Algorithm Design and Analysis Lecture notes, Fall 95

These notes are in reverse order by date

Monday, Dec 18, 10:30-12:30 am

• Final exam.

Dec 7.

• Parallel algorithms (chapters 28, 30)

Dec 5.

• Homework set #5 due.
• Finish FFT
• RSA (chapter 33)

Nov 30.

• FFT (chapter 32)

Nov 28.

• Matrices (chapter 31), Strassen's algorithm,
• Equivalence of mult, invert, solve linear system.

Nov 23. Thanksgiving

Nov 21.

• Hand out HW set #5.
• P-time reductions, the many, many problems in NPC (chapter 36)

Nov 16.

• Homework set #4 due.
• P, NP, NPC, NP-hard, NP completeness of CIRCUIT-SAT

Nov 14.

• P and NP, the reduction to binary encodings (chapter 36)

Nov 9.

• General closure over a star semi-ring
• Network flows (chapter 27)

Nov 7.

• shortest path algorithms (chapter 25 and 26).
• Single source shortest paths. Dijkstra's, Bellman-Ford
• All source shortest paths. Floyd-Warshall, Transitive Closure,

Nov 2.

• Homework set #4 assigned.
• finish Kruskal's and Prim's algorithms for MST.

Oct 31.

• Homework set #3 due.
• Graph algorithms (chapter 25) Minimal spanning trees

Oct 26.

• Graph algorithms (chapter 24)

Oct 24.

• Graph algorithms (chapter 24) Breadth first search, spanning trees

Oct 19.

• Analysis of Union-Find (chapter 22).

Oct 17.

• Union-Find (chapter 22). Ackermann's function and lg*.

Oct 12.

• Homework set #2 due.
• Amortized analysis (see chapter 18 for reference) of Fibonacci and Binomial Heaps (chapter 21).

Oct 10.

• Fibonacci Heaps (chapter 21).

Oct 5.

• Binomial Heaps (chapter 20).

Oct 3.

• Finish on B-trees (chapter 19).

Sept 28.

• finish Red-Black trees (ch 14), handed out paper copy of fixed up red-black tree code. Corrections made during class are reflected in ~saunders/621/rbt.cc .
• Started on B-trees (chapter 19).
• Homework set #2 assigned .

Sept 26.

• Red-Black trees (ch 14), see also ~saunders/621/rbt.cc .

Sept 21.

• Homework set #1 due
• finish Order Statistics (ch 10), see also ~saunders/621/select .
• Search trees (ch 13), see also ~saunders/621/bst.cc .

Sept 19.

• Finish showing Buildheap runs in theta(n) time.
• Order Statistics (ch 10)

Sept 14.

• Heap sort, priority queues (ch 7)
• Order Statistics (ch 10), see also ~saunders/621/quicksort-select .

Sept 12.

• Homework set #1 assigned.
• Quick sort analysis (ch 8)
• Heap sort, priority queues (ch 7)

Sept 7.

• lg(n!) = \theta(nlg(n)) because (n/2)^(n/2) <= n! <= n^n plus a detail.
• Quick sort (ch 8)

Sept 5.

• Function comparison using O, \Theta, \Omega (ch 2).
• Master Theorem (ch 4.3)
• Merge sort (is in ch 1).
• Decision tree based lower bound for sorting by comparisons (ch 9.1). (see also ch 2.2 for relevant mathematics)

August 31.

• Karatsuba algorithm for integer multiplication.
• The conventional multiplication of 2 n digit numbers can be expressed in terms of 4 multiplications of n/2 digit numbers. The karatsuba algorithm reduces this to 3 multiplications of n/2 digit numbers and \Theta(n) additions and subtractions of digits, The cost in digit operations then satisfies the recurrence T(n) = 3T(n/2) + \Theta(n), so that T(n) = \Theta(n^{lg(3)}). Empirical data shows that the gnu mulitprecision arithmetic library uses this method.
• Reading: Scan chapters 1-6 (we will refer to these topics as the occasion arises), pay closer attention to chapters 2 and 4.

saunders@cis.udel.edu