ADVANCED ALGORITHMS (Professional Elective - V) IV Year B.Tech. CSE I -Sem JNTUH R-18

1. Explain the role of algorithms in computing and analyze the importance of different order notations for runtime complexity.

2. Derive and solve recurrence relations for algorithms like Fibonacci sequence and binary search to analyze their performance.

3. Compare and contrast the efficiency of Heap sort, Quick sort, and Merge sort for different input sizes and data distributions.

4. Explain the concept of in-place sorting and discuss why algorithms like Bubble sort require more memory while algorithms like Merge sort are considered space-efficient.

5. Analyze the limitations of comparison-based sorting and discuss the potential of counting sort and radix sort for specific types of data.

Unit 2: Greedy Algorithms and Graph Algorithms:

1. Describe the principles of greedy algorithms and explain how they are used to solve problems like Huffman code generation and activity selection.

2. Analyze the amortized time complexity of operations like union-find in disjoint-set structures to understand their average-case performance.

3. Explain the algorithms for Topological sorting, finding Minimum Spanning Trees (Kruskal's and Prim's algorithms), and Single Source Shortest Paths (Dijkstra's algorithm).

4. Apply Maximum Flow algorithms like Ford-Fulkerson to model and solve real-world problems involving resource allocation and network flow optimization.

5. Discuss the trade-offs between time complexity and space complexity in the context of different graph algorithms and choose appropriate algorithms for specific scenarios.

Unit 3: Sorting Networks and Matrix Operations:

1. Explain the concept of sorting networks and analyze the efficiency of comparison networks like bitonic sorting network.

2. Use the zero-one principle to prove that any sorting network that sorts n numbers must have at least log2(n!) comparisons.

3. Describe Strassen's algorithm for matrix multiplication and compare its time complexity with the traditional method.

4. Discuss efficient algorithms for inverting matrices and solving systems of linear equations, considering factors like numerical stability and error propagation.

5. Analyze the practical applications of advanced matrix operations in fields like image processing, scientific computing, and data analysis.

Unit 4: String Matching:

1. Implement and analyze the Naive String Matching algorithm and discuss its limitations for large datasets.

2. Explain the Rabin-Karp algorithm for string matching and analyze its time complexity with hashing techniques.

3. Describe how finite automata can be used for pattern matching and discuss their advantages and limitations compared to traditional algorithms.

4. Analyze the Knuth-Morris-Pratt (KMP) algorithm for string matching and explain its efficient pattern pre-processing technique.

5. Apply string matching algorithms to solve real-world problems like plagiarism detection, information retrieval, and bioinformatics sequence analysis.

Unit 5: NP-Completeness and Approximation Algorithms:

1. Define the concepts of polynomial time and polynomial time verification in the context of algorithm complexity.

2. Explain the idea of NP-completeness and reducibility, and discuss how it helps classify problems based on their computational difficulty.

3. Identify and analyze examples of NP-complete problems like Vertex Cover and Traveling Salesman Problem.

4. Discuss the role of approximation algorithms in dealing with NP-complete problems and analyze the trade-offs between optimality and efficiency.

5. Apply approximation algorithms for problems like Vertex Cover and Traveling Salesman Problem and evaluate their performance compared to exact solutions.