CS270: Combinatorial Algorithms and Data Structures

Spring 2005

Announcements

May 9	Clarifications noted in the final exam.
May 5	Here is the final exam.
May 3	Update: The final will go out this Thursday and will be due a week later. Also remember that the final project report is due on Thursday.
Apr. 26	Homework 2 has been handed back. Stop by Brighten's office if you didn't get yours (or your Homework 1).
Apr. 25	There will be no class this Thursday, April 28, due to the faculty retreat.
Apr. 12	Brighten's office hours Apr. 13 will be delayed until about 2-3pm due to a talk.
Apr. 7	The final project paper will be due May 5. The final will go out May 3 and be due a week later.
Apr. 5	Some of you found bugs in Problem 5(c), and rather than fix them at the last minute, we are cancelling the problem.
Mar. 24	Clarification in Homework 2 (in red).
Mar. 16	Homework 2 is now available. It's due Tuesday, April 5.
Mar. 15	Brighten's office hours tomorrow (Wednesday Mar. 16) are cancelled due to a conference.
Mar. 10	There will be no lecture on Thursday March 17. Christos's extended office hours next week are Tuesday March 15, 3:30 - 6:00, and Wednesday March 16, 10:00 - 12:00.
Mar. 8	Since you will be asked to demonstrate progress on your project in the next homework set, we are having extra office hours this week and next for project help. Brighten will be in Soda 475 Wednesday 1:30 - 3:00, Thursday 3:30 - 5:00, and by appointment. Christos' additional hours will be next week.
Feb. 23	Homework 1 solutions posted (minor update March 1). Prof. Papadimitriou's office hours are 5-6 pm Tue and Wed, not 4-5 pm as previously reported here.
Feb. 15	Tomorrow, Feb. 16, at 11 a.m. in Soda 306, we will have our first discussion section, a project bazaar. If you are satisfied with your project topic, you need not attend.
Feb. 9	Homework lateness policy: Over the course of the semester, you have 7 free late days. You may allocate these among the homeworks as you see fit.
Feb. 8	Minor update to homework 1. Posted Lec. 1 notes.
Feb. 1	Homework 1 has been posted below. It is due Feb. 15.
Jan. 18	The new slot for the discussion section is Wednesdays 11:00 a.m. - 12:00 p.m. in Soda 306. The section will meet when announced.

Administrative Information

Instructor: Christos Papadimitriou (christos@cs.berkeley.edu)
Office Hours: 5:00 - 6:00 Tuesday and Wednesday
TA: Brighten Godfrey (pbg@cs.berkeley.edu)
Office Hours: Wednesday 1:30-2:30, Soda 475
Lecture: Tuesdays and Thursdays 2:30-4:00 in Soda 306
Section: Wednesdays 11:00-12:00 in Soda 306, when announced.
Assessment: Your grade will be based 30% on homework (2 sets), 30% on the project, 30% on the final, and 10% on scribe notes.

Homeworks

Over the course of the semester, you have 7 free late days. You may allocate these among the homeworks as you see fit.

Homework 1, due Feb. 15 [ps | pdf]
Homework 2, due Apr. 5 [ps | pdf]

Notes

Please use this template for writing scribe notes.

Lecture 1 (Jan. 18): SAT
Lecture 2 (Jan. 20): 2SAT, strong connectivity, DFS
Lecture 3 (Jan. 25): Shortest paths, heaps
Lecture 4 (Jan. 27): Shortest paths (Floyd-Warshall), Flows (max flow/min cut, Ford-Fulkerson)
Lecture 5 (Feb. 1): Max flow (Edmonds-Karp), maximum matching
Lecture 6 (Feb. 3): Min cut (Karger), linear programming
Lecture 7 (Feb. 8): Linear programming (Simplex, Ellipsoid)
Lecture 8 (Feb. 10): LP duality, application to game theory
Lecture 9 (Feb. 15): Seidel's LP algorithm, recurrences, divide & conquer (Gauss's multiplication, median finding) (updated May 5)
Lecture 10 (draft): (Feb. 17): FFT
Lecture 11 (Feb. 22): Dynamic programming part I
Lecture 12 (Feb. 24): Dynamic programming part II
Lecture 13 (draft) (Mar. 1): Coding
Lecture 14 (Mar. 3): Information theory I
Lecture 15 (Mar. 8): Information theory II: Shannon's theorem
Lecture 16 (draft) (Mar. 10): Linear codes
Lecture 17 (Mar. 15): P, NP, and reductions
Lecture 18 (Mar. 29): NP-completeness of various problems
Lecture 19 (Mar. 31): More NP-completeness
Lecture 20 (Apr. 5): Approximation algorithms I
Lecture 21 (Apr. 7): Approximation algorithms II
Lecture 22 (Apr. 12): Approximating set cover
Lecture 23 (Apr. 14): Set cover by randomized rounding, inapproximability, PCP
Lecture 24 (Apr. 19): Planar graphs
Lecture 25 (Apr. 21): Balls 'n' bins load balancing, power of 2 choices (alternate verson)
Lecture 26 (Apr. 26): Multicriteria optimization
Lecture 27 (May 3): Perfect hashing, Bloom filters
Lecture 28 (May 5): High-dimensional geometry

If the notes you're looking for are not yet available, try the 2004, 2003, or 1997 versions of the course.

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 (notice how detailed and accurate it is for the first ten lectures!-):

Lectures 1-2 (Jan. 21-23): Introduction and SAT, depth-first search, strongly connected components, graph structure. References: Any algorithms book like [CLR].
Lectures 3-4-5 (Jan. 28-30, Feb. 4): Shortest paths (Dijkstra, negative edges, transitive closure) and maximum flows (max-flow min-cut, duality and linear programming, preflow-push algorithm). Reference: [CLR], book by [Papadimitriou and Steiglitz], book (and handout) by [Ahuja, Magnanti, and Orlin].
Lectures 6-7-8 (Feb. 6-11-13). Linear Programming. Algorithms; simplex, Seidel's, interior point.
Lectures 9-10 (Feb. 18-20): Randomized algorithms for min cuts, fingerprinting, polynomial equivalence. Reference: Book (and handout) by [Motwani and Raghavan].
Lectures 11-12-13 (Feb. 25-27, March 4, plus a meeting on the project): Divide-and-conquer, mostly with geometric applications, but also sorting, selection, duplicate detection. Reference: [CLR].
Lectures 14-15-16 (March 6-11-13) Dynamic programming. Reference: [CLR].
Lectures 17-18 (March 18-20) NP-completeness. Reference: [CLR].
Lectures 19-20-21 (March 25-27, April 1) Heuristics (Approximation algorithms, branch-and-bound and backtracking, local search and simulated annealing, etc.). Reference: [CLR], book by [Hochbaum], book (and handout) by [Lewis and Papadimitriou]
Lectures 22 (April 3-8) PCP Application and Theorem.
Lectures 23-24-25-26-27 Other topics. Possiblities include coding theory, chernoff bounds, balls in bins anaylsis, fft.
Project presentations. During the last weeks of the class we shall present a selection of the projects, and lead the class in addressing questions related to them.