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Unformatted text preview: CSE 830: Design and Theory of Algorithms Sample Questions for Exam #2 Spring 2008 1. Graph Traversal. Given the following graph, determine the orders that both BreadthFirst Search and DepthFirstSearch would traverse (mark as discovered) the vertices, starting from A. Break all ties in alphabetical order. 2. Switching Underlying Data Types. Give an O(n 2 ) algorithm to convert from an adjacency matrix to adjacency lists. 3. Bipartite Gaphs. If the maximum degree in a graph is 2, must it be bipartite? If a graph has cycles of only even length, must it be bipartite? Prove or give a counter example for each. 4. Hamiltonian paths. A Hamiltonian path is a simple path that passes through every vertex in a graph exactly once. Finding a Hamiltonian path in an arbitrary graph can be hard, but in a DAG (directed acyclic graph), it can be found (or decided that no such path exists) in only O( n + m ) time. Describe how this is possible. 5. Vertex Cover. The vertex cover problem (choosing a minimum set of vertices where each edge has at least one vertex in the set) is known to be a hard problem, but some instances of it are solvable in polynomial time. Describe three such algorithms if we know that the graph is (a) a ring (a connected graph where all vertices are degree 2.), (b) a tree. or (c) a grid....
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This note was uploaded on 07/25/2008 for the course CSE 830 taught by Professor Ofria during the Spring '08 term at Michigan State University.
 Spring '08
 OFRIA
 Algorithms

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