# Fundamental Algorithms - Winter 13

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**Term**- Winter 13
**Lecturer**- Prof. Dr. Michael Bader
**Time and Place**- Mon 8.30-10.00, lecture hall MI HS 3 (first lecture on Oct 21, 8.30)
**Audience**- Computational Science and Engineering; Biomedical Computing (elective)
**Tutorials**- ---
**Exam**- repeat exam: Tue, Apr 8, 2014 (17.00, MI 02.07.023, written exam)
**Semesterwochenstunden / ECTS Credits**- 2 SWS (2V) / 3 ECTS
**TUMonline**- https://campus.tum.de/tumonline/lv.detail?clvnr=950121698 (lecture),

https://campus.tum.de/tumonline/wbStpModHB.detailPage?&pKnotenNr=458187 (module description)

## Contents

# Contents

The course will provide an overview on the analysis of fundamental algorithms. Topics will be:

- Fundamentals: Models of Computation, Complexity Measures
- Sorting: Bubble-Sort, Merge-Sort, Quick-Sort, Median-Algorithms, Lower Bounds, etc.: sorting in parallel
- Searching: Hashing, Search Tress, etc.
- Arithmetic Problems: parallel prefix computation, parallel matrix and vector operations
- Foundations of parallel algorithms and simple models of parallel computation
- Algorithms on (weighted) graphs: traversals, shortest paths, etc.

# Announcements

- in the slot on Dec 23, we will do a short (40min) test exam, with discussion of solutions afterwards;

participation is entirely optional (questions and solutions will be made available towards the end of the Christmas holidays) - the lectures will start on Monday, Oct 21 (no lecture on Oct 14, due to semester opening)

# Lecture Notes and Material

## Lecture Slides

- Introduction - Algorithms, Fibonacci example, Asymptotics (Oct 21, Oct 28)
- slides
- Sorting - InsertSort, MergeSort, QuickSort (Oct 28, Nov 4, Nov 11)
- slides (with corrected proof for InsertionSort)
- Recurrences (Nov 11)
- slides
- Parallel Algorithms and PRAM (Nov 18, Nov 25)
- slides
- Parallel Sorting, Odd-Even MergeSort (Nov 25, Dec 2)
- slides
- Searching (Dec 2, Dec 9)
- slides
- AVL trees(Dec 9, Dec 16)
- slides
- Hash Tables (Dec 16, Jan 13)
- slides
- MidTerm Test (Dec 23)
- exercises and solutions
- Graphs (Jan 13, Jan 20)
- slides (DF/BF traversals updated)
- Weighted Graphs (Jan 20, Jan 27)
- slides (Dijkstra and Prim Algorithm are excluded for the exam)
- Exam (Feb 3)
- Due to the exam on Feb 3, there will be no lecture on that day

## Worksheets

- O-notation, etc. (Oct 21)
- worksheet and solution
- Complexity and Sorting (Oct 28)
- worksheet and solution
- MergeSort (Nov 4)
- worksheet and solution
- Recurrences(Nov 11)
- worksheet and solution (with slightly updated solution for Exercise 1)
- PRAM - Linear Algebra and Prefix Problem (Nov 18)
- worksheet and solution (slightly updated; leaves Ex. 3 for next week)
- PRAM - Prefix Problem and BucketSort (Nov 25)
- worksheet and solution (includes Ex. 3 from previous week)
- Sequential and Binary Search (Dec 2)
- worksheet and solution
- AVL trees (Dec 9)
- worksheet and solution
- Hashing (Dec 16)
- worksheet and solution
- Graphs (Jan 13)
- worksheet and solution
- Hypergraphs and Bipartite Graphs (Jan 20)
- worksheet and solution

## Exam

- a
**repeat exam**will be offered on**Tue, Apr 8, 17.00 (MI 02.07.023)**- the exam will be written
- all rules (helping material, etc.) are identical to the first exam

- Working time will be 90 minutes.
- Helping material: you are allowed to use
**one sheet (size A4) of paper**with**hand-written(!) notes**(on both sides) during the exam. Any further helping material (books, calculators, etc.) is forbidden! - Please use only blue or black ink during the exam.
- Exam topics are all topics covered during the lectures; see, in particular, the worksheets for this course
- Dijkstra and Prim Algorithm from Chapter 9 (Weighted Graphs) are excluded from the exam

## Literature

- Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms; MIT Press
- Berman, Paul: Algorithms: Sequential, Parallel, and Distributed; Cengage Learning Emea 2004
- Heun: Grundlegende Algorithmen; Vieweg 2000
- Sedgewick: Algorithms; Pearson Education
- Shackleford, Computing and Algorithms; Addison Wesley Longman
- Kleinberg, Tardos: Algorithm Design; Pearson Education