Algorithms 2008

All tests will be closed book/notes - no electronics aids. You are allowed a 1 page 3 pages 2-sided crib sheet, letter sized.

• Midterm 1 from 2007
  • 2008 topics: everything upto and including BSTs (in particular, balanced BSTs are included)
  • Discussion space for midterm 1
  • Midterm 1 2008; stats
• Midterm 2 from 2007
  • 2008 topics: everything after BSTs upto and including all-pairs shortest paths
  • Midterm 2 2008: stats
• Final from 2007
  • 2008 topics: comprehensive, with an emphasis on latter material, including the unit on coping with intractability
  • Time conflicts
  • Final stats
• Link to student discussion space.
• Feedback from students

• Introduction
  • Here's some basic material on processes, function/system calls, OS/user mode, and libraries.
• Discrete mathematics CLR Appendix B (my notes)
  • See this tutorial on how to read and do proofs. Here's a page of inequalities that I find useful.
• Program performance CLR 1, 2.1, 2.2, 3 (my notes)
  • Here's some code that uses hardware counters on Pentium-derived processors for very accurate timing: timing.h
  • Here's some code that measure space and time usage for various constructs: perf.c. Here's how a Core2 performs.
• Heaps CLR 6 (my notes)
  • Here's some heap code I wrote: heap.h, heap.c
  • Robert Sedgewick's Algorithms text has hard numbers for many sorting algorithms
• Stacks, Queues and Lists CLR 10.1, 10.2, 10.3 (my notes)
  • Here's some code for lists: list.h, list.c; for dynamically resizable arrays array.h, array.c; and for circular buffers circbuf.h, circbuf.c
• Hashing CLR 11 (my notes)
  • The ultimate hash implementation: Bigtable powers 60 different Google applications
• Binary Search Trees CLR 12 (my notes)
  • Here's a nice paper showing tradeoffs between different trees on real applications; a new paper comparing treaps to AVL trees.
  • Also, a summary of BSTs in GNU.
  • Bill Gates contribution to algorithms—figuring out a good way to sort a stack of pancakes
  • Deterministic skip lists are a very simple alternative to balanced trees
• Graph Search CLR 22 (my notes)
  • Andrew Goldberg has high-quality implementations of many graph algorithm. (See also this repository.)
• Shortest Paths CLR 24,25 (my notes)
  • In practice, no one algorithm is best - refer to this study
• Dynamic Programming CLR 15 (my notes)
  • Wikipedia entry; Applications to games, control theory
• Greedy Algorithms CLR 16 (my notes)
  • Examples where the greedy algorithm fails
  • Remarkably, Shannon's attempt at source coding was suboptimum; here's the Wikipedia page on Huffman coding
• Coping with intractable problems
  • This material is not in CLRS - we will use Dasgupta, Papadimitriou, and Vazirani (DPV), specifically Chapter 9 (Pages 283–309)
  • Topics: intelligent exhaustive search, approximation, local search. Backtrack, Branch-and-bound, Vertex cover, K-clusters, TSP with MST 1, TSP with MST 2,TSP local search,Local Search,Graph Partitioning,Simulated Annealing
  • A nice paper on branch-and-bound using linear programming by Stan Liao
• NP-Completeness CLR 34 (my notes)
  • For the final exam, you can assuume the following problems are NPC: Circuit SAT, Formula, SAT, CNF SAT, 3-CNF SAT, k-CLIQUE, k-Vertex Cover, Hamiltonian Cycle, TSP, Subset Sum

The theme this year is computational finance. If you enjoy these labs, you may like the following text—Mathematics for Finance and this survey article. Marketocracy.com and Sharesleuth.com are good sites to learn about the practice of finance.

• PA1: compute relationships between stocks, based on historical prices. Due Feb 6, 11:59pm
  • Objective: get up to speed with Eclipse and the general tool flow we'll be using in the class
  • Documentation, FAQ and tips
  • Justin Enderle found some good references on finite word-length effects in variance computations
• PA2: implement a sparse hash table. Due Feb 22, 11:59pm
  • Objective: get familiar with hashing, and performance measurement and tuning
  • Documentation, FAQ and tips
  • Some Java test cases
• PA3: build a stock quote server. Due Mar 19, 11:59pm
  • Objective: get familiar with BSTs, augmenting data structures
  • Documentation, FAQ and tips
• PA4: look for arbitrage opportunities in currency trades. Wednesday, April 9, 2008, 11:59pm
  • Objective: get familiar with graph algorithms, specifically shortest-path techniques
  • Documentation, FAQ and tips
• PA5: experiment with algorithms for clustering. Due Wednesday, April 30, 2008, 11:59pm
  • Objective: get familiar with approximation algorithms, heuristics, as well as applications of clustering
  • Documentation, FAQ and tips
  • Here is the old lab on portfolio optimization

• Gayatri Ramachandran,
• Senthil Kumar,

• Language tutorials by Brian Kernighan
• Reference Coding Methodology
• Examples of quality code
• Systematic testing
  • Examples of tests
  • Bugs can be very insiduous: The Excel 2007 "65535" Bug
• How to use a debugger
• How to use a profiler
• Recovering lost files on the LRC machines
• Working remotely - Developing from home
• Browse through the Azinix source for an example of Doxygen documentation
• Getting started with Eclipse
• Version control with CVS
• Michael Ogg's notes on C++ might be a good way to refresh your object-oriented programming skills
  • Read Tom Anderson's warnings on C++ (source for the examples is here)

• Programming Brian Kernighan's Advanced Programming Techniques is a fabulous class. His book The Practice of Programming is the best programming book I've ever read.
  • Prof. Kernighan Spring 2008 class, linked above, does not have all the notes in place; you can get them from the Spring 2005 version of the class.
  • George Necula's class on software engineering talks about many critical issues software development. It's tuned towards much larger projects than the ones we've been doing, but still worth reading through.
  • An OS class can help you understand what goes on under the hood—CS162 at Berkeley is the one I learned from.
  • The Art of Unix Programming - free online version, see especially Chapter 1. “Those who do not understand Unix are condemned to reinvent it, poorly”
• Algorithms MIT makes all its courses avaible freely - here's the algorithms class at MIT, including videos of lectures; it's co-taught by Leiserson, the L in CLRS.
  • Similar classes at Berkeley, Stanford, UIUC, Washington, Cornell
• Discrete Mathematics John Canny's class at Berkeley
• Computational Finance Steve Skiena's SUNY Stony Brook class

• Algorithm Design by Jon Kleinberg and Eva Tardos
• Introduction to Algorithms by Udi Manber
• Algorithms by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani
• Data Structures and Algorithms by Al Aho, Jeff Ullman, and John Hopcroft (older, but a classic)
• Data Structures and Network Algorithms by Robert Tarjan (more advanced)
• Algorithms in Java by Robert Sedgewick
• Network Flows: Theory, Algorithms, and Applications by Ravindra Ahuja, Thomas Magnanti, and James Orlin (advanced graph algorithms)
• Convex Optimization by Steven Boyd and Lieven Vandenberghe (continuous rather than discrete optimization, but an absolutely brilliant book)