RongJaye Chen

1
Introduction to Algorithm
Rong-Jaye Chen
2
Design Strategies

• The Recursive Method
• The reliability analysis for linear
  consecutive-k-out-of-nF systems
• The reliability analysis for circular
  consecutive-k-out-of-nF systems
• Dynamic Programming
• Matrix chain multiplication
• Elements of dynamic programming
• Longest common subsequence
• The traveling salesperson problem

3
Design Strategies

• The Greedy Method
• An activity-selection problem
• Huffman codes
• Matroid theory
• A task-scheduling problem
• Divide-and-Conquer
• Matrix multiplication
• The fast Fourier transform
• Complexity analysis

4
Design Strategies

• Backtracking
• The 8-queens problem
• Sum of subsets
• Branch and Bound
• The 15-puzzle
• 0/1 knapsack problem

5
Design Strategies

• Mathematical Programming Approaches
• Linear program
• Network program
• Integer program
• LINDO package
• Advanced Data Structure
• Binomial heaps
• Fibonacci heaps
• Data structures for disjoint sets
• Applications

6
Algorithm Subjects

• Graph Algorithms
• All-Pairs Shortest Paths
• Maximum Flow
• Geometric Algorithms
• Convex Hulls
• Closest Pair

7
Algorithm Subjects

• Algebraic Algorithms
• Euclids algorithm
• Modular arithmetic
• Exponentiation
• Galois fields
• Algorithmic Number Theory
• The RSA public-key cryptosystem
• Primality testing
• Integer factorization
• Discrete logarithm

8
Computation Models

• DNA Computation
• Quantum Computing
• Parallel Computation
• NP-Completeness (Theory of computation)