Exponential and NP Algorithms

Steven J. Zeil

Old Dominion University, Dept. of Computer Science

Table of Contents

1. A Hard Problem - Graph Coloring
1.1. Graph Coloring: A Backtracking Solution
2. NP Problems
2.1. A Parallel Approach to Graph Coloring
2.2. Nondeterministic Machines
2.3. NP-Complete Problems
2.4. So, is P = NP?
3. If you can't get across, go around.

We've spent a lot of time and effort this semester worrying about finding efficient algorithms, and learning how to tell if they are efficient in the first place. It's fitting that we end up by noting that there are some very practical problems for which no known efficient solution exists, and for which there is considerable reason to doubt that an efficient solution is possible.

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