CS 170
Efficient Algorithms and Intractable Problems
a.k.a. Introduction to CS Theory

Prof. David Wagner
Spring 2009

  Contact address: cs170@inst.eecs
  Web page: http://www-inst.eecs.berkeley.edu/~cs170/

  MWF, 3:00-4:00, 100 Lewis

  101. Tu 10:00-11:00, 3105 Etcheverry (Preda)
  102. Tu 11:00-12:00, 85 Evans (Rabkin)
  103. Tu 2:00-3:00, 6 Evans (Abernethy)
  104. Tu 3:00-4:00, 121 Wheeler (Abernethy)
  105. Tu 4:00-5:00, 3105 Etcheverry (Rabkin)
  106. W 9:00-10:00, 3102 Etcheverry (Preda)
  107. Tu 5:00-6:00, 75 Evans (Abernethy)
  108. Tu 2:00-3:00, 79 Dwinelle (Rabkin)
  109. Tu 3:00-4:00, 242 Dwinelle (Preda)

Office Hours:
  Jake Abernethy: Wed 4-6pm (751 Soda)
  Daniel Preda: Mon 2-3pm (711 Soda), Wed 10-11am (711 Soda)
  Ari Rabkin: Mon 5-6pm (711 Soda), Thu 4-5pm (711 Soda)
  David Wagner: Mon 4-5pm (629 Soda), Fri 4-5pm (100 Lewis / 629 Soda)



The following schedule is tentative and subject to change.

Topic Readings
1/21 Introduction, reasoning about algorithms Chapter 0.1
1/23 Efficiency analysis, asymptotic running time, big-O notation Chapter 0.2, 0.3
1/26 Divide-and-conquer algorithms Chapter 2.1
1/28 Recurrence relations Chapter 2.2, 2.3
1/30 Median-finding Chapter 2.4
2/2 Fast Fourier transform Chapter 2.6
2/4 Fast Fourier transform Chapter 2.6
2/6 Graph search Chapter 3.1, 3.2
2/9 Depth-first search Chapter 3.3
2/11 Topological sorting Chapter 3.3
2/13 Strongly connected components Chapter 3.4
2/16    (no class)
2/18 Breadth-first search Chapter 4.1, 4.2
2/20 BFS and shortest paths Chapter 4.2, 4.3
2/23 Dijkstra's algorithm Chapter 4.4
2/25 Shortest paths: Bellman-Ford Chapter 4.6
2/27 Directed acyclic graphs Chapter 4.7
3/2 Midterm review
3/4 Minimal spanning trees, Prim's algorithm Chapter 5.1.0, 5.1.2, 5.1.5
3/6 MST, Kruskal's algorithm, greedy algorithms Chapter 5.1.1, 5.1.3
3/9 Union-find data structure Chapter 5.1.4
3/11 Greedy algorithms: Horn clauses Chapter 5.3
3/13 Greedy algorithms: Huffman codes Chapter 5.2
3/16 Dynamic programming Chapters 6.1, 6.2
3/18 Dynamic programming: edit distance Chapter 6.3
3/20 Dynamic programming: knapsack problems Chapter 6.4
3/23    (no class)
3/25    (no class)
3/27    (no class)
3/30 Dynamic programming: bio-computing applications (Chapter 6.3)
4/1 Dynamic programming: shortest paths Chapter 6.6
4/3 Midterm review
4/6 Midterm 2
4/8 Linear programming Chapter 7.1
4/10 Network flow Chapter 7.2
4/13 Network flow, cont. Chapter 7.2
4/15 Min-cut problems; applications of network flow Optional: Lecture notes
4/17 Matching Chapter 7.3
4/20 Search problems Chapter 8.1
4/22 2-party zero-sum games Chapter 7.5
4/24 P, NP Chapter 8.2, 8.3
4/27 Reductions; NP-completeness; 3SAT is NP-complete Chapter 8.2, 8.3
4/29 Reductions; NP-complete problems Chapter 8.3
5/1 SAT solvers Chapter 9.1
5/4 Coping with NP-completeness: Approximation algorithms Chapter 9.2
5/6 Coping with NP-completeness: heuristics Chapter 9.3
5/8 PageRank (none)
5/11 Finite-state machines (none)


Homeworks are due on Friday at 2:45 p.m. in the drop box labelled "CS 170" in 283 Soda, unless otherwise stated. Make sure to print your name, your TA's name, your discussion section time, and the homework number prominently on the first page and staple all pages together. You risk receiving no credit for any homework lacking this information.

No late homeworks will be accepted. Out of a total of approximately 12 homework assignments, the lowest two scores will be dropped. Homeworks will be made available the Friday evening before they are due.


Quizzes must be completed online once a week, before 10am on each Monday. The quizzes will check your progress so far, so you should be doing the reading for the prior week before taking the quiz. Quizzes must be done on your own (no collaboration, and no discussion of the questions or your answers with others). Quizzes will be made available on this web page the Friday before they are due.


