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1. Consider an (arbitrary) spanning tree T of a graph G. Show how to label each node in Tas 0 or 1 so that whenever arc (i,j) is contained in the tree, nodes i and} have different labels. Using this result, prove that G is bipartite if and only if for every nontree arc (k, I), nodes k and I have different labels. Using this characterization, describe an O(m) algorithm for determining whether a graph is bipartite or not.
2. In an acyclic network G = (N, A) with a specified source node s, let o:(i) denote the number of distinct paths from node s to node i. Give an O( m) algorithm that determines aU) for all i ∈ N. (Hint: Examine nodes in a topological order.)
The estimated economic results for the project (after taxes), in the foreign currency (T-marks), is shown in the following table for the seven-year analysis period being used. The company requires an 18% rate of return in U.S. dollars.
As workers become more educated, their human capital increases as does their value marginal product to firms. How do you think your education will improve the value of your marginal product? What impact will this have on your life
Penelope wants to buy a car that is worth $43,195 by making a $4300 down payment and arranging a four-year lease that calls for monthly payments in advance, interest of 2.91 percent compounded monthly, and a buyout payment of $20,000
Jen left a job paying $60,000 per year to start her own florist shop in a building she owns. The market value of the building is $150,000. She pays $40,000 per year for flowers and other supplies, and has a bank account
You are starting your own Internet business. You decide to form a company that will sell cookbooks online. Justcookbooks.com is scheduled to launch 6 months from today. You estimate that the annual cost of this business will be as follows: Technol..
In the clinic renovation example what if management thinks that the likelihood of current demand remaining is 30%, the likelihood of a moderate increase is 25%, and the likelihood of a large increase is 45%? What should they do, according to the e..
Show a snippet of PHP code for disconnecting from the database. Explain the meaning of the code.
Find the smallest and largest values of children in the sample. What is the average of children? Does any woman have exactly the average number of children?
What is Firm 1's profit-maximizing quantity, given that Firm 2 produces an output of 50 units per year? What is Firm 1's profit-maximizing quantity when Firm 2 produces 20 units per year?
Why is real GDP targeting the riskier of the two strategies?
Let X be an allocation in the interior of the box. Show that all of the allocations that both George and Harriet believe to be at least as good as X lie within a triangular or diamond-shaped area.
Suppose that there are only three types of fruit sold in the United States. Annual sales are 1 million tons of blueberries, 5 million tons of strawberries, and 10 million tons of bananas.
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