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6.856J Randomized Algorithms (MIT) 6.856J Randomized Algorithms (MIT)

Description

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms. This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

Subjects

Randomized Algorithms | Randomized Algorithms | algorithms | algorithms | efficient in time and space | efficient in time and space | randomization | randomization | computational problems | computational problems | data structures | data structures | graph algorithms | graph algorithms | optimization | optimization | geometry | geometry | Markov chains | Markov chains | sampling | sampling | estimation | estimation | geometric algorithms | geometric algorithms | parallel and distributed algorithms | parallel and distributed algorithms | parallel and ditributed algorithm | parallel and ditributed algorithm | parallel and distributed algorithm | parallel and distributed algorithm | random sampling | random sampling | random selection of witnesses | random selection of witnesses | symmetry breaking | symmetry breaking | randomized computational models | randomized computational models | hash tables | hash tables | skip lists | skip lists | minimum spanning trees | minimum spanning trees | shortest paths | shortest paths | minimum cuts | minimum cuts | convex hulls | convex hulls | linear programming | linear programming | fixed dimension | fixed dimension | arbitrary dimension | arbitrary dimension | approximate counting | approximate counting | parallel algorithms | parallel algorithms | online algorithms | online algorithms | derandomization techniques | derandomization techniques | probabilistic analysis | probabilistic analysis | computational number theory | computational number theory | simplicity | simplicity | speed | speed | design | design | basic probability theory | basic probability theory | application | application | randomized complexity classes | randomized complexity classes | game-theoretic techniques | game-theoretic techniques | Chebyshev | Chebyshev | moment inequalities | moment inequalities | limited independence | limited independence | coupon collection | coupon collection | occupancy problems | occupancy problems | tail inequalities | tail inequalities | Chernoff bound | Chernoff bound | conditional expectation | conditional expectation | probabilistic method | probabilistic method | random walks | random walks | algebraic techniques | algebraic techniques | probability amplification | probability amplification | sorting | sorting | searching | searching | combinatorial optimization | combinatorial optimization | approximation | approximation | counting problems | counting problems | distributed algorithms | distributed algorithms | 6.856 | 6.856 | 18.416 | 18.416

License

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18.310 Principles of Discrete Applied Mathematics (MIT) 18.310 Principles of Discrete Applied Mathematics (MIT)

Description

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component. This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Subjects

probability | probability | probability theory counting | probability theory counting | pigeonhole principle | pigeonhole principle | Van der Waerden's theorem | Van der Waerden's theorem | Chernoff bounds | Chernoff bounds | counting | counting | coding | coding | sampling | sampling | random sampling | random sampling | Catalan families | Catalan families | generating functions | generating functions | chord diagrams | chord diagrams | linear programming | linear programming | simplex method | simplex method | Zero-Sum matrix | Zero-Sum matrix | network flows | network flows | maximum flow problem | maximum flow problem | sorting algorithms | sorting algorithms | QUICKSORT | QUICKSORT | median finding | median finding | sorting networks | sorting networks | Batcher's algorithm | Batcher's algorithm | Euclid's algorithm | Euclid's algorithm | Chinese Remainder Theorem | Chinese Remainder Theorem | cryptography | cryptography | RSA code | RSA code | primaility testing | primaility testing | FFT | FFT | Fast Fourier Transform | Fast Fourier Transform | Shannon's coding theorems | Shannon's coding theorems | Lempel-Ziv codes | Lempel-Ziv codes | linear codes | linear codes | hamming code | hamming code

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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18.310 Principles of Discrete Applied Mathematics (MIT)

Description

This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.

Subjects

probability | probability theory counting | pigeonhole principle | Van der Waerden's theorem | Chernoff bounds | counting | coding | sampling | random sampling | Catalan families | generating functions | chord diagrams | linear programming | simplex method | Zero-Sum matrix | network flows | maximum flow problem | sorting algorithms | QUICKSORT | median finding | sorting networks | Batcher's algorithm | Euclid's algorithm | Chinese Remainder Theorem | cryptography | RSA code | primaility testing | FFT | Fast Fourier Transform | Shannon's coding theorems | Lempel-Ziv codes | linear codes | hamming code

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.856J Randomized Algorithms (MIT)

Description

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

Subjects

Randomized Algorithms | algorithms | efficient in time and space | randomization | computational problems | data structures | graph algorithms | optimization | geometry | Markov chains | sampling | estimation | geometric algorithms | parallel and distributed algorithms | parallel and ditributed algorithm | parallel and distributed algorithm | random sampling | random selection of witnesses | symmetry breaking | randomized computational models | hash tables | skip lists | minimum spanning trees | shortest paths | minimum cuts | convex hulls | linear programming | fixed dimension | arbitrary dimension | approximate counting | parallel algorithms | online algorithms | derandomization techniques | probabilistic analysis | computational number theory | simplicity | speed | design | basic probability theory | application | randomized complexity classes | game-theoretic techniques | Chebyshev | moment inequalities | limited independence | coupon collection | occupancy problems | tail inequalities | Chernoff bound | conditional expectation | probabilistic method | random walks | algebraic techniques | probability amplification | sorting | searching | combinatorial optimization | approximation | counting problems | distributed algorithms | 6.856 | 18.416

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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