There will be two midterms. Midterm 1 will be on Monday, March 2, 5:30-7:30pm in 2050 Valley LSB. Midterm 2 will be in class on Monday, April 6. The final exam will be on Monday, May 18, 2009, 5:00-8:00pm in 155 Dwinelle. A study guide for the final exam is available.


We will use an absolute grading scale. The lowest 2 homework scores and the lowest 2 quiz scores will be dropped, and then we will compute a weighted average, as follows: 30% for homeworks, 5% for quizzes, 20% for Midterm 1, 15% for Midterm 2, 30% for the final exam. Then, letter grades will be assigned according to the following chart:
   A: 90-100 A-: 82-90
  B+: 74-82 B: 67-74 B-: 60-67
  C+: 50-60 C: 45-50 C-: 40-45
  D: 30-40 F:0-30
An A+ is awarded only at the instructors' discretion. We reserve the right to add extra points to your final score (e.g., if the exams were unexpectedly harder than intended).


Contact information: If you have a question, the best way to contact us is via the class newsgroup, ucb.class.cs170. The staff (instructor and TAs) will check the newsgroup regularly, and if you use the newsgroup, other students will be able to help you too. Please avoid posting answers to homework questions before the homework is due. Information on how to access the class newsgroup can be found here and here. A RSS feed of the newsgroup is also available.

If your question is personal or not of interest to other students, send email to cs170@inst.eecs. Email to this address is forwarded to the instructor and all TAs. We prefer that you use this group address, rather than directly emailing the instructor and/or your TA. If you wish to talk with one of us individually, you are welcome to come to our office hours. If the office hours are not convenient, you may make an appointment with any of us by email. Please reserve email for the questions you can't get answered in office hours, in discussion sections, or through the newsgroup.

Announcements: The instructor and TAs will periodically post announcements, clarifications, etc. to the newsgroup. Hence it is important that you check the newsgroup frequently throughout the semester.

Prerequisites: The prerequisites for CS 170 are CS 61B and either CS 70 or Math 55. It is important that you be comfortable with mathematical induction, big-O notation, basic data structures, and programming in a standard imperative language (e.g., Java or C). You will need to be familiar with the Unix operating system and basic tools. If you need help, the CSUA runs help sessions.

Collaboration: You are encouraged to work on homework problems in study groups of two to four people; however, you must always write up the solutions on your own. You must never read or copy the solutions of other students, and you must not share your own solutions with other students. Similarly, you may use books or online resources to help solve homework problems, but you must always credit all such sources in your writeup and you must never copy material verbatim. We believe that most students can distinguish between helping other students and cheating. Explaining the meaning of a question, discussing a way of approaching a solution, or collaboratively exploring how to solve a problem within your group is an interaction that we encourage. On the other hand, you should never read another student's solution or partial solution, nor have it in your possession, either electronically or on paper. You must never share your written solutions, or a partial solutions, with another student, even with the explicit understanding that it will not be copied. You should write your homework solution strictly by yourself. You must explicitly acknowledge everyone who you have worked with or who has given you any significant ideas about the homework. Not only is this good scholarly conduct, it also protects you from accusations of theft of your colleagues' ideas.

Warning: Your attention is drawn to the Department's Policy on Academic Dishonesty. In particular, you should be aware that copying or sharing solutions, in whole or in part, from other students in the class or any other source without acknowledgment constitutes cheating. Any student found to be cheating risks automatically failing the class and being referred to the Office of Student Conduct.

Computer accounts: We will use 'named' accounts this semester. If you do not already have an instructional account, go to a Unix machine in 273 Soda and login as 'newacct' (password: 'newacct') to receive a named account (further information is available). After you have obtained your account, you will need to register with our grading software.

Textbook: We will use Algorithms (Dasgupta, Papadimitriou, and Vazirani) as our textbook. An earlier draft of the textbook is available online; however, the chapter and exercise numbers may differ. All chapter numbers and exercise numbers in this course refer to the official paper textbook, not the online version.

Discussion sections: Please enroll in a discussion section via Telebears, if you have not already. You may only enroll in a discussion section that has space available; see the online schedule. You may switch discussion sections only with the approval of the TA of the section you want to switch to, and only if that section is not full. Outside of your discussion section, you should feel free to attend any of the staff office hours (not just your section TA's office hours) and ask any of us for help.

Grading policies: On homeworks, we insist that you provide a clear explanation of your algorithm. It is not acceptable to provide a long pseudocode listing with no explanation. In our experience, in such cases the algorithm usually turns out to be incorrect. Even if your algorithm turns out to be correct, we reserve the right to deduct points if it is not clearly explained. We will not grade messy or unreadable submissions.

