4003-515-01: Homework, Quizzes, Reading and Slides


Week 1

• Slides for this week: Introduction - pdf (ppt), MergeSort/HeapSort/RadixSort - pdf (ppt)


• Monday, March 4
  • Covered in class: Course logistics, see the main course website
  • Covered in class: Introduction to Algorithms and asymptotic analysis (read Chapter 1 and Sections 2.1 and 2.2 in the book)
  • Covered in class: Some linear-time geometric algorithms: point inside a polygon, area of a polygon (not in the book)
  • A note for students with disabilities: RIT is committed to providing reasonable accommodations to students with disabilities. If you would like to request accommodations such as special seating, testing modifications, or note taking services due to a disability, please contact the Disability Services Office. It is located in the Eastman Building, Room 2342; the Web site is www.rit.edu/dso. After you receive accommodation approval, it is imperative that you see me during office hours so that we can work out whatever arrangement is necessary.


• Wednesday, March 6
  • Covered in class: finished the algorithm computing area of a polygon
  • Covered in class: finished surveying common running times (Section 2.4)
  • Covered in class: MergeSort and introduction to recurrences (Section 5.1), RadixSort (not in the book)


• Homework 1, due 13 March 2013, 10:00am: click here

• Slides for this week: we will continue with last week's slides; after that Convex Hulls - pdf (ppt) and Select/median algorithm - pdf (ppt)


• Monday, March 11
  • Covered in class: A lower-bound on comparison-based sorting Omega(n log n) (not in the book)
  • Covered in class: convex hulls (not in the book)


• Wednesday, March 13
  • Covered in class: finished convex hulls: the divide and conquer approach
  • Covered in class: Median/Select (the worst-case O(n) is not in the book but the randomized version is in Section 13.5)


• Homework 2, due 20 March 2013, 10:00am: click here

• Slides for this week: we will continue with last week's slides, after that Interval Scheduling and the Longest Increasing Subsequence - pdf (ppt)


• Monday, March 18
  • Covered in class: the randomized Select (Section 13.5)
  • Covered in class: Master Theorem (not in the book)
  • Covered in class: introduction to Interval Scheduling (Sections 4.1 and 6.1-2)



• Wednesday, March 20
  • Covered in class: finished Interval Scheduling (Sections 4.1 and 6.1-2)


• Homework 3, due 27 March 10:00: click here

• Slides for this week: The Knapsack problem and Huffman coding - pdf (ppt)


• Monday, March 25
  • Covered in class: Longest Increasing Subsequence (not in the book)
  • Covered in class: Knapsack, the divisible and indivisible version (Section 6.4)


• Wednesday, Jan 5
  • In class: quiz 3.
  • Covered in class: finished indivisible Knapsack
  • Covered in class: solutions of Hw1 and Hw2 (sorry, the notes we wrote on the tablet did not get saved...)
  • Covered in class: started Huffman coding (Section 4.8)


• Homework 4, due 5 April 14:00 (for Sol, at the end of the day on Thursday :): click here

• Slides for this week: Longest Common Subsequence and Matrix Chain Multiplication - pdf (ppt)


• Wednesday, April 3
  • Covered in class: finished Huffman coding (Section 4.8)
  • Covered in class: Longest Common Substring/subsequence (not in the book but a similar problem is discussed in Section 6.6)
  • Recall that our make-up class for Easter Monday is tomorrow, Thursday, April 4, in room 3 (if the room is taken, we will move to room 31).
  • Next week: midterm, tentatively scheduled for Monday, 12-14, in room 3 (i.e., our 10-12 class time is shifted to 12-14).


• Thursday, April 4
  • Covered in class: Matrix Chain Multiplication (not in the book but a similar interval-based dynamic programming technique is used in Section 6.5)
  • No homework due next week :)

• Slides for this week: Introduction to Graph Algorithms: BFS,DFS - pdf (ppt)


• Monday, April 8
  • In class: midterm.


• Wednesday, April 10
  • Covered in class: solutions of the midterm
  • Covered in class: revisited the reconstruction of the matrix chain multiplication solution
  • Covered in class: introduction to graph algorithms (Chapter 3)


• Homework 5, due 17 April 10:00: click here

• Slides for this week: Minimum spanning trees and Shortest paths - pdf (ppt)


• Monday, April 15
  • Covered in class: Strongly connected components (connectivity discussed in Section 3.5, the O(n+m) algorithm is not in the book)
  • Covered in class: Minimum Spanning Tree - Kruskal (Section 4.5) and the related Union-Find data structure (Section 4.6)


• Wednesday, April 17
  • Covered in class: the running time analysis of the Union-Find data structure, the correctness of Kruskal, and the Prim's algorithm for Minimum Spanning Trees (Sections 4.5 and 4.6)
  • Announcements: May 1 class moved to April 30, 2-4pm, room TBA. Please think about possible dates for the final exam so that we can reserve a room.


• Homework 6, due April 24, 10:00: click here

• Slides for this week: we will continue with last week's slides, then Network Flow - pdf (ppt)
• Monday, April 22
  • Covered in class: Dijkstra's algorithm (Section 4.4)
  • Covered in class: Floyd-Warshall's algorithm (not in the book)
  • Covered in class: solution of Problems 1 and 3, Hw 5


• Wednesday, April 24
  • Covered in class: Bellman-Ford's algorithm (Sections 6.8-6.10)
  • Covered in class: Flow networks, Ford-Fulkerson's algorithm (Chapter 7)


• Homework 7, due 1 May, 10:00am: click here

• Slides for this week: we will cover the material from the last week's slides


• Monday, April 29
  • Covered in class: Scaling Network Flow algorithm (Section 7.3), and Edmonds-Karp algorithm
  • Covered in class: Max-Flow-Min-Cut Theorem, proof of correctness of Ford-Fulkerson-type algorithms
  • Note: Due to Turizmijada, next class takes place tomorrow, at 12:00, in room 31.


• Tuesday, April 30
  • Covered in class: Applications of Flow Networks (multiple sources/sinks, finding a minimum cut, maximum number of edge-disjoint s-t paths, maximum bipartite matching - see Chapter 7 for these and more applications)
  • Covered in class: a very brief introduction to linear programming (Section 11.6)


• Homework 8, due by the end of the day, 8 May 2013: click here
  Note: the last problem has a long description but the answer is short and simple.

• Slides for this week: NP-completeness - pdf (ppt)


• Monday, May 6
  • Information about the final exam is here.
  • Covered in class: more on linear programming
  • Covered in class: reductions, class P (for P, NP, and NP-completeness, see Chapter 8)


• Wednesday, May 8
  • Covered in class: NP, and NP-completeness (Chapter 8)
  • Take-home points related to P, NP, NP-complete (and useful things to remember for the final):
    • Definition of classes P, NP, and NP-complete.
    • Looking at a problem, you should be able to recognize basic problems from P (like the decision versions of most of the problems from class).
    • You should be able to sketch the proof that a problem is in NP - specify the witness, then describe a polynomial-time verification algorithm.
    • You should be able to do reductions of about the same difficulty as the problem on the homework (Problem 3, Hw8).
    • Big open problem: P = NP (we do NOT know if P=NP).
    • NP-complete problems are the "hardest" problems in NP.
    • If somebody finds a polynomial-time algorithm for an NP-complete problem, then P=NP.
    • If somebody shows that there does not exist a polynomial-time algorithm for an NP-complete problem, then P is not equal to NP.
    • If somebody finds an easy polynomial-time algorithm for an NP-complete problem, then this algorithm probably does not work :)
    • You should be familiar with the NP-complete problems we discussed in class.
  • Good luck with your finals!