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About 10,000 papers for “approximation algorithms”

Approximation Algorithms

Weihe, Karsten · TIB KMO / FLOWWORKS GmbH · 2012

Auf Basis analytischer Sachverhalte entwickeln wir algorithmische Ideen für Verfahren auf Graphen. Daraus entstehen zunächst generische Verfahren, welche formal bezüglich ihrer Korrektheit und Laufzeit analysiert werden. Im Anschluss daran werden in jedem Kapitel Techniken zur Verbesserung und Beschleunigung vorgestellt. Abgerundet wird der Stoffplan durch zahlreiche Modellierungs- und Anwendungsbeispiele und der (optionalen) Implementierung eines Benchmarks verschiedener algorithmischer Varianten.

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Approximation Algorithms

Lecturer Michel, Michel X. Goemans · 1994

Introduction Many of the optimization problems we would like to solve are NP-hard. There are several ways of coping with this apparent hardness. For most problems, there are straightforward exhaustive search algorithms, and one could try to speed up such an algorithm. Techniques which can be used include divide-and-conquer (or the refined branch-and-bound which allows to eliminate part of the search tree by computing, at every node, bounds on the optimum value), dynamic programming (which sometimes leads to pseudo-polynomial algorithms), cutting plane algorithms (in which one tries to refine a linear programming relaxation to better match the convex hull of integer solutions), randomization, etc. Instead of trying to obtain an optimum solution, we could also settle for a suboptimal solution. The latter approach refers to heuristic or "rule of thumb" methods. The most widely used such methods involve some sort of local search of the problem space, yielding a lo

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Approximation algorithms

Darija Ćorić · Repository of Faculty of Science · 2022

Glavni cilj ovog rada je predstaviti najefikasnije načine rješavanja zadanih algoritama.

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Approximation Algorithms

Schulz, Andreas S., Shmoys, David B., Williamson, David P. · DepositOnce · 1997

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models which capture 106 separate "yes" or "no" decisions to be made. Although one could, in principle, try all 210^6 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past six years, there have been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees: this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

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Approximation Algorithms

Hans Jürgen Prömel, Angelika Steger · Advanced lectures in mathematics · 2002

In Chapter 3 we have seen that the Steiner problem in networks is 𝒩𝒫-complete. It is thus unlikely that there exists an efficient (polynomial time) algorithm for its solution.

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CS880: Approximation Algorithms

Scribe Tom, Watson Lecturer, Shuchi Chawla · 2008

In this lecture we continue our discussion of inapproximability by discussing results based on probabilistically checkable proofs (PCPs). In particular, we show how the PCP Theorem, a deep result in computational complexity, is essentially equivalent to the inapproximability of MAX-3SAT. We also show how a strengthening of the PCP Theorem leads to a tight inapproximability result for MAX-3SAT, and we discuss other issues related to PCPs. 28.1 Probabilistically Checkable Proofs Recall the template developed in the last lecture for proving inapproximability results. One exhibits a reduction from an NP-complete problem such as SAT to an optimization (say, maximization) problem L in such a way that Yes instances are mapped to instances with optimal objective value at least some α and No instances are mapped to instances with optimal objective value at most some β. The existence of such a reduction proves that L is NP-hard to approximate within any factor better than α/β. In the last lecture we saw examples where standard NP-hardness reductions were used to obtain weak inapproximability results in the above way, and self-reductions were used to magnify the hardness factor achieved. These reductions primarily exploited properties of the problem for which an inapproximability result was desired, i.e. the problem being reduced to. In

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