IEOR 6614, Spring 2006 : 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. List your previous degrees.
   2. Have you had a course in data structures and/or algorithms? If so, briefly describe the course.
   3. Have you had a course in linear programming? If so, briefly describe the course.
   4. Have you had a courses combinatorics, graph theory, and/or discrete mathematics? If so, briefly describe the course.
   5. Describe your computer programming experience.
2. Problem 2.10. Connectivity in graphs.
3. Problem 3.4. Function ranking.
4. Problem 3.6. Big-O and Big-Omega
5. 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
6. The node-arc incidence matrix N is defined on page 32 of the textbook. Explain what the matrix product N N^T represents.

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