NP Completeness

External

• https://www.coursera.org/learn/algorithms-npcomplete/lecture/8HT5O/polynomial-time-solvable-problems
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/o1CGE/reductions-and-completeness
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/vZ9Bc/definition-and-interpretation-of-np-completeness-i
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/3JqiX/definition-and-interpretation-of-np-completeness-ii
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/VZY2Z/the-p-vs-np-question
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/jugfP/algorithmic-approaches-to-np-complete-problems
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/fxmkY/the-vertex-cover-problem
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/2or0q/smarter-search-for-vertex-cover-i
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/lPiFO/smarter-search-for-vertex-cover-ii
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/EAWJa/a-greedy-knapsack-heuristic
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/OR1PW/analysis-of-a-greedy-knapsack-heuristic-i
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/kGddv/analysis-of-a-greedy-knapsack-heuristic-ii
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/gXaGS/a-dynamic-programming-heuristic-for-knapsack
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/qtdIZ/knapsack-via-dynamic-programming-revisited
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/ApF82/ananysis-of-dynamic-programming-heuristic
• https://www.coursera.org/learn/algorithms-npcomplete/lecture/8Pe2F/stable-matching-optional

Internal

• Algorithms

Overview

Almost all the algorithms mentioned so far have been polynomial-time algorithms, which is to say that on an input of size n, their worst running time is O(n^k) for some constant k. Generally, we think of a problem that is solvable by a polynomial-time algorithm as tractable or easy. A problem that requires super-polynomial time is designated intractable or hard. There are also problems whose status is unknown: no polynomial-time algorithm has been yet discovered for them, nor has anyone yet been able to prove that no polynomial-time algorithm can exist for any of them. This class of problems is called NP-complete problems. The set of NP-complete problems has the property that if an efficient algorithm exists for any one of them, then efficient algorithms exist for all of them. There are methods to show that a problem is NP-complete, and if that is the case, an approximation algorithm instead of a polynomial-time algorithm, can be developed form it.

TODO.

Subjects

• Traveling Salesman Problem
• Local Search
  • The Maximum Cut Problem
  • The 2SAT Problem