Searching for combinatorial optimization : 7 results found | RSS Feed for this search

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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18.997 Topics in Combinatorial Optimization (MIT) 18.997 Topics in Combinatorial Optimization (MIT)

Description

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms. In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

Subjects

combinatorial optimization | combinatorial optimization | Ear decompositions | Ear decompositions | Nonbipartite matching | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Minimization of submodular functions | Matroid intersection | Matroid intersection | Polymatroid intersection | Polymatroid intersection | Jump systems | Jump systems | Matroid union | Matroid union | Matroid matching | path matchings | Matroid matching | path matchings | Packing trees and arborescences | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Graph orientation | Connectivity tree and connectivity augmentation | Connectivity tree and connectivity augmentation | Multicommodity flows | Multicommodity flows | Connectivity tree | Connectivity tree | connectivity augmentation | connectivity augmentation | Gallai-Milgram Theorem | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | Bessy-Thomasse Theorem | paritioning graphs | paritioning graphs | covering graphs | covering graphs | directed paths | directed paths | directed cycles | directed cycles | matroid matching | matroid matching | path matching | path matching | packing directed cuts | packing directed cuts | Luchessi-Younger Theorem | Luchessi-Younger Theorem | packing trees | packing trees | arborescences | arborescences | submodular flows | submodular flows | Edmonds-Giles Theorem | Edmonds-Giles Theorem

License

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18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomization

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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18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomization

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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18.997 Topics in Combinatorial Optimization (MIT)

Description

In this graduate-level course, we will be covering advanced topics in combinatorial optimization. We will start with non-bipartite matchings and cover many results extending the fundamental results of matchings, flows and matroids. The emphasis is on the derivation of purely combinatorial results, including min-max relations, and not so much on the corresponding algorithmic questions of how to find such objects. The intended audience consists of Ph.D. students interested in optimization, combinatorics, or combinatorial algorithms.

Subjects

combinatorial optimization | Ear decompositions | Nonbipartite matching | Gallai-Milgram and Bessy-Thomasse theorems on partitioning/covering graphs by directed paths/cycles | Minimization of submodular functions | Matroid intersection | Polymatroid intersection | Jump systems | Matroid union | Matroid matching | path matchings | Packing trees and arborescences | Packing directed cuts and the Lucchesi-Younger theorem | Submodular flows and the Edmonds-Giles theorem | Graph orientation | Connectivity tree and connectivity augmentation | Multicommodity flows | Connectivity tree | connectivity augmentation | Gallai-Milgram Theorem | Bessy-Thomasse Theorem | paritioning graphs | covering graphs | directed paths | directed cycles | matroid matching | path matching | packing directed cuts | Luchessi-Younger Theorem | packing trees | arborescences | submodular flows | Edmonds-Giles Theorem

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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18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.

Subjects

linear programming | combinatorial optimization | network flow | matching theory | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms | NP-hard problems | discrete mathematics | fundamental algorithmic techniques | convex programming | flow theory | randomization

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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