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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 TheoremLicense

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.htmSite sourced from

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This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms). This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms).Subjects

algorithms | algorithms | efficient algorithms | efficient algorithms | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide-and-conquer | divide-and-conquer | dynamic programming | dynamic programming | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | computational geometry | computational geometry | number-theoretic algorithms | number-theoretic algorithms | polynomial and matrix calculations | polynomial and matrix calculations | caching | caching | parallel computing | parallel computing | SMA 5503 | SMA 5503 | 6.046 | 6.046License

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See all metadata6.046J Introduction to Algorithms (MIT) 6.046J Introduction to Algorithms (MIT)

Description

This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.Subjects

algorithms | algorithms | efficient algorithms | efficient algorithms | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide-and-conquer | divide-and-conquer | dynamic programming | dynamic programming | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | computational geometry | computational geometry | number-theoretic algorithms | number-theoretic algorithms | polynomial and matrix calculations | polynomial and matrix calculations | caching | caching | parallel computing | parallel computing | 6.046 | 6.046 | 18.410 | 18.410License

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.htmSite sourced from

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See all metadata6.006 Introduction to Algorithms (MIT) 6.006 Introduction to Algorithms (MIT)

Description

Includes audio/video content: AV lectures. This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. Includes audio/video content: AV lectures. This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.Subjects

algorithms | algorithms | data structures | data structures | algorithm performance | algorithm performance | algorithm analysis | algorithm analysis | sorting | sorting | trees | trees | hashing | hashing | numerics | numerics | graphs | graphs | shortest paths | shortest paths | dynamic programming | dynamic programming | Python | PythonLicense

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.htmSite sourced from

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Includes audio/video content: AV lectures. This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms). Includes audio/video content: AV lectures. This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms).Subjects

algorithms | algorithms | efficient algorithms | efficient algorithms | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide-and-conquer | divide-and-conquer | dynamic programming | dynamic programming | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | computational geometry | computational geometry | number-theoretic algorithms | number-theoretic algorithms | polynomial and matrix calculations | polynomial and matrix calculations | caching | caching | parallel computing | parallel computingLicense

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.htmSite sourced from

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See all metadata1.225J Transportation Flow Systems (MIT) 1.225J Transportation Flow Systems (MIT)

Description

Design, operation, and management of traffic flows over complex transportation networks are the foci of this course. It covers two major topics: traffic flow modeling and traffic flow operations. Sub-topics include deterministic and probabilistic models, elements of queuing theory, and traffic assignment. Concepts are illustrated through various applications and case studies. This is a half-term subject offered during the second half of the semester. Design, operation, and management of traffic flows over complex transportation networks are the foci of this course. It covers two major topics: traffic flow modeling and traffic flow operations. Sub-topics include deterministic and probabilistic models, elements of queuing theory, and traffic assignment. Concepts are illustrated through various applications and case studies. This is a half-term subject offered during the second half of the semester.Subjects

transportation | transportation | transportation flow systems | transportation flow systems | traffic | traffic | traffic flow | traffic flow | networks | networks | transportation networks | transportation networks | flow modeling | flow modeling | flow operations | flow operations | deteministic models | deteministic models | probabilistic models | probabilistic models | queuing theory | queuing theory | queues | queues | traffic assignment | traffic assignment | case studies | case studies | cumulative plots | cumulative plots | airport runway capacity | airport runway capacity | runway capacity | runway capacity | road traffic | road traffic | shortest paths | shortest paths | optimizations | optimizations | highway control | highway control | ramp metering | ramp metering | simulation models | simulation models | isolated signals | isolated signals | operations | operations | operational problems | operational problems | air traffic operation | air traffic operation | air | air | road | road | component | component | 1.225 | 1.225 | ESD.205 | ESD.205License

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See all metadata6.046J Design and Analysis of Algorithms (MIT) 6.046J Design and Analysis of Algorithms (MIT)

Description

Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow, computational geometry, number-theoretic algorithms, polynomial and matrix calculations, caching, and parallel computing. Techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics include sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; greedy algorithms; amortized analysis; graph algorithms; and shortest paths. Advanced topics may include network flow, computational geometry, number-theoretic algorithms, polynomial and matrix calculations, caching, and parallel computing.Subjects

sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide and conquer | divide and conquer | dynamic programming | dynamic programming | greedy algorithms | greedy algorithms | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest pathsLicense

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.htmSite sourced from

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See all metadata6.006 Introduction to Algorithms (MIT) 6.006 Introduction to Algorithms (MIT)

Description

This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems. This course provides an introduction to mathematical modeling of computational problems. It covers the common algorithms, algorithmic paradigms, and data structures used to solve these problems. The course emphasizes the relationship between algorithms and programming, and introduces basic performance measures and analysis techniques for these problems.Subjects

algorithms | algorithms | python | python | python cost model | python cost model | binary search trees | binary search trees | hashing | hashing | sorting | sorting | searching | searching | shortest paths | shortest paths | dynamic programming | dynamic programming | numerics | numerics | document distance | document distance | longest common substring | longest common substring | dijkstra | dijkstra | fibonacci | fibonacci | image resizing | image resizing | chaining | chaining | hash functions | hash functions | priority queues | priority queues | breadth first search | breadth first search | depth first search | depth first search | memoization | memoization | divide and conquer | divide and conquerLicense

