CSCI 2300 Spring 2012

Rensselaer Polytechnic Institute
Department of Computer Science

CSCI 2300: Introduction to Algorithms

Spring 2012

ANNOUNCEMENTS

All graded homeworks (including 6 and 7) are available in the box outside Lally 302. An up-to-date snapshot of grades has been posted to LMS (this does not include a course grade). If you see any problems with your grades please email all three of Sanmay, Fred, and Bhavana immediately!

The final exam is scheduled for Wednesday May 16, 11:30-2:30 PM in Sage 3510.

A second set of mid-semester grades are now available on LMS. If any of your scores are incorrect, please talk to Sanmay or one of the TAs about it. You can also send email to all three of us noting the issue, and someone will respond.These should be updated up to HW5, Lab 5 and Midterm 2. The "grade" column shows your current grade if the class were to end now.

Regular hours for the undergraduate programming mentors at ALAC are now set. They are as follows:
Matthew Dippel: Sundays from 6-8 PM
Samuel Sandeen: Tuesdays from 8-10 PM
Cameron Helm: Wednesdays from 8-10 PM

Welcome to Intro to Algorithms! We will meet on Mondays and Thursdays at noon in Amos Eaton 214. The first meeting will be on the 23rd of January. There will be no labs the first week of class.

OVERVIEW

This is a foundational course in the design and analysis of algorithms and the data structures they are coupled with. While we will concentrate on the theoretical design and analysis of algorithms and data structures, we will reinforce the theory with examples, laboratories, and applied homework questions.

The goal of this course is to provide a strong foundation in algorithms and data structures in preparation for jobs in industry or for more advanced courses. Algorithms are the basic language of computer science. After taking this course, you should be able to prove the correctness of and analyze the running times of different algorithms. You should also be able to use different algorithm-design techniques to solve particular problems. Data structures and algorithms also form a major component of any software system. After taking this course you should be able to make intelligent decisions about alternative techniques in the context of practical problems, choosing from existing data structures and algorithms or designing your own when necessary.

STAFF

Instructor: Sanmay Das
Office: Lally 302
Phone: x2782
Office hours: Mondays from 3:30-5:00 PM, and by appointment.

TA: Fred Sisenda (sisenf at rpi)
Labs: W 2-4 PM in Sage 2715 with undergraduate programming mentor Matthew Dippel.
and W 4-6 in Lally 104 with undergraduate programming mentor Cameron Helm.

TA: Bhavana Malhotra (malhob at rpi)
Labs: W 10 AM - 12 noon in Lally 104 with undergraduate programming mentor Samuel Sandeen.
and W 12 noon - 2 PM in Lally 104 with undergraduate programming mentors Cameron Helm and Samuel Sandeen.

POLICIES

TEXTBOOKS

There are two textbooks for this class

DPV: Algorithms by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani, McGraw-Hill, ISBN 0073523408.
CLRS: Introduction to Algorithms (2nd or 3rd Ed is fine) by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, MIT Press/McGraw-Hill, ISBN 0070131511 (for the 2nd Ed).

PROGRAMMING

This is not a programming class. The labs involve programming, but you are expected to be a competent C++ programmer coming in -- the lectures will not discuss any code. The TAs and undergraduate programming mentors can provide some help on programming issues in lab. Neither of the textbooks deals with programming issues at all. You may want to consult your textbooks from CS2, or Stroustrup's The C++ Programming Language.

LECTURES

Lectures will be on Mondays and Thursdays from 12pm to approximately 1:30pm in Amos Eaton 214. The "Mathematical Background" appendix of CLRS is background reading for the whole class. In the readings, chapter numbers for CLRS are for the 3rd edition.The table of contents for the 3rd edition is here, if you want to compare to another edition.

SCHEDULE

The schedule below is provided to help you plan, but please bear in mind that it is tentative and subject to change based on the progress of the class. Some changes to the schedule are almost always necessary!

