Algorithmen - kurz gefasst (German Edition) by Uwe Schöning

By Uwe Schöning

In kompakter shape macht das Buch mit den wesentlichen Themen vertraut, die in einer Vorlesung über Algorithmen behandelt werden. Im Mittelpunkt stehen dabei die verschiedensten sequentiellen Algorithmen, deren Komplexitätsanalyse und allgemeine Algoithmen-Paradigma. Prof. Schöning gelingt es, kurz, konkret und verständlich die wichtigsten algorithmischen Aufgabenstellungen (Selektion, Sortieren, Hashing), Algorithmen auf Graphen, algebraische und zahlentheoretische Verfahren zu behandeln. Hinzu kommen heuristische Algorithmenprinzipien wie z.B. genetisches Programmieren.

Show description

Read Online or Download Algorithmen - kurz gefasst (German Edition) PDF

Similar algorithms and data structures books

Bayesian estimation of state-space models using the Metropolis-Hastings algorithm within Gibbs sampling

During this paper, an try is made to teach a basic technique to nonlinear and/or non-Gaussian state-space modeling in a Bayesian framework, which corresponds to an extension of Carlin et al. (J. Amer. Statist. Assoc. 87(418} (1992) 493-500) and Carter and Kohn (Biometrika 81(3} (1994) 541-553; Biometrika 83(3) (1996) 589-601).

Statistical Analysis of Spherical Data

This is often the 1st entire, but truly offered, account of statistical tools for analysing round info. The research of knowledge, within the kind of instructions in area or of positions of issues on a round floor, is needed in lots of contexts within the earth sciences, astrophysics and different fields, but the technique required is disseminated during the literature.

Algorithmic Problem Solving (2007)

Algorithmic challenge fixing by way of Roland Backhouse.

2007 version (latest version is 2011).

Additional info for Algorithmen - kurz gefasst (German Edition)

Sample text

6. The problem is that it is not clear how to compute P(dl,... ,dj) efficiently. Hence, we use a different weight function U with the following properties: 1. U 0 < 1. 2. U(dl,... ,dj) >1m i n { U ( d l , . . ,dj,0), U(dl,... ,dj, 1)}. 3. U is an upper bound on P. 4. U can be computed in polynomial time. 50 Chapter 3. Derandomization The first two properties ensure that we can use U as a weight function. By the same inequality as for P we obtain U ( d l , . . , dr) < 1. Since U is an upper bound on P, this implies P ( d l , .

We only prove the first statement. The second statement can be proved in a similar way. We apply Markov's inequality to the moment generating function e tx and obtain for each t > 0: Prob[X > (1 + $)m] = Prob[e tx > e t(l+6)m] < e - t ( l + 8 ) m E[etX]. Now we exploit the independence of the Xj. 48 Chapter 3. Derandomization e-tO+~) m E[e tx] = = e-tO+~)m E[e~,lxl . . . E[~o~xq = e-t(l+~)'~H~jeta' +(1-pj)l]. 3) j-----1 Now we may choose t = In(1 + 5) and obtain r r (1 + 5)-(1+~)~ 1 ] [PJ (1 + 5)~ + 1 - pj] <.

2. 2. Las Vegas and Monte Carlo Algorithms 31 Note that a Las Vegas algorithm is a Monte Carlo algorithm with error probability 0. 3. The efficiency of such Las Vegas algorithm depends heavily on the time needed to verify the correctness of a solution to a problem. Thus, for decision problems, a Las Vegas algorithm derived from a Monte Carlo algorithm is in general useless. We may apply these definitions to the complexity classes introduced in the previous chapter: - The problems in the class ZT~P have efficient Las Vegas decision algorithms.

Download PDF sample

Rated 4.26 of 5 – based on 31 votes