# 272-0302-00L Approximation and Online Algorithms

Semester | Spring Semester 2020 |

Lecturers | H.‑J. Böckenhauer, D. Komm |

Periodicity | yearly recurring course |

Language of instruction | German |

Abstract | This lecture deals with approximative algorithms for hard optimization problems and algorithmic approaches for solving online problems as well as the limits of these approaches. |

Objective | Get a systematic overview of different methods for designing approximative algorithms for hard optimization problems and online problems. Get to know methods for showing the limitations of these approaches. |

Content | Approximation algorithms are one of the most succesful techniques to attack hard optimization problems. Here, we study the so-called approximation ratio, i.e., the ratio of the cost of the computed approximating solution and an optimal one (which is not computable efficiently). For an online problem, the whole instance is not known in advance, but it arrives pieceweise and for every such piece a corresponding part of the definite output must be given. The quality of an algorithm for such an online problem is measured by the competitive ratio, i.e., the ratio of the cost of the computed solution and the cost of an optimal solution that could be given if the whole input was known in advance. The contents of this lecture are - the classification of optimization problems by the reachable approximation ratio, - systematic methods to design approximation algorithms (e.g., greedy strategies, dynamic programming, linear programming relaxation), - methods to show non-approximability, - classic online problem like paging or scheduling problems and corresponding algorithms, - randomized online algorithms, - the design and analysis principles for online algorithms, and - limits of the competitive ratio and the advice complexity as a way to do a deeper analysis of the complexity of online problems. |

Literature | The lecture is based on the following books: J. Hromkovic: Algorithmics for Hard Problems, Springer, 2004 D. Komm: An Introduction to Online Computation: Determinism, Randomization, Advice, Springer, 2016 Additional literature: A. Borodin, R. El-Yaniv: Online Computation and Competitive Analysis, Cambridge University Press, 1998 |