Instructors: Dr. Nilanjan Datta, Dr. Laltu Sardar and Dr. Ritankar Mandal
Course Objective:
The course introduces the basics of computational complexity analysis and various algorithm design paradigms. The goal is to provide students with solid foundations to deal with a wide variety of computational problems, and to provide a thorough knowledge of the most common algorithms and data structures. After the course, a student should be able to analyze the asymptotic performance of algorithms, write rigorous correctness proofs for algorithms, and apply important algorithmic design paradigms and methods of analysis.
Syllabus:
- Introduction: Algorithm, Instance of a problem, Efficiency of algorithm, Growth of Functions, Asymptotic notation, Worst case, Best case, Average Case time complexity, Substitution method, Recursion tree method, Masters Theorem.
- Elementary Data Structure: Array, Linked list, Stack, Queue, Heap, Binary Search Tree, AVL Tree, Hash table, Disjoint Set Data Structure.
- Searching, Sorting and Order Statistics: Linear and Binary Search, Heap Sort, Quick Sort, Sorting in linear time, Order statistics, Finding Median in linear time.
- Divide and Conquer Paradigm: Merge Sort, Counting Inversion, Closest Pair of Points.
- Greedy Algorithms: Interval Scheduling Problem and its variants, Optimal Caching Problem, Minimum Spanning tree Problem, Huffman
Code, Clustering Problem, Fractional Knapsack problem, Dijkstra Algorithm. - Dynamic Programming: Matrix Chain Multiplication, Longest Common Subsequence, Optimal Binary Search Tree, Segmented Least Square Problem, 0/1-Knapsack Problem, Subset Sum Problem, Bellman Ford Algorithm.
- Graph algorithms: BFS, DFS, Floyd Warshall, Fold Fulkerson.
- Advanced Topics: P, NP, NPC (Circuit Satisfiability, Vertex Cover, Graph Coloring), Approximation Algorithm of some NPC Problems, Probabilistic Algorithm: Miller Rabin Primality Algorithm.
References:
[1] T. H. Cormen, C. E. Leiserson and R. L. Rivest: Introduction to Algorithms, PrenticeHall of India, New Delhi, 1998.
[2] J. Kleinberg, E. Tardos: Algorithm Design, Pearson Education, 2006.
[3] A. Aho, J. Hopcroft and J. Ullman: The Design and Analysis of Computer Algorithms, A. W. L, International Student Edition, Singapore, 1998.
[4] E. Horowitz, S. Sahni, S. A. Freed: Fundamentals of Data Structures in C, 2008.
[5] S. Baase: Computer Algorithms: Introduction to Design and Analysis, 2nd ed., Addison-Wesley, California, 1988.
Assignments:
- Assignment 1 [PDF] (Deadline: 16/02/2023)
- Assignment 2 [PDF] (Deadline: 28/02/2023)
- Assignment 3 [PDF] (Deadline: 30/03/2023)
- Assignment 4 [PDF] (Deadline: 31/05/2023)
Classes (by Dr. Nilanjan Datta):
- Introduction to Algorithms, Insertion Sort, Correctness using Loop Invariants, Analysis of Algorithms: Best Case, Average Case, Worst Case Analysis. [Class 1]
- Asymptotic Notation, Partitioning Array corresponding to a pivot element, Quick Sort, Merge Sort. [Class 2]
- Merging two arrays in linear time, In-place Merge Sort, Stable Sorting. [Class 3]
- Data Structures: Static and Dynamic array, Linked-list; Static and Dynamic Interfaces, Max-Heap, Building a Heap. [Class 4] [Data Structure: Video Lecture by Erik Demaine]
- Heap Sort, Priority Queue, The Lower bound time complexity of comparison-based Sorting. [Class 5]
- Selection in expected O(n) running time. [Class 6]
- Linear Time Sorting: Counting Sort, Radix Sort, Bucket Sort. [Class 7]
- Randomized Algorithms and Probabilistic Analysis: Hire Assistant Problem, Avg case complexity of Randomized Quick Sort, Randomized Selection, Bucket Sort. [Class 8]
- Order Statistics: Number of comparisons required to report the minimum, 2nd minimum, simultaneous minimum and maximum element, Selection in O(n) worst case. [Class 9]
- Runway Reservation Problem, Balanced Binary Search Tree, AVL Trees – Search, Insertion, Deletion. [Class 10] [Ref: Video Lecture by Erik Demaine]
- Red Black Tree: Definition, Properties, Searching in a Red Black Tree. [Class 11]
- Insertion in Red Black Tree, Optimal Binary Search Trees, Dynamic programming to solve Optimal Binary Search Trees. [Class 12] [Ref: Lecture Note]
- Class P, NP, NP-Complete, NP-Hard [Ref: Video Lecture by Erik Demaine]
- Approximation Algorithms, Vertex Cover Problem, Traveling Salesman Problem with triangle inequality. [Class 13]
Classes (by Dr. Laltu Sardar):
- Divide and Conquer Algorithms I: Finding the Closest Pair
- Divide and Conquer Algorithms II: The maximum Sub-array Problem
Classes (by Dr. Ritankar Mandal):
- Dynamic Programming [Notes]:
- Longest Increasing Sub-sequence
- Knapsack Problem
- Shortest Reliable Paths
- All-pair Shortest Path
- Travelling Salesman Problem
- Maximum Independent Set in a Tree
- Matrix Chain Multiplication