Introduction to Graph Algorithms

ABOUT THE COURSE: A Computer is basically an information processing system and this means it can be used for solving only abstract mathematical problems. That is why, solving a Real World Problem (RWP) by using a computer, begins with a formulation of the RWP as a Mathematical problem in an appropriate mathematical domain. For example, privacy and security problems are formulated as cryptographic problems in Number Theory, Elliptic Curves and Linear Algebra.Mathematical domains such as combinatorics, Geometry, Sets and Relations, Number Theory, Stringology and Graph Theory are among most frequently used domains to arrive at mathematical problems that are equivalent to the real-world problems.In this course we focus on basic graph algorithms. Problems arising in communication networks, social networks and transportation networks are naturally modelled as problems on graphs. Graph algorithms are among the extensively investigated and applied topics in computer science. INTENDED AUDIENCE: UG/PG StudentsPREREQUISITES: Discrete Mathematics, Graph Theory, Basics of Programming and Data StructuresINDUSTRY SUPPORT: Infosys, TCS, MSR

Week 1: Principles of algorithms

Week 2:Introduction to directed and undirected graphs

Week 3:DAGs and incremental algorithms

Week 4:DFS, BFS of directed and undirected graph

Week 5:Application of DFS – cut vertices/bridges of a graph

Week 6:MST

• Incremental greedy template
• Krushkals algorithms and partition ADT
• PRIMS algorithm and Fibonacci Heaps

Week 7:SSSP

Week 8:APSP