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1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by using potentials:
i) Show there is a potential y* for the new costs for which the paths in the tree to each node v have cost y*v, and
ii) explain why this proves it. What is the relationship between the shortest path distances of the modified problem and those of the original problem?
b) Can adding a constant k to the length of every arc coming out from a non-root node produce a change in the shortest path tree? Justify your answer.
what is 5+10
Convert measurements between the English system? To convert measurements between the English system and the metric system: 1. Look up the conversion between the two units of
How to Make Equations of Conics Easier to Read ? If you want to graph a conic sections, first you need to make the equation easy to read. For example, say you have the equatio
a) A husband and wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is th
Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve
265 divided by 7
R is called as a transitive relation if (a, b) € R, (b, c) € R → (a, c) € R In other terms if a belongs to b, b belongs to c, then a belongs to c. Transitivity be uns
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A company makes 2 products, Product A and Product B. The product characteristics are shown in the following table. Product A B
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