## CS447 Computer Algorithms (Fall 2004)

#### Course Prerequisites: CS344 Algorithms and Data Structures and (MA211
Foundations or MA346 Applied Algebra and Discrete Mathematics)

### Course Contact Information

**Instructor**: Chris
Lynch

**Lectures**: MWF 11am SC 354

**Office hours**: MW 2-4pm and F
3-4pm SC 377

**Contact**: SC 377, clynch@clarkson.edu

**Text:** *Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest,
Clifford Stein*, **Introduction to Algorithms**
(2nd ed.) MIT Press (2001).

### Topical Outline

This course studies the algorithmic techniques for
solving computational problems efficiently. In particular, the following
techniques are covered: basic divide-conquer techniques and analysis using
recurrences, dynamic programming, greedy methods, and amortized analysis. Some
emphasis will be put on graph-theoretic problems and data structures that are
relevant to them. Finally, a discussion of the theory of NP-completeness on the
limitations of solving problems efficiently will end the course.

### Objectives and outcomes

The objective of this course is to learn
fundamental algorithmic techniques, to gain the ability to evaluate the
efficiency of algorithms, and to understand certain intractability issues
concerning hard algorithmic questions.
The specific outcomes are basic knowledge of the following:

- Asymptotic notation for comparing cost measures.
- Tools for dealing with summations and recurrences.
- Design and analysis techniques: dynamic programming, greedy algorithms,
and amortized analysis.
- Graph theory and some of its algorithmic problems.
- Rudimentary theory of NP-completeness.

### Requirements and Policies

Although attendance is not mandatory, students
are responsible for all course materials covered in lectures given during class
periods. Students that need to make up missing course work must provide the
required Clarkson official exempt form. All students must submit their own work;
the exchange of ideas are encouraged but ultimately the submitted work must be
the student's own. If a student exchanges ideas with another student or gets
ideas from another source, then that source must be mentioned on the homework
paper. If that is not done, then it is consdidered cheating. Of course it is
also considered cheating to copy something even if the source is referenced.
Please refer to the Clarkson University Regulations for more guidelines on
academic integrity and related matters.

### Grading Scheme

There is no final exam in this course (pending approval).
- Tests (2): 60% (tentative dates: October ??)
- Homework: 30%
- Project: 10% (due early December)

### Tentative Course Schedule

- (Chapters 1,2) Analyzing efficiency of loops.
Divide-conquer and recurrence analysis for recursive programs.
- (Chapter 3) Asymptotic growth of functions: big-Oh,
big-Omega, little-oh, little-omega, and big Theta. Summations (Appendix A):
arithmetic, geometric, Harmonic, splitting techniques, telescoping
sums.
- (Chapter 4) Recurrences: substitution method, recursion
tree method, the Master Theorem.
- (Chapters 6-9) Review of Sorting programs and Analysis of
SELECTION problem.
- (Chapter 15) Dynamic Programming: assembly line
scheduling, longest common subsequence, matrix chain multiplication..
- (Chapter 16) Greedy algorithms: activity selection
problem, fractional knapsack.
- (Chapter 17) Amortized analysis.
- (Chapters 22-26) Graph algorithms: basic searches: BFS,
DFS. Topological sorting. Strongly connected components. Minimum Spanning
Trees (Kruskal & Prim). Single-source Shortest Paths (Dijkstra). All-pairs
Shortest Paths: matrix multiplication, Floyd-Warshall. Maximum Flow: Edmonds-Karp algorithm.
- (Chapter 32) String Matching.
- (Chapter 34) NP-Completeness; efficient reductions:
CLIQUE, INDEPENDENT SET, VERTEX COVER.