lecture notes

This page contains a brief summary of each class topic and the associated reading. This page morphs frequently, being updated at least weekly. You may need to reload it at each viewing to avoid being shown a stale version from your browser cache. Most recent items are at the top. Last updated May 12, 2011.

Tue, May 17

• Fast Fourier Transform and application to polynomial multiplication
• Harder than NP complete and impossible problems.
• exam review

Thu, May 12

• Polynomial and integer multiplication
• Reading: Chapter 30
• Homework set was revised today: hw2.pdf

Tue, May 10

• balanced binary trees
• Red-black trees
• Reading: chapters 12, 13.

Thu, May 5

• More dynamic programming
• longest common subsequence (15.4)
• matrix chain multiplication (15.2)
• a problem to be named later
• Homework set: hw2.pdf (since revised on May 12)

Tue, May 3

• dynamic programming and memoization
• longest increasing subsequence, lis.mpl
• edit distance, editDist.h
• Reading: Chapter 15

Thu, Apr 28

• The RSA encryption scheme.
• fast modular exponentiation and addition chains
• Reading: 31.6, 31.7

Tue, Apr 26

Graham Scan algorithm for convex hull.
Divide and conquer algorithm for closest pair of points.
Reading: sections 33.3, 33.4.
• Homework #1 due

Thu, Apr 21

• All pairs shortest paths, transitive closure, and the DAG of strong components
• Public key encryption and NP

Tue, Apr 19

• Completion of reduction Vertex Cover to HAM
• Approximation algorithms
• Reading: Sections 34.5.1, 35.1, 35.2

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Past: Brief summaries of class topics covered in reverse chronological order.

Thu, Apr 14

• Reduction of 3-SAT to Hamiltonian cycle
• Reduction of Vertex Cover to Hamiltonian cycle to TSP
• Reading: Chapter 34

Tue, Apr 12

• Cook's theorem
• Reduction of Circuit-SAT to boolean formula SAT to CNF-SAT to 3-SAT

Thu, Apr 7

• Optimization/Search/Decision problems
• problem classes P and NP
• Reductions among problems
• Vertex Cover and Independent Vertex Set

Tue, Apr 5 Midterm Exam

Thu, Mar 24

• Amortized analysis with a potential function

Tue, Mar 22

• Dynamic Tables and STL vector<>.
• Fibonacci Heaps
• Reading: Chapter 17.4, 19
• Reading:

Thu, Mar 17

• analysis: Union-Find with path compression
• Amortized analysis, accounting method
• Reading: Chapter 21, 17.2

Tue, Mar 15

• Kruskal's algorithm
• Dynamic Disjoint Sets
• Union-Find
• lg*(n): definition and basic properties
• Reading: Chapter 23

Thu, Mar 10

• Follow up on breadth first algorithms
  • correctness proof for Dijkstra's SSSP algorithm.
  • review of implementation options for priority queue
  • beginning on fibonacci heaps
  • correctness proof for Prim's MST algorithm.
• Reading: Chapter 19.1, 24.3

Tue, Mar 8

• Breadth first search
  • Single source shortest path problems
    • in unweighted graphs
    • in weighted graphs (Dijkstra's algorithm)
  • For Minimal Spanning Tree (MST) problem.
• Reading: Chapter 22.2, 24

Thu, Mar 3

• Completion of Quick Sort analysis
• Introduction to graphs
• Reading: 7.4, 22.1

Tue, Mar 1

• Completion of d-heaps analysis
• Quick Sort
• Partition
• Introspective sort
• Reading: Chapter 7

Thu, Feb 24

• Priority queues, heaps, heap_sort
• Reading: Chapter 6

Tue, Feb 22 Class canceled - weather

Thu, Feb 17

• Master theorem
• Reading: Chapter 4

Tue, Feb 15

• asymptotic notation
• divide and conquer algorithms
  • exponentiation: T(n) = T(n/2) + Θ(1).
  • merge sort: T(n) = 2T(n/2) + Θ(n).
  • Karatsuba poly mult: T(n) = 3T(n/2) + Θ(n).
  • Classical poly mult: T(n) = 4T(n/2) + Θ(n).
  • Strassen matrix mult: T(n) = 7T(n/2) + Θ(n²).
  • Classical matrix mult: T(n) = 8T(n/2) + Θ(n²).
• Reading: Chapter 3

Thu, Feb 10

• merge
• Analysis of merge sort
• a lower bound for comparison based sorting.
• Reading: Chapter 2

Tue, Feb 8

• course overview
• insertion sort
• merge sort
• Reading: Chapter 1

saunders@udel.edu