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.htmSite sourced from

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See all metadata6.856J 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 | 18.416License

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See all metadata11.332J Urban Design (MIT) 11.332J Urban Design (MIT)

Description

For many years, Cambridge, MA, as host to two major research universities, has been the scene of debates as to how best to meet the competing expectations of different stakeholders. Where there has been success, it has frequently been the result, at least in part, of inventive urban design proposals and the design and implementation of new institutional arrangements to accomplish those proposals. Where there has been failure it has often been explained by the inability - or unwillingness - of one stakeholder to accept and accommodate the expectations of another. The two most recent fall Urban Design Studios have examined these issues at a larger scale. In 2001 we looked at the possible patterns for growth and change in Cambridge, UK, as triggered by the plans of Cambridge University. And i For many years, Cambridge, MA, as host to two major research universities, has been the scene of debates as to how best to meet the competing expectations of different stakeholders. Where there has been success, it has frequently been the result, at least in part, of inventive urban design proposals and the design and implementation of new institutional arrangements to accomplish those proposals. Where there has been failure it has often been explained by the inability - or unwillingness - of one stakeholder to accept and accommodate the expectations of another. The two most recent fall Urban Design Studios have examined these issues at a larger scale. In 2001 we looked at the possible patterns for growth and change in Cambridge, UK, as triggered by the plans of Cambridge University. And iSubjects

urban planning | urban planning | community | community | stakeholders | stakeholders | development | development | urban growth | urban growth | MIT | MIT | Cambridge | Cambridge | Cambridgeport | Cambridgeport | institutional mechanisms | institutional mechanisms | housing | housing | universities | universities | built form | built form | public space | public space | landscape | landscape | path and access systems | path and access systems | parking | parking | density | density | activity location and intensity | activity location and intensity | planning | planning | finance | finance | public/private partnerships | public/private partnerships | parcelization | parcelization | phasing | phasing | multi-disciplinary teams | multi-disciplinary teams | town and gown | town and gown | Massachusetts | Massachusetts | research universities | research universities | urban design | urban design | Fort Washington | Fort Washington | urban form | urban form | biotech research industry | biotech research industry | activity location | activity location | activity intensity | activity intensity | access systems | access systems | paths | paths | 11.332 | 11.332 | 4.163 | 4.163License

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See all metadata18.S66 The Art of Counting (MIT) 18.S66 The Art of Counting (MIT)

Description

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment. The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.Subjects

enumerative combinatorics | enumerative combinatorics | finite set | finite set | sum of positive integers | sum of positive integers | bijective proofs | bijective proofs | bijection (one-to-one correspondence) | bijection (one-to-one correspondence) | permutations | permutations | partitions | partitions | Catalan numbers | Catalan numbers | Young tableaux | Young tableaux | lattice paths and tilings | lattice paths and tilingsLicense

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.htmSite sourced from

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See all metadataFolk Psychology, the Reactive Attitudes and Responsibility

Description

In this talk we first argue that the reactive attitudes originate in very fast non-voluntary processes involving constant facial feedback. In the second part we examine the supposed constitutive relation between the reactive attitudes and responsibility. This talk explores the connections between the folk psychological project of interpretation, the reactive attitudes and responsibility. The first section argues that the reactive attitudes originate in very fast and to a significant extent, non-voluntary processes involving constant facial feedback. These processes allow for smooth interaction between participants and are important to the interpretive practices that ground intimate relationships as well as to a great many less intense interactions. We will examine cases of facial paralysi Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Subjects

social relationships | facial paralysis | interpretation | psychopaths | facial feedback | Moebius Syndrome | reactive attitudes | Botox | social relationships | facial paralysis | interpretation | psychopaths | facial feedback | Moebius Syndrome | reactive attitudes | BotoxLicense

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See all metadataESD.36J System and Project Management (MIT) ESD.36J System and Project Management (MIT)

Description

The course is designed for students in the System Design and Management (SDM) program and therefore assumes that you already have a basic knowledge of project management. The objective is to introduce advanced methods and tools of project management in a realistic context such that they can be taken back to the workplace to improve management of development projects. In contrast to traditional courses on the subject we will emphasize scenarios that cannot be fully predicted such as task iterations, unplanned rework, perceived versus actual progress and misalignments between tasks, product architectures and organizations. This class was also offered in Course 13 (Department of Ocean Engineering) as 13.615J. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanica The course is designed for students in the System Design and Management (SDM) program and therefore assumes that you already have a basic knowledge of project management. The objective is to introduce advanced methods and tools of project management in a realistic context such that they can be taken back to the workplace to improve management of development projects. In contrast to traditional courses on the subject we will emphasize scenarios that cannot be fully predicted such as task iterations, unplanned rework, perceived versus actual progress and misalignments between tasks, product architectures and organizations. This class was also offered in Course 13 (Department of Ocean Engineering) as 13.615J. In 2005, ocean engineering subjects became part of Course 2 (Department of MechanicaSubjects

system and project management | system and project management | product development | product development | PERT | PERT | CPM | CPM | design structure matrix | design structure matrix | DSM | DSM | system dynamics | system dynamics | SD | SD | SPM | SPM | product development process | product development process | PDP | PDP | concurrent engineering | concurrent engineering | project monitoring | project monitoring | resource consumption | resource consumption | critical paths | critical paths | project progress | project progress | corrective action | corrective action | system dynamics models | system dynamics models | ESD.36 | ESD.36 | 1.432 | 1.432License

