Shortest Paths Revisited, NP-Complete Problems and What To Do About Them

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Shortest Paths Revisited, NP-Complete Problems and What To Do About Them

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  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: The primary topics in this part of the specialization are: shortest paths (Bellman-Ford, Floyd-Warshall, Johnson), NP-completeness and what it means for the algorithm designer, and strategies for coping with computationally intractable problems (analysis of heuristics, local search).

Who is this class for: Learners with at least a little bit of programming experience who want to learn the essentials of algorithms. In a University computer science curriculum, this course is typically taken in the third year.

Created by:  Stanford University
  • Taught by:  Tim Roughgarden, Professor

    Computer Science
Basic Info Course 4 of 4 in the Algorithms Sp…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

About this course: The primary topics in this part of the specialization are: shortest paths (Bellman-Ford, Floyd-Warshall, Johnson), NP-completeness and what it means for the algorithm designer, and strategies for coping with computationally intractable problems (analysis of heuristics, local search).

Who is this class for: Learners with at least a little bit of programming experience who want to learn the essentials of algorithms. In a University computer science curriculum, this course is typically taken in the third year.

Created by:  Stanford University
  • Taught by:  Tim Roughgarden, Professor

    Computer Science
Basic Info Course 4 of 4 in the Algorithms Specialization Level Intermediate Commitment 4 weeks of study, 4-8 hours/week Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Coursework

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Stanford University The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is an American private research university located in Stanford, California on an 8,180-acre (3,310 ha) campus near Palo Alto, California, United States.

Syllabus


WEEK 1


Week 1
The Bellman-Ford algorithm; all-pairs shortest paths.


14 videos, 4 readings expand


  1. Reading: Week 1 Overview
  2. Reading: Overview, Resources, and Policies
  3. Reading: Lecture Slides
  4. Video: Single-Source Shortest Paths, Revisted
  5. Video: Optimal Substructure
  6. Video: The Basic Algorithm I
  7. Video: The Basic Algorithm II
  8. Video: Detecting Negative Cycles
  9. Video: A Space Optimization
  10. Video: Internet Routing I [Optional]
  11. Video: Internet Routing II [Optional]
  12. Video: Problem Definition
  13. Video: Optimal Substructure
  14. Video: The Floyd-Warshall Algorithm
  15. Video: A Reweighting Technique
  16. Video: Johnson's Algorithm I
  17. Video: Johnson's Algorithm II
  18. Reading: Optional Theory Problems (Week 1)

Graded: Problem Set #1
Graded: Programming Assignment #1

WEEK 2


Week 2
NP-complete problems and exact algorithms for them.


11 videos, 2 readings expand


  1. Reading: Week 2 Overview
  2. Video: Polynomial-Time Solvable Problems
  3. Video: Reductions and Completeness
  4. Video: Definition and Interpretation of NP-Completeness I
  5. Video: Definition and Interpretation of NP-Completeness II
  6. Video: The P vs. NP Question
  7. Video: Algorithmic Approaches to NP-Complete Problems
  8. Video: The Vertex Cover Problem
  9. Video: Smarter Search for Vertex Cover I
  10. Video: Smarter Search for Vertex Cover II
  11. Video: The Traveling Salesman Problem
  12. Video: A Dynamic Programming Algorithm for TSP
  13. Reading: Optional Theory Problems (Week 2)

Graded: Problem Set #2
Graded: Programming Assignment #2

WEEK 3


Week 3
Approximation algorithms for NP-complete problems.


6 videos, 1 reading expand


  1. Reading: Week 3 Overview
  2. Video: A Greedy Knapsack Heuristic
  3. Video: Analysis of a Greedy Knapsack Heuristic I
  4. Video: Analysis of a Greedy Knapsack Heuristic II
  5. Video: A Dynamic Programming Heuristic for Knapsack
  6. Video: Knapsack via Dynamic Programming, Revisited
  7. Video: Ananysis of Dynamic Programming Heuristic

Graded: Problem Set #3
Graded: Programming Assignment #3

WEEK 4


Week 4
Local search algorithms for NP-complete problems; the wider world of algorithms.


11 videos, 3 readings expand


  1. Reading: Week 4 Overview
  2. Video: The Maximum Cut Problem I
  3. Video: The Maximum Cut Problem II
  4. Video: Principles of Local Search I
  5. Video: Principles of Local Search II
  6. Video: The 2-SAT Problem
  7. Video: Random Walks on a Line
  8. Video: Analysis of Papadimitriou's Algorithm
  9. Video: Stable Matching [Optional]
  10. Video: Matchings, Flows, and Braess's Paradox [Optional]
  11. Video: Linear Programming and Beyond [Optional]
  12. Video: Epilogue
  13. Reading: Optional Theory Problems (Week 4)
  14. Reading: Info and FAQ for final exam

Graded: Problem Set #4
Graded: Programming Assignment #4
Graded: Final Exam
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