# Advance Algorithms Semester 7 (BE Fourth Year) BE Computer Engineering University of Mumbai Topics and Syllabus

CBCGS [2019 - current]
CBGS [2015 - 2018]
Old [2000 - 2014]

## Syllabus

100 Introduction
• Asymptotic notations Big O, Big Θ,Big Ω,ο ,ω notations, Proofs of master theorem, applying theorem to solve problems.
• Red-Black Trees:- properties of red-black trees, Insertions, Deletions 2.2 B-Trees and its operations.
• Binomial Heaps:- Binomial trees and binomial heaps, Operation on Binomial heaps.
300 Dynamic Programing
• Matrix chain multiplication, cutting rod problem and its analysis.
400 Graph Algorithms
• Bellman ford algorithm, Dijkstra algorithm, Johnson’s All pair shortest path algorithm for sparse graphs
500 Maximum Flow
• Flow networks, the ford Fulkerson method, max bipartite matching, push Relabel Algorithm, The relabel to front algorithm.
600 Linear Programing
• Standard and slack forms, Formulating problems as linear programs, simplex algorithm, Duality, Initial basic feasible solution.
700 Computational Ggeometry
• Line Segment properties, Determining whether any pair of segment intersects, finding the convex hull, Finding the closest pair of points.