Date	Topics	Readings
Jan 23	Introduction. Course policies. Course overview. Some interesting problems.	DPV Chapter 0
Jan 26	Generating random permutations. Fibonacci numbers. Basic arithmetic.	CLRS Section 5.3 (Randomized Algorithms), DPV Chapter 0, Section 1.1.
Jan 30	Integer division. Divide and conquer algorithms, recurrence relations, the Master Theorem.	DPV Sections 1.1, 2.1, 2.2
Feb 2	Mergesort. Sorting lower bound. Medians and Selection. Matrix multiplication.	DPV Sections 2.3, 2.4, 2.5.
Feb 6	Quicksort.	CLRS Chapter 7.
Feb 9	Heaps and heapsort. Modular arithmetic.	CLRS Chapter 6. DPV Section 1.2.
Feb 13	Modular arithmetic contd. Intro to graphs.	DPV Sections 1.2, 3.1.
Feb 16	Reachability. Depth-first search.	DPV Sections 3.1-3.3.
Feb 20	No class. President's Day.
Feb 23	Topological sort. Strongly connected components.	DPV Sections 3.3-3.4.
Feb 27	Breadth-First Search. Dijkstra's algorithm. Negative edge lengths.	DPV Sections 4.1-4.6.
Mar 1	Shortest paths contd. Minimum spanning trees.	DPV Sections 4.7, 5.1.
Mar 5	Midterm #1.
Mar 8	Midterm discussion. The Disjoint Set data structure.	DPV Section 5.1. CLRS Chapter 21.
Mar 19	Amortized analysis of path compression. Amortized analysis in general.	DPV 5.1, CLRS 21.4, 17.1-17.3.
Mar 22	Huffman coding. Greedy approximation for set cover.	DPV 5.2 and 5.4.
Mar 26	Hashing. Chaining, open addressing, cuckoo hashing.	CLRS 11.1, 11.2, 11.4; Cuckoo hashing notes from Rasmus Pagh
Mar 29	Bloom Filters. Universal hashing. Horn formulas.	Wikipedia on Bloom Filters; CLRS 11.3, DPV 1.5, 5.3.
Apr 2	Intro to dynamic programming: shortest paths in DAGs, longest increasing subsequence, edit distance	DPV 6.1-6.3.
Apr 5	Dynamic programming: knapsack, chain matrix multiplication	DPV 6.4-6.5.
Apr 9	Dynamic programming: shortest paths, independent sets in trees	DPV 6.6-6.7.
Apr 12	Midterm #2.
Apr 16	The DP approach to TSP. Flows and max-flow.	DPV 7.2; CLRS 26.1-26.2
Apr 19	Midterm discussion and return. Flows contd.
Apr 23	Max-flow min-cut theorem. Bipartite matching. Intro to NP-completeness.	CLRS 26.3. DPV 7.3, 8.1.
Apr 26	NP-completeness contd. Reductions: Rudrata path to Rudrata cycle. 3SAT to Independent Set. SAT to 3SAT. Independent Set to Vertex Cover.	DPV 8.2, 8.3.
Apr 30	More reductions. Independent Set to Clique. 3SAT to 3-D Matching. 3-D Matching to ZOE. ZOE to Subset Sum.	DPV 8.3.
May 3	Reductions: ZOE to RCWPE. RCWPE to Rudrata Cycle. Rudrata Cyle to TSP.	DPV 8.3.
May 7	Reduction: Circuit SAT to SAT. Sketch for reducing all of NP to Circuit SAT. Unsolvable problems.	DPV 8.3.

LABS

Jan 25: No lab
Feb 1: Lab 1
Feb 8: Recitation/OH
Feb 15: Lab 2. Required additional files are here.
Feb 22: Recitation/OH
Feb 29: Recitation/OH
Mar 7: Lab 3. Required additional files are here
Mar 21: Recitation/OH
Mar 28: Recitation/OH
Apr 4: Lab 4. Required additional files are here.
Apr 11: Recitation/OH
Apr 18: Lab 5. Required additional files are here.
Apr 25: Recitation/OH
May 2: Lab 6. Required additional files are here.

HOMEWORKS

HW1: Due Feb 9.
HW2: Due Feb 23.
HW3: Due Mar 1.
HW4: Due Mar 29.
HW5: Due Apr 9.
HW6: Due Apr 30.
HW7: Due May 7.