IEOR 6605, Fall 2001: Homework 01

General Instructions

1. Please review the course information.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Network Flows .

Problems

1. 1. What is your email address?
   2. List your previous degrees.
   3. Have you had a course in data structures and/or algorithms? If so, briefly describe the course.
   4. Have you had a course in linear programming? If so, briefly describe the course.
   5. Have you had a courses combinatorics, graph theory, and/or discrete mathematics? If so, briefly describe the course.
   6. Describe your computer programming experience.
2. Problem 2.38. Strongly connected graphs and powers of adjacency matrices. The matrix H is the adjacency matrix discussed in class.
3. Problem 3.4. Function ranking.
4. Problem 3.6. Big-O. The definition of big-Omega is on page 63.
5. Problem 3.28. Breadth-first and depth-first search.
6. Given a directed graph G=(V,E), with vertex set V and edge set E, we define the transpose graph, G^T=(V,E^T), to be G with all its edges reversed. That is, if G has an edge (v,w) then G^T will have an edge (w,v).
   1. Give an algorithm for computing G^T from G, when G is given by an adjacency matrix.
   2. Give an algorithm for computing G^T from G, when G is given by an adjacency list
7. The node-arc incidence matrix N is defined on page 32 of the textbook. Explain what the matrix product N N^T represents.
8. Give an O(n+m)-time algorithm that traverses each edge in an undirected graph exactly once in each direction. Explain how to use this algorithm to find your way out of a maze, given that you have a large stack of pennies with you.

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