Algorithms and Complexity

  • Dieter Jungnickel
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 5)

Abstract

In this chapter, we show in an intuitive manner what an algorithm is and develop a way to measure the quality of algorithms. In particular, we consider some basic aspects of graph theoretic algorithms such as, for example, the problem of how to represent a graph. Moreover, we need a way to formulate the algorithms we deal with. We shall illustrate and study these concepts quite thoroughly using two specific examples, namely Euler tours and acyclic digraphs. At the end of the chapter we consider a class of apparently very difficult problems (the so-called NP-complete problems) which plays a central role in complexity theory; we will meet this type of problem over and over again in this book.

Keywords

Polynomial Time Decision Problem Complexity Theory Hamiltonian Cycle Vertex Cover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dieter Jungnickel
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

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