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.htmSite sourced from

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See all metadata6.046J Design and Analysis of Algorithms (MIT) 6.046J Design and Analysis of Algorithms (MIT)

Description

Includes audio/video content: AV lectures. This is an intermediate algorithms course with an emphasis on teaching techniques for the design and analysis of efficient algorithms, emphasizing methods of application. Topics include divide-and-conquer, randomization, dynamic programming, greedy algorithms, incremental improvement, complexity, and cryptography. Includes audio/video content: AV lectures. This is an intermediate algorithms course with an emphasis on teaching techniques for the design and analysis of efficient algorithms, emphasizing methods of application. Topics include divide-and-conquer, randomization, dynamic programming, greedy algorithms, incremental improvement, complexity, and cryptography.Subjects

algorithm | algorithm | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide and conquer | divide and conquer | dynamic programming | dynamic programming | greedy algorithms | greedy algorithms | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | cryptography | cryptographyLicense

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.htmSite sourced from

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See all metadata18.997 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 TheoremLicense

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.htmSite sourced from

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See all metadata6.046J Introduction to Algorithms (SMA 5503) (MIT)

Description

This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms).Subjects

algorithms | efficient algorithms | sorting | search trees | heaps | hashing | divide-and-conquer | dynamic programming | amortized analysis | graph algorithms | shortest paths | network flow | computational geometry | number-theoretic algorithms | polynomial and matrix calculations | caching | parallel computingLicense

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.htmSite sourced from

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See all metadataDescription

Subjects

cornelluniversitylibrary | mountainpasses | mountains | paths | rock | snow | tröllhálssnæfellsnesoghnappadalssýslaiceland | culidentifier:value=1923537 | culidentifier:lunafield=accessionLicense

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See all metadataTröllháls. N. Coast Snæfellsnes.

Description

Subjects

cornelluniversitylibrary | mountainpasses | mountains | paths | rock | snow | tröllhálssnæfellsnesoghnappadalssýslaiceland | culidentifier:value=1923536 | culidentifier:lunafield=accessionLicense

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cornelluniversitylibrary | lava | paths | rockformations | water | almannagjáþingvelliriceland | culidentifier:value=1923646 | culidentifier:lunafield=accessionLicense

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cornelluniversitylibrary | farmbuildings | farmhouses | farms | paths | turfhouses | grundborgarfjarðarsýslaicelandfarmstead | culidentifier:value=1923514 | culidentifier:lunafield=accessionLicense

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cornelluniversitylibrary | farmhouses | fences | paths | rock | turfhouses | reykholtborgarfjarðarsýslaicelandfarmstead | culidentifier:value=1923516 | culidentifier:lunafield=accessionLicense

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See all metadataThe Avalanche in the Path of Democratic Success

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cornelluniversitylibrary | politicalcartoons | portraits | sheetsinformationartifacts | illustrations | clevelandgrover | animals | donkeys | politics | caricatures | sugar | monopolies | mountains | paths | democraticparty | barrels | culidentifier:value=2214ca0032 | culidentifier:lunafield=idnumber | usfoodcartelsmonopolies | leaveourstaplefoodsaloneLicense

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Labanotation | movement | score | gestures | positions | paths | turns | jumps | hold signs | JISC digitisation and content | dance | notation | CCCEEDLicense

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

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Labanotation | movement | score | gestures | positions | paths | turns | jumps | hold signs | JISC digitisation and content | dance | notation | CCCEEDLicense

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

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See all metadataESD.36J System and Project Management (MIT)

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The course is designed for students in the System Design and Management (SDM) program and therefore assumes that you already have a basic knowledge of project management. The objective is to introduce advanced methods and tools of project management in a realistic context such that they can be taken back to the workplace to improve management of development projects. In contrast to traditional courses on the subject we will emphasize scenarios that cannot be fully predicted such as task iterations, unplanned rework, perceived versus actual progress and misalignments between tasks, product architectures and organizations. This class was also offered in Course 13 (Department of Ocean Engineering) as 13.615J. In 2005, ocean engineering subjects became part of Course 2 (Department of MechanicaSubjects

system and project management | product development | PERT | CPM | design structure matrix | DSM | system dynamics | SD | SPM | product development process | PDP | concurrent engineering | project monitoring | resource consumption | critical paths | project progress | corrective action | system dynamics models | ESD.36 | 1.432License

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.htmSite sourced from

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