Advanced Algorithms
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Follow on Instagram for UpdatesAdvanced Algorithms Syllabus — Unit-wise Content
The official GTU curriculum for Advanced Algorithms (subject code ME02000301) as prescribed for ITAC · Semester 2 divides the course into 6 units, covering 30 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (ME02000301)Unit 1 Sorting
- Review of various sorting algorithms
- topological sorting Graph: Definitions and Elementary Algorithms: Shortest path by BFS, shortest path in edge-weighted case (Dijkasra's)
- depth-first search and computation of strongly connected components
- emphasis on correctness proof of the algorithm and time/space analysis
- example of amortized analysis
Unit 2 Matroids
- Introduction to greedy paradigm
- algorithm to compute a maximum weight maximal independent set
- Application to MST
- Graph Matching: Algorithm to compute maximum matching
- Characterization of Maximum matching by augmenting paths
- Edmond's Blossom algorithm to compute augmenting path
Unit 3 Flow-Networks
- Maxflow-min cut theorem
- Ford-Fulkerson Method to comput e maximum flow
- Edmond-Karp maximum-flow algorithm
- Matrix Computations: Strassen's algorithm and introduction to divide and conquer paradigm
- inverse of a triangular matrix
- relation between the time complexities of basic matrix operations
Unit 4 Shortest Path in Graphs
- Floyd-Warshall algorithm and introduction to dynamic programming paradigm
- More examples of dynamic programming
- Modulo Representation of integers/polynomials: Chinese Remainder Theorem
- Conversion between base-representation and modulo-representation
- Extension to polynomials
- Application: Interpolation problem
Unit 5 Linear Programming
- Geometry of the feasibility region and Simplex Algorithm NP-completeness: Examples
- proof of NP-hardness and NP- completeness
- One or more of the following topics based on time and interest Approximation algorithms
- Randomized Algorithms
- Interior Point Method
- Advanced Number Theoretic Algorithm
Unit 6 Recent Trends
- Recent Trends in problem solving paradigms using recent searching and sorting techniques by applying recently proposed data structures
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