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1. For an acyclic network G with a specified source node s, outline an algorithm that enumerates all distinct directed paths from the source node to every other node in the network. The running time of your algorithm should be proportional to the total length of all the paths enumerated (i.e., linear in terms of the output length.)
2. In an undirected connected graph G = (N, A), an Euler tour is a walk that starts at some node, visits each arc exactly once, and returns to the starting node. A graph is Eulerian if it contains an Euler tour. Show that in an Eulerian graph, the degree of every node is even. Next, show that if every node in a connected graph has an even degree, the graph is Eulerian. Establish the second result by describing an O(m) algorithm for determining whether a graph is Eulerian and, if so, will construct an Euler tour. (Hint: Describe an algorithm that decomposes any graph with only even-degree nodes into a collection of arc-disjoint cycles, and then converts the cycles into an Euler tour.)
It is often claimed that "differencing" the regression model will reduce the degree of autocorrelation. Consider this claim by using as the model: yt = xt + ut and ut = ut1 + t where (t) is white noise with mean zero and variance 2.Show that the ..
Assume that the short run cost and demand data given in the table below confront a monopolistic competitor selling a given product and engaged in a given amount of product promotion. Compute the marginal cost and marginal revenue of each unit of o..
while growth in the standard of living (for example) is considered a primary goal. Why do you think that is so?
Use the given equation and determine the demand equation as a function of Ps if the price of other pastas (Po) is $2,
Write a summary paragraph that outlines the findings evident from the ratios and notes any particular adjustments made in the calculations of the ratios that is material to the analysis.
Suppose that the government wishes to decrease the market equilibrium price by increasing the supply of corn. Assuming that demand remains unchanged, by how many tons of corn would the government have to increase the supply of corn in order to get..
what extra semiannual expenditure for five years would be justified for the maintenance of a machine in order to avoid
industry demand curve equals Q=900-100P and the long run average cost is a constant $1.50 per unit of output. Calculate market output, price, consumer surplus, and producer surplus in a competitive market.
Your money is tied up and you need to borrow $ 10,000. The following two alternatives are being offered by the lender: ( 1) pay $ 3,288.91 at the end of each year for 5 years, starting at the end of the first year
If we have a demand curve which can be described by Pd= 72.33-1.76Q, and we have a starting price of $50, what happens to TR when the price falls to $40 Find whether MR is positive or negative
summary outputregression statisticsmultiple r 0.973178112r square 0.947075637adjusted r square 0.9417832standard error
If the government operates on a balanced budget before interest payments are taken into account, at what rate must GDP grow in order for the debt-GDP ratio to remain unchanged?
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