Tue, May 17

• Linear time reductions and Matrix problem equivalences
• Linear algebra in a parallel model, the class NC.
• Parallel computation: the parallel prefix kernel. Blelloch reference.

Thu, May 12

• Warmup: Bipartite Cliques and Bipartite Matchings
• Network flows. Reading: Chapter 26
• 3-SAT reduces to Subset-Sum.
• hwIV solution sketches

Tue, May 10

• Polynomial time reductions and NP problems.
  • Circuit SAT reduces to (formula-)SAT,
  • 3-SAT reduces to Clique,
  • Subset-Sum reduces to Partition
• recipe for showing a decision problem is in NPC.
• homework assignment V (hw problems 14,15,16,17), due 4am, May 19.

Thu, May 5

• Dijkstra's single source shortest path algorithm, Reading: Chapter 24.3
• P and NP, Reading: Chapter 34, Sections 3,4.
• NP Completeness: Cook's theorem (34.7)

Tue, May 3

• Further applications of DFS, Topological Sort.
• The halting problem. c program
• P and NP, Reading: Chapter 34, Sections 1,2.
• HWIV due by 8am, beginning of class

Thu, Apr 28

• Minimal Spanning Trees, Reading: Chapter 23
  • Prim's algorithm
  • Kruskal's algorithm

Tue, Apr 26

• Graph Algorithms, Reading: Chapter 22
  • Graph representation,
  • Breadth first search,
  • depth first search

Thu, Apr 21

• Dynamic Programming, continued
  • LCS: Longest common subsequence
  • LIS: Longest increasing subsequence
  • Matrix chain product
• homework assignment IV (hw problems 10,11,12,13), due 8am, May 3.

Tue, Apr 19

• HWIII accepted (with minor penalty) until 8am.
• Dynamic Programming
• Reading: Chapter 15

Thu, Apr 14

• HWIII due by 7pm to TA (in 201 Smith Hall)
• Chinese remainder theorem
• Reading: Chapter 30
• Fast polynomial and integer arithmetic via FFT
• 3-primes FFT, Johnson's slides

Tue, Apr 12

• RSA continued
  • Extended Euclidean algorithm
  • digital signatures
• Blockchain (Bitcoin) is application of hashing and PKE
• Nakamoto bitcoin article.

Thu, Apr 7

• Universal hashing
• Reading: Chapter 31.7
• RSA public key encryption
  • Key construction
  • Encryption and decryption using public and private keys
• Modular exponentiation

Tue, Apr 5

• Reading: Chapter 11
• Hash tables, separate chaining, linear probing.
• Simple uniform hash functions
• Midterm return. Answer key.

Tue, Mar 29,31 spring break

Thu, Mar 24

• Midterm exam
• HWIII assignment will be given (due April 14) .
• homework assignment III (hw problems 7,8,9), due April 14.

Tue, Mar 22

• Reading: Chapter 13
• 2-3-4 trees and red-black trees
• Left leaning red-black trees, Sedgewick notes
• Review for midterm, review sheet. Sample questions about red-black trees

Thu, Mar 17

• HWII due by 7pm to TA (in 201 Smith Hall)
• Analyze union/find.
• Reading: Chapter 12
• Binary search trees, bst notes.

Tue, Mar 15

• Reading: Section 17.2 and 17.4
• Amortized analysis and dynamic arrays (dynamic tables).
• Algorithm sketch: Kruskal's MST
• Reading: Chapter 21 Disjoint Sets
• union/find, Dynamic partition operations

Thu, Mar 10

• Binomial Heaps, reference binomialheap.h.
  • Union operation,
  • worst case cost of mergable heap operations
  • Amortized cost of operation sequence.

Tue, Mar 8

• Mergable priority queues (also called meldable heaps)
• Reading: NOT Chapter 19 (the chapter on binomial heaps is removed in 3rd edition!)
• Reading: binomialheap.h
• Also the wikipedia article on binomial heaps is somewhat helpful.
• Group first meeting

Thu, Mar 3

• Reading: Chapter 10: Linked lists and basic data structures.
• homework assignment II (hw problems 4,5,6, due March 17).
• No Saunders office hour today due to travel.

Tue, Mar 1

• HWI due 8am in class (counted as late after 8:01am)
• Analysis of Randomized QuickSort.
• Comparison based sorting is in Ω(nlog(n)).
• brief quiz on chapters 1-9 (not counted in grading)

Thu, Feb 25

• Reading: Chapter 6: priority queues and HeapSort
• Putting things together: IntrospectiveSort
• sorting: timings of insertionSort, mergeSort, quickSort, heapSort, introspectiveSort.
• HWI due by 7pm to TA (in 201 Smith Hall) [now extended to Tuesday at 8am in class]

Tue, Feb 23

• MergeSort and QuickSort compared.
• Index variables and expected value of random variables.
• Analysis of Select and Randomized Select,
• Discuss exercise 4.5-4
• Reading: Chapters 5,7

Thu, Feb 18

• homework assignment I (hw problems 1,2,3).
• ω, Ω, Θ, Big O, Little o
• Reading: Chapter 9, Randomized-Select (refer to chapter 5 as needed), Select
• Reading: Chapter 4. Divide and Conquer algorithms,
• Master method, a geometric viewpoint
• Discussed exercise 2.3-7

Tue, Feb 16

• Class cancelled by UD(due to weather)

Thu, Feb 11

• Reading: Chapters 1,2,3: Conventions, notation, some commonly ocurring math:
• Discuss exercises: 2.3-3, 2.3-7, problem 1.1
• Introduction to divide and conquer strategies
• MergeSort
• Karatsuba's algorithm for polynomial and integer multiplication

Tue, Feb 9

• Introductory discussion of a collection of problems concerning arrays of numbers.
• In particular, order statistics (Max,Min,MaxMin).
• MaxMin using about 3n/2 comparisons, worst case, is possible and is best possible.
• InsertionSort, discuss exercise 2.3-4