our research is focused on the online scheduling problems. Our research is based on the worst-case analysis of studied problems and algorithms; thus we use methods of the competitive analysis during our research. Althrough there are many "real-world" industrial and theoretical applications of the online scheduling problems there are still so many open problems with so simple description. Therefore it is important, interesting and also challenging to study the online scheduling problems and their simplified variants as well. In this thesis we have shown the following our results of our research on the online scheduling problems: A 1.58-competitive online algorithm for the problem of randomized scheduling of unit jobs on a single processor, where the jobs are arriving over time and the total weight of processed jobs ismaximized. A lower bound 1.172 on the competitive ratio for the problem of randomized scheduling of 2-uniform unit jobs on a single processor, where the jobs are arriving over time andthe totalweight of processed jobs is maximized. A lower bound 1.25 on the competitive ratio for the problem of randomized scheduling of s-uniform unit jobs on a single processor where s is tending to...Katedra aplikované matematikyDepartment of Applied MathematicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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