What are algorithms 2
• Introduction: The satisfiability problem, 2-Sat, probabilistic algorithm for 2-SAT.
• NP completeness: meaning, examples.
• Graph algorithms: minimal cut, shortest paths between all pairs of nodes, matching, the marriage problem, 3-colorability.
• Algebraic and number theoretic algorithms: multiplication of large numbers, matrix multiplication, modular exponentiation, factorization: Pollard's rho and (p-1) algorithms, quadratic sieve.
• Approximation algorithms: 0/1 Rucksack, Max-Cut, Traveling-Salesman and Delta-TSP, Max-k-SAT, # DNF-SAT
• Parameterized algorithms. Basic methods: restricted search trees, reduction to the core of the problem, graph properties that can be changed, color coding.
• On-line algorithms: The paging problem and the distribution of work problem: deterministic and probabilistic algorithms.
|leaf||Lecture material||Material / links||correction|
|page 1||Cover, SAT, complexity classes|
Turing reduction, min cut2-SAT
|Sheet 3||APD algorithm||Java Matrix Package|
|Sheet 4||APSP algorithm||Proposed solution|
- T.H. Cormen, C.E. Leiserson, R.L. Rivest: Introduction to Algorithms. MIT Press, 1990.
- M.R. Garey, D.S. Johnson: Computers and Intractability - A Guide to the Theory of NP Completeness. Freeman, 1979.
- A. Gibbons, W. Rytter: Efficient Parallel Algorithms. Cambridge University Press, 1988.
- M. Goemans: Lecture Notes on On-Line Algorithms. ftp://theory.lcs.mit.edu/pub/classes/18.415/notes-online.ps
- D. Kozen: The design and Analysis of Algorithms. Springer, 1992.
- N. Lynch: Distributed Algorithms. Morgan Kaufmann, 1996.
- R. Motwani, P. Raghavan: Randomized Algorithms. Cambridge University Press, 1995.
- R. Niedermeier: Parameterized algorithm script from the University of Tübingen. http://www-fs.informatik.uni-tuebingen.de/lehre/ss99/paal.html
- C.H. Papadimitriou: Computational Complexity. Addison-Wesley, 1994.
- U. Schöning: Algorithmics. Spectrum Academic Publishing House, 2001.
- A. Lenstra: Integer factoring. Designs, Codes and Cryptography 19, 101-128 (2000).
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