Mathematics 243 (Combinatorial and Discrete Geometry)
Review: Examination II (Part II)
York College (CUNY)
Jamaica, NY 11451
web page: http://www.york.cuny.edu/~malk
1. Use Konig's alternating path algorithm to find a larger matching for the graph below, starting with the partial matching indicated using bold edges:
2. Use Konig's algorithm to find a maximum cardinality matching for the graphs below:
3. Using the matrix of jobs (rows) and workers (columns) below find:
a. A matching whose total weight is as large as possible
b. A matching whose total weight is as small as possible
c. A matching whose maximum weight edge is as small as possible
d. A matching whose smallest weight edge is as large as possible.
|Worker 1||Worker 2||Worker 3|
e. What interpretation of the numbers above might lead one to want to minimize the total weight of a matching?
f. What interpretation of the numbers above might lead one to want to maximize the the total weight of a matching?