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Lectures Synopsis page, CISC 320 Algorithms, Spring, 2011
This page contains a brief summary of each class topic and the
associated reading, with links to online "handouts" that were referenced.
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Last updated May 16, 2011.
Resources:
UDAlgorithms notes
Skiena's slides
Future: Brief predictions of class topics to be covered.
Mon, May 23 8:00AM-10:00AM Final Exam in Gore 117 (our classroom).
- Basics of reading covered:
Skiena chapters 1-9 excluding 7,
class notes (as outlined below),
UDAlgorithms notes (on early topics),
Selected items in hitchhiker's guide (Skiena part II),
homeworks.
- Types of question: similar to midterm
- Emphasis: 3/4 on second half, 1/4 on first half.
Mon, May 16
- FFT, polynomial and integer multiplication
- easy, hard, harder, impossible
- review
- Homework #6 programming problem phase 2 due. Submit by email to Tim
Past: Brief summaries of class topics covered in reverse chronological order.
Fri, May 13
- quiz
- Red-Black trees
- Reading: Ch 3.4, 12.1
- Phase 1 program suitable as starting point for phase 2 is ~saunders/algorithms/lcss.cc on Strauss.
Wed, May 11
- Dictionary data structure
- Reading: Ch 3.3
- Homework #6 programming problem phase 1 due
Mon, May 9
- Implementing dynamic programming for longest common subsequence
- Reading: Ch 8
- Homework #6 problems 1, 2 due.
Fri, May 6
- Longest common subsequence
- Reading: Ch 8
Wed, May 4
- Matrix chain multiplication
- Reading: Ch 8
Mon, May 2
- Edit Distance
- more problems that yield to dynamic programming
- Reading: Ch 8
Fri, Apr 29
- Introduction to dynamic programming
- fibonacci and longest increasing subsequence
- Reading: Chapter 8.
Wed, Apr 27
- Closest pair of points (another problem from computational geometry).
- Divide and conquer algorithm for closest pair of points
- Tools for manipulating graphs
Mon, Apr 25
- Finish Graham scan algorithm for convex hull
Fri, Apr 22
- Graham scan algorithm for convex hull
- Reading: 17.2, Wikipedia Graham_scan article
- Homework #4 due
Wed, Apr 20
- Introduction to the use of NP for cryptography.
- RSA public key encryption scheme
- Reading: 18.6 and Wikipedia RSA article
- Reading: 18.6
Mon, Apr 18
- quiz 2 on approximation, reductions
- reduction of vertex cover to HAM (sketch)
- Reading: Chapter 9.
Fri, Apr 15
- Reduction of 3-SAT to vertex cover.
- Summary of NP-Completeness
- Reading: Chapter 9.
Wed, Apr 13
- Cook's theorem
- Homework #3 due
- Reading: Chapter 9.
Mon, Apr 11
- Traveling Salesman Problem
- Approximation for TSP
- Reading: Chapter 9.
Fri, Apr 8
- quiz on reductions in section 9.2, 9.3
- Maximal independent set (IS): reduction to GMS
- Hamiltonian cycle Problem (HAM)
Wed, Apr 6
- Optimization/Search/Decision problems
- The nature of reductions
- reduction of Sorting to Convex Hull.
- Vertex cover (VC): Def (in 9.5) and reduction to IS
- Reading: 9.2, 9.3, VC Def in 9.5, notes on hard problems
Mon, Apr 4
- exam results
- movie scheduling: Def and solution.
- Generalized movie scheduling (GMS) and maximal independent set (IS): defs.
- Reading: 1.2, 9.3
Fri, Mar 25 Midterm exam
Wed, Mar 23
Mon, Mar 21
- log*(x) function
- All pairs shortest paths
- Reading: Ch 6.3
- Homework assignment, hw2.pdf, is due Wed, April 6.
Fri, Mar 18
Wed, Mar 16
- Kruskal's MST alg.
- dynamic disjoint sets
Mon, Mar 14
- Analysis of Prim's's MST alg.
Fri, Mar 11
- Correctness of Dijkstra's SSSP alg.
- Correctness of Prim's's MST alg.
- Run time of Dijkstra SSSP, Prim MST algorithms
Wed, Mar 9
- From BFS to Dijkstra to Prim
- Single source shortest paths in weighted graphs
- Dijkstra's SSSP algorithm
- Prim's MST algorithm
- Reading: 6.1 6.3
Mon, Mar 7
- Graph representation
- Breadth First Search and shortest paths.
- Reading: Chapter 5
Past: Brief summaries of class topics covered in reverse chronological order.
Fri, Mar 4
- Quick Sort
- Introspective Sort
- Reading: 4.6
Wed, Mar 2
- Priority queues, heaps, heapsort
- Reading: 3.5, 3.6, 4.3, 4.4
Mon, Feb 28
- Priority queues, heaps, heapsort
- Reading: 3.5, 3.6, 4.3, 4.4
Fri, Feb 25
- svn, course environment, makefiles, speedup
Wed, Feb 23
- Combining merge sort and insertion sort
- Subtleties of timing processes.
Mon, Feb 21
- Master theorem proof sketch
- Course programming environment:
- location of headers for sequence, data structures, algorithms
- timing and testing framework
- Reading: sections 4.3 and 4.4 (priority queues and heap_sort)
Data structures for graphs
Fri, Feb 18
- Faster polynomial multiplication: T(n) = 3T(n/2) + Θ(n).
- Master theorem.
- Reading: Scan Chapter 3 (Data Structures).
- Homework assignment, hw1.pdf, is due Wed, March 2.
Wed, Feb 16
- Function approximation, "big-O" and friends.
- Exponentiation, binary search: T(n) = T(n/2) + Θ(1).
- polynomial multiplication: T(n) = 4T(n/2) + Θ(n).
- recall merge_sort: T(n) = 2T(n/2) +Θ(n).
- recall insertion_sort: T(n) = T(n-1) +Θ(n).
- Reading: Chapter 2 (emphasis on second half).
Mon, Feb 14
- Merge Sort (Skiena section 4.5, page 120.)
- Recurrence solution or upper bound by substitution method (guess, then inductively prove).
- Reading: Chapter 2 (emphasis on second half).
Fri, Feb 11
- Discussed two algorithms for Max_n_2nd_largest, one using about 3n/2 comparisons
and one using about n + lg(n) comparisons.
- Insertion sort requires about n2/2 comparisons.
- Reading: Chapter 2 (emphasis on first half).
Wed, Feb 9
- Syllabus, Sakai site.
- Max_n_min problem solved in about 3n/2 comparisons.
- That is optimal (lower bound proof)
- Max_n_2nd_largest problem posed.
Mon, Feb 7
- Algorithmic problems are well specified.
- Maximum of a sequence requires n-1 comparisons.
- Moore's law continues but with new consequences (multiprocess vs GHz).
Some useful links:
The Standard Template Library.
The STL Documentation at SGI.
saunders@udel.edu