ADVANCED TREES: Definitions Operations on Weight Balanced Trees (Huffman Trees), 2-3 Trees and Red- Black Trees.
Augmenting Red-Black Trees to Dynamic Order Statistics and Interval Tree Applications. Operations on Disjoint sets and its
union-find problem Implementing Sets. Dictionaries, Priority Queues and Concatenable Queues using 2-3 Trees.
Units: II
MERGEABLE HEAPS: Mergeable Heap Operations, Binomial Trees Implementing Binomial Heaps and its
Operations, 2-3-4. Trees and 2-3-4 Heaps. Amortization analysis and Potential Function of Fibonacci Heap
Implementing Fibonacci Heap. SORTING NETWORK: Comparison network, zero-one principle, bitonic sorting and
merging network sorter.
Units: III
GRAPH THEORY DEFINITIONS: Definitions of Isomorphic Components. Circuits, Fundamental Circuits, Cut-sets. Cut-
Vertices Planer and Dual graphs, Spanning Trees, Kuratovski's two Graphs.
Units: IV
GRAPH THEORY ALGORITHMS: Algorithms for Connectedness, Finding all Spanning Trees in a Weighted Graph and
Planarity Testing, Breadth First and Depth First Search, Topological Sort, Strongly Connected Components and Articulation
Point. Single Min-Cut Max-Flow theorem of Network Flows. Ford-Fulkerson Max Flow Algorithms
Units: V
NUMBER THEORITIC ALGORITHM: Number theoretic notation, Division theorem, GCD recursion, Modular
arithmetic, Solving Linear equation, Chinese remainder theorem, power of an element, RSA public key Crypto system,
primality Testing and Integer Factorization.