CS2013-final-report

Course textbooks and materials
Algorithm Design by Kleinberg and Tardos, supplemented liberally with my own lecture notes. There are two
programming assignments, one in Python and one in Java.
Why do you teach the course this way
The goal of Algorithms is for students to learn and practice a variety of problem solving strategies and analysis
techniques. Students develop algorithmic maturity. They learn how to think about problems, their solutions, and
the quality of those solutions.
I have taught Algorithms since 2007 except for 2010 when I was on sabbatical. My sense is that my course is nontrivial
revision of the offering pre-2007. Students consider the course challenging in a rewarding way.
Body of Knowledge coverage
KA
Knowledge
Unit
Topics Covered
Hours
AL Basic Analysis Asymptotic analysis including definitions of asymptotic upper, lower, and
tight bounds. Discussion of worst, best, and expected running time (Monte
Carlo and Las Vegas for randomized algorithms and a brief discussion about
making assumptions about the distribution of the input). Natural complexity
classes in P (log n, linear quadratic, etc.), recurrence relations and their
solutions (mostly via the recursion tree and master method although we
mention generating functions as a more general solution).
5
AL
Algorithmic
Strategies
Brute-force algorithms (i.e., try-‘em-all), divide and conquer, greedy
algorithms, dynamic programming, and transformations. We do not cover
recursive backtracking, branch and bound, or heuristic programming although
these topics are given some attention in Artificial Intelligence.
6
AL
Fundamental
Data Structures
and Algorithms
Order statistics including deterministic median, We do not cover heaps
directly in this course although we mention various heap implementations and
their trade-offs (e.g., Fibonacci heaps, soft heaps, etc.) when discussing
shortest path and spanning tree algorithms. Undirected and directed graphs,
bipartite graphs, graph representations and trade-offs, fundamental graph
algorithms including BFS and DFS, shortest-path algorithms, and spanning
tree algorithms. Many of the topic areas included in this knowledge unit are
covered in Data Structures so we review them quickly and use them as a
launching point for more advanced material.
4
AL
Basic
Automata,
Computability
and Complexity
Algorithm Design and Analysis contains very little complexity theory–these
topics are all covered in detail in our Theory of Computation course.
However, we do spend 1 lecture on the complexity classes P and NP, and
approaches to dealing with intractability including approximation algorithms
(mentioned below).
1
AL
Advanced Data
Structures,
Algorithms and
Analysis
A quick review of ordered dynamic dictionaries (including balanced BSTs
like Red-Black Trees and AVL-Trees) as a way of motivating Skip Lists.
Graph algorithms to find a maximum matching and connected components.
Some advanced data structures like union-find (including the log*n amortized
analysis). Suffix trees, suffix arrays (we follow the approach of Karkkainen
and Sanders that recursively builds a suffix array and then transforms it into a
suffix tree). Network flow including max-flow, min-cut, bipartite matching
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