CS702 : Advanced Algorithms Analysis and Design

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Course Info

Course Category

Computer Science/Information Technology

Course Level


Credit Hours





Dr. N. A. Zafar
Ph.D Computer Science
Kyushu University, Japan

Course Contents

Introduction, Mathematical Tools, Logic and Proving Techniques, Proofs, Validation, Verification, Strong Math. Induction, Fibonacci Sequences, Recurrence Relations: Mathematical Models, Analysis Techniques, Recurrence Relations: Algorithms Design and Analysis Techniques, Further Techniques Solving Recurrence Relations, Time Complexity Measuring Notations, Relations over Asymptotic Notations, Brute Force Approach: Introduction, Starting with Primality, Sorting sequence of numbers, Designing Algorithms using Brute Force and Divide & Conquer Approaches, Designing Algorithms using Divide & Conquer Approaches, Dynamic Programming for Solving Optimization Problems: Chain Matrix Multiplication Problem, Chain Matrix Multiplication Problem using Dynamic Programming, Assembly-Line Scheduling Problem, 2-Line Assembly Scheduling Problem, n-Line Assembly Scheduling Problem, 0-1 Knapsack Problem's Algorithm using Dynamic Programming, Optimal Weight Triangulation, Optimal Weight Triangulation using Dynamic Programming, Longest Common Subsequence, Optimal Binary Search Trees, Dynamic Programming: Optimal Binary Search Trees, Greedy Algorithms, Greedy Algorithms: Activity Selection Algorithm, Fractional Knapsack, Coin Change Making, Greedy Algorithms: Huffman Coding, Huffman Coding Problem, Road Trip Problem, Graph Theoretic Concepts, Breadth First Search: Shortest Paths, Proof of Breadth First Search Algorithm, Depth First Search, Proof of White Path Theorem, Applications of Depth First Search, Backtracking, Branch & Bound Algorithms, Minimal Spanning Tree Problem, Kruskal's Algorithm, Prim's Algorithm, Road Map Problem, Paths and Shortest Paths, Bellman-Ford Algorithm, Proof: Bellman Ford Algorithm, Shortest Paths in Directed Acyclic Graphs, Dijkstra's Algorithm: Problem Statement, Analysis, Correctness, All-Pairs Shortest Paths, Shortest Paths and Matrix Multiplication, The Floyd-Warshall Algorithm, Johnson's Algorithm, Number Theoretic Algorithms: Definitions and Some Important Results, Number Theoretic Algorithms: GCD, Euclid's Algorithm, Groups and Rings, Groups and Rings, Chinese Remainder Theorem, RSA Cryptosystem, Fermat Theorem, Euler's Theorem, RSA Cryptosystem, String Matching Problem, String Matching: Naive Algorithm, Rabin-Karp Algorithm, String Match. with Finite Automata, Polynomials and Fast Fourier Transform: Representation of Polynomials, The DFT and FFT, NP Completeness: Circuit Satisfiability; Proof: Formula Satisfiability, 3-CNF; Clique