CS270: Combinatorial Algorithms and Data Structures

Spring 2007

Announcements

May 7	FINAL EXAM: The final exam is due Wednesday May 16, noon, at 593 SODA Hall.
May 2	The final exam will be given out in class on Monday May 7 and will be due on Wednesday May 16.
May 2	The final project report is due on Monday May 7.
April 18	Problem Set 3 (see below) is due next Monday.
March 24	Project: you are expected to submit a two-page description of your project on Wednesday after spring break, that is April 4.
March 24	April 2 discussion section is rescheduled for April 4.
March 18	Grading: we may only grade a subset of the problems in the problems sets/midterm; you are encouraged to try all problems equally hard.
March 14	The midterm, which is due March 21st in class, has been posted here.
March 2	Midterm: the midterm has been scheduled for March 21st.
March 2	Solutions for Assignment 1 have been posted.
March 2	Project Description: Please submit a separate page with your project description when handing in your 2nd homework.
March 2	Please submit you homework on time. Our policy will be to not accept late homework.
March 2	No discussion section on Monday March 5.
Feb. 16	Correction to Assignment 1. You don't need to hand in Problem 4 of Chapter 5 in the book.
Feb. 12	Discussion Section is rescheduled: Mondays, 5-6, in 310 Soda.
Feb. 12	First problem set is due Feb 21. See details here.
Feb. 5	Costis' office hours this week are on Thursday 3.40-4:40 pm, 593 Soda.
Jan. 18	The current slot for the discussion section is Fridays 3:00 p.m. - 4:00 p.m. in Soda 405.

Administrative Information

Instructor: Richard Karp
Office Hours: 2:00 - 3:00 Mondays and Wednesdays.

TA: Constantinos Daskalakis
Office Hours: Tuesdays 3.40-4:40, 593 Soda.

Lecture: Mondays and Wednesdays 10:30-12:00, 310 Soda.
Section: Mondays 5:00-6:00 in Soda 310.
Textbook: Algorithm Design, by Jon Kleinberg and Eva Tardos.
Lecture Notes: Professor Karp will provide informal handwritten notes for each lecture.

Assessment: Your grade will be based 20% on homework (tentatively 5 problem sets), 20% on the midterm, 20% on the project and 40% on the final.

Assignments

Assignment 1, due Feb. 21. Files: Page1, Page2
Solutions for assignment 1. Files: Solutions1

Assignment 2, due Mar. 7. Files: File

Midterm, due March 21.

Assignment 3, due April. 23. Files: File

Final, due May 16.

Course Outline

There is a significant dynamic component to the course, as topics drop in and out, or get longer or shorter treatment, depending on audience interest/reaction/resistence. We consider this a feature. Given this, here is a rough outline of the course material:

Introduction Stable Marriage Algorithm.

Searching a Graph Breadth-first-and Depth-first search, Strongly Connected Components, Graph Structure, Topological Ordering.

Greedy Algorithms Dijkstra's shortest path algorithm; implementation using priority queues; splay trees. Minimum spanning tree algorithms; implementation of Kruskal's algorithm using union-find data structure.

Divide-and-Conquer Algorithms Quicksort and Mergesort; fast matrix multiplication; fast Fourier transform and its applications.

Dynamic Programming Bellman-Ford algorithm for shortest paths; detecting negative cycles. Longest path in a DAG; longest increasing subsequence; subset sum problem; sequence alignment; traveling salesman problem.

Linear Programming Simplex algorithm; duality theorem; polynomial-time linear programming algorithms.

Network Flows Maximum flows and minimum cuts; augmenting path and push-relabel algorithms; minimum-cost flow.

NP and Computational Intractability Polynomial-time transformations; The complexity classes P and NP; NP-completeness; NP-completeness proofs.

Approximation Algorithms Set cover; vertex cover; max-cut.

Local Search Heuristics Hillclimbing and simulated annealing; Kernighan-Lin heuristic for max-cut.

Randomized Algorithms Minimum cuts in graphs; fingerprinting and string matching; universal hashing; Bloom filters; Miller-Rabin primality test.

Online Resources

Notes from Spring 2005.

Lecture 1: SAT
Lecture 2: 2SAT, strong connectivity, DFS
Lecture 3: Shortest paths, heaps
Lecture 4 : Shortest paths (Floyd-Warshall), Flows (max flow/min cut, Ford-Fulkerson)
Lecture 5: Max flow (Edmonds-Karp), maximum matching
Lecture 6: Min cut (Karger), linear programming
Lecture 7: Linear programming (Simplex, Ellipsoid)
Lecture 8: LP duality, application to game theory
Lecture 9: Seidel's LP algorithm, recurrences, divide & conquer (Gauss's multiplication, median finding)
Lecture 10 (draft): (Feb. 17): FFT
Lecture 11: Dynamic programming part I
Lecture 12: Dynamic programming part II
Lecture 13 (draft): Coding
Lecture 14: Information theory I
Lecture 15: Information theory II: Shannon's theorem
Lecture 16 (draft): Linear codes
Lecture 17: P, NP, and reductions
Lecture 18: NP-completeness of various problems
Lecture 19: More NP-completeness
Lecture 20: Approximation algorithms I
Lecture 21: Approximation algorithms II
Lecture 22: Approximating set cover
Lecture 23: Set cover by randomized rounding, inapproximability, PCP
Lecture 24: Planar graphs
Lecture 25: Balls 'n' bins load balancing, power of 2 choices (alternate verson)
Lecture 26: Multicriteria optimization
Lecture 27: Perfect hashing, Bloom filters
Lecture 28: High-dimensional geometry

You can also try the 2004 or 2003 versions of the course.