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Concept of Polynomial Time Computation
by Mayank Kumar
February 2, 2023
Unit 6: Intractability
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Syllabus
Unit 1: Searching, Sorting, Selection
- Linear Search
- Binary Search
- Insertion Sort
- Selection Sort
- Bubble Sort
- Heapsort
- Linear Time Sorting
- Selection Problem
- running time analysis and correctness
Unit 2: Graphs
- Review of graph traversals
- Graph connectivity
- Testing bipartite-ness
- Directed Acyclic Graphs and Topological Ordering
Unit 3: Divide and Conquer
- Introduction to divide and conquer technique
- Merge Sort
- Quick Sort
- Maximum-subarray problem
- Strassen’s algorithm for matrix multiplication
Unit 4: Greedy Algorithms
- Introduction to the Greedy algorithm design approach
- application to minimum spanning trees
- Fractional knapsack problem
- Correctness and Analysis of time complexity of Greedy Algorithms
Unit 5: Dynamic Programming
- Introduction to the Dynamic Programming Approach
- Application to subset sum
- integer knapsack problem
- Correctness and analysis of time complexity of Dynamic Programming
Unit 6: Intractability
- Concept of polynomial time computation
- Polynomial time reductions
- Decision vs optimization problems
- Introduction to NP
- NP-hard and NP-Complete classes