# Which is the best classified script online

## Approximation and online algorithms

### Dr. H.-J. Böckenhauer, Dr. D. Komm - Department of Computer Science - FS 2020

### Content of the lecture

This learning unit deals with approximate methods for difficult optimization problems and algorithmic approaches for solving online problems as well as the limits of these approaches.

### Events

The lecture and the exercises are now taking place as a video conference with the zoom system. The students enrolled for the lecture will each receive an invitation with the meeting number by email.

lecture | Wednesday | 13–15 | CAB G 59 | Start: February 19, 2020 |

Exercises | Wednesday | 15–16 | CAB G 59 | Start: February 26, 2020 |

### Lecture content

The references in the lecture part about approximation algorithms refer to the book given below *Algorithmics for Hard Problems* by J. Hromkovi & ccaron ;.

The references in the lecture part about online algorithms refer to the book given below *An Introduction to Online Computation* by D. Komm as well as the script given below by D. Komm.

**19.02.2020**Informal introduction*(Definition 4.2.1.1)*, Approximation algorithms for the metric TSP: spanning tree algorithm, Christofides algorithm*(Section 4.3.5 up to before exercise 4.3.5.6)***26.02.2020**Approximation algorithms for vertex covers*(Section 4.3.2 up to and including Lemma 4.3.2.5)*, Set cover*(see script below)*and weighted vertex cover*(Section 4.3.2 from the text after Exercise 4.3.2.18)***04.03.2020**Polynomial approximation schemes (PTAS and FPTAS)*(Definition 4.2.1.6)*, PTAS for the simple backpack problem (SKP)*(Section 4.3.4 up to and including Theorem 4.3.4.3)*, Definition of general backpack problem (KP) and exact algorithm for KP*(Section 3.2.2)***11.03.2020**FPTAS for the general backpack problem (KP)*(Section 4.3.4 from the text according to Theorem 4.3.4.10)*, Classification of optimization problems according to their approximability*(see script below)*, pseudopolynomial algorithms and strong NP severity*(Sections 3.2.1 and 3.2.4)***18.03.2020**Introduction of non-approximability*(Sections 4.4.1 and 4.4.2)*, AP reductions*(Section 4.4.3 up to and including Lemma 4.4.3.5)***25.03.2020**GP reductions*(Remainder of Section 4.4.3 from the text after Exercise 4.4.3.9 without Lemma 4.4.3.14)***01.04.2020**Probabilistic verifiers, the PCP theorem and its application to the proof of inapproximability*(Section 4.4.4)***08.04.2020**Unique-Games-Conjecture and connection with non-approximability*(see script below)*; Introduction to online algorithms*(Preface and section 1.1 to before definition 1.4 in the script; corresponds roughly to section 1.2 to and with Theorem 1.3 in the book)***23.04.2020**Definitions Online Minimization Problems, Online Algorithms, and Competitive Factor; the paging problem; FIFO is (strictly)*k*-competitive*(Script 1.1)*; no online algorithm is better than*k*-competitive*(Script 1.2)***29.04.2020**Randomized online algorithms and expected competitive factor*(Script 1.3)*; the randomized marking algorithm is (strictly)*H*-competitive_{k}*(Script 1.4)***06.05.2020**Introduction of lower bounds for randomized online algorithms; Yao's principle (Lemma 1.13 and Theorem 1.15,*Script 1.5*); lower bound of*H*for the expected costs of randomized online algorithms in paging (_{k}*Script 1.7*)**13.05.2020**The*k*-Server problem (*Script 3.0*), the*k*-Server guess that is randomized*k*-Server, the greedy algorithm on the line (*Script 3.1*), Potential functions (*Script 3.2*), the double coverage algorithm (*Script 3.3*)**20.05.2020**Introduction to advice complexity (*Script 4.0*), the advice complexity of paging (*Script 4.1*, except Proposition 4.7 all propositions without evidence), the advice complexity of*k*-Server (*Script 4.2*, all sentences without evidence)**27.05.2020**Advice and randomization (*Script 6.0*), the online backpack problem (*Script 5.0*) and deterministic (*Script 5.1*), Advice- (*Script 5.2 without the proof of Theorem 5.8*) and randomized (*Script 5.4, without the proof of Theorems 5.10, 5.11*) Algorithms

### Examination material

The examination material includes everything that was dealt with in the lecture, as well as the material of the exercise sheets and solutions.

### Scripts

Here there are links to scripts for topics of the lecture that are not included in this form in the specified literature.

### Exercises

### literature

- J. Hromkovič:
*Algorithmics for Hard Problems,*2004, Springer-Verlag, ISBN: 3-540-44134-4. - D. Come:
*An Introduction to Online Computation: Determinism, Randomization, Advice,*2016, Springer-Verlag, ISBN: 3-319-42747-4;

a script containing parts of the book is available online.

**Contact:** Dr. Dennis Come on, **Disclaimer of liability**, **last change:** 28.05.2020 13:50.

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