Re-grading policies: Regrading of homeworks or exams will only be undertaken in cases where you believe there has been a genuine error or misunderstanding. If you believe that your homework or exam answer was correct and you should have received full points, prepare a written note explaining which question you believe was misgraded and justify your opinion, staple this to the cover of your homework, and return it to your section TA. We will not accept verbal regrade requests or regrade requests without a cover sheet stapled on. We will not regrade your homework on the spot; we will regrade it in batch mode. We will only accept regrade requests for up to one week after your graded solution is returned to you. For homework grading appeals, we will only accept homework regrade requests if you believe that your answer on that problem is 100% correct and you should have received full credit; we will not regrade homeworks in cases where you believe that you should have received more partial credit.

Bear in mind that our primary aim in grading is consistency, so that all students are treated the same; for this reason, we will not adjust the score of one student on an issue of partial credit unless the score allocated clearly deviates from the grading policy we adopted for that problem.

Homeworks: Your homework solutions must be written legibly and contain your name, your TA's name, your discussion section time, and the homework number. You might receive no credit for assignments that are turned in without this information. We do not attempt to grade messy and unreadable solutions. If a problem can be interpreted in more than one way, clearly state the assumptions under which you solve the problem. In writing up your homework you are allowed to consult any book, paper, or published material. If you do so, you are required to cite your source(s). Model solutions will be made available after the due date. Grade problem sets will be returned in discussion section.

Late homework policy: We will give no credit for homeworked turned in after the deadline. No exceptions. Please don't ask for extensions. We don't mean to be harsh, but we prefer to make model solutions available shortly after the due date, which makes it impossible to accept late homeworks.

Exams: The midterms and final exam are mandatory. If you are unable to attend for any reason, contact the instructor without delay.

Don't be afraid to ask for help: Are you struggling? We'd rather you approached us for help, rather than falling behind gradually over the semester until things become untenable. Sometimes this happens when students are afraid of an unpleasant conversation with a professor if they admit to not understanding something. We would much rather deal with your misunderstanding early than deal with its consequences later. Even if you are convinced that you are the only person in the class that doesn't understand the material, and that it is entirely your fault for having fallen behind, please overcome your feeling of guilt and ask for help as soon as you need it. Remember that the other students in the class are working under similar constraints--they are taking multiple classes and are often holding down outside employment. Don't hesitate to ask us for help--helping you learn the material is what we're paid to do, after all!


The following tips are offered based on our experience with CS 170.

1. Don't fall behind! In a conceptual class such as this, it is particularly important to maintain a steady effort throughout the semester, rather than hope to cram just before homework deadlines or exams. This is because it takes time and practice for the ideas to sink in. Make sure you allocate a sufficient number of hours every week to the class, including enough time for reading and understanding the material as well as for doing assignments. (As a rough guide, you should expect to do at least one hour of reading and two hours of problem solving for each hour of lecture.) Even though this class does not have any major projects, you should plan to spend as much time on it as your other technical classes.

2. Do the homeworks! The homeworks are explicitly designed to help you to learn the material as you go along. Although the numerical weight of the homeworks is not huge, there is usually a strong correlation between homework scores and final grades in the class. (The most common denominator among people who do poorly in the class is that they skipped several homework assignments or multiple homework problems.)

Also, regardless of how well you did on the homework, read the sample solutions, even for the problems you got right. You may well learn a different way of looking at the problem, and you may also benefit from emulating the style of the solutions. (In science people learn a lot from emulating the approach of more experienced scientists.)

3. Don't wait until the last minute to start homeworks! My best advice is to read through the homework problems as soon as they are available, and let them percolate in your brain. Think through possible approaches while you are waiting in line, or stuck in an elevator, or whatever. Sleeping on a problem has often helped people to come up with a creative approach to it. Definitely do not wait until the night before it is due to start working on the homework.

4. Make use of office hours! The instructor and TAs hold office hours expressly to help you. It is often surprising how many students do not take advantage of this service. You are free to attend as many office hours as you wish (you are not constrained just to use the office hours of your section TA). You will also likely get more out of an office hour if you have spent a little time in advance thinking about the questions you have, and formulating them precisely. (In fact, this process can often lead you to a solution yourself!)

5. Take part in discussion sections! Discussion sections are not auxiliary lectures. They are an opportunity for interactive learning. The success of a discussion section depends largely on the willingness of students to participate actively in it. As with office hours, the better prepared you are for the discussion, the more you are likely to get out of it.

6. Form study groups! As stated above, you are encouraged to form small groups (two to four people) to work together on homeworks and on understanding the class material on a regular basis. In addition to being fun, this can save you a lot of time by generating ideas quickly and preventing you from getting hung up on some point or other. Of course, it is your responsibility to ensure that you contribute actively to the group; passive listening will likely not help you much. And recall the caveat above that you must write up your solutions on your own. I strongly advise you to spend some time on your own thinking about each problem before you meet with your study partners; this way you will be in a position to compare ideas with your partners, and it will get you in practice for the exams. Make sure you work through all problems yourself. I've seen a few groups that split up the problems ("you do Problem 1, I'll do Problem 2, then we'll swap notes"); not only is this a punishable violation of our collaboration policies, it also ensures you will learn a lot less from this course.

Mail inquiries to cs170@inst.eecs.berkeley.edu.