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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.
The mean height of eight children is 136cm. if the height of seven children are 143,125,133,140,120,135 and 152,find the height of eighth student.
what is tan 45 degrees?
A plastic manufacturer has 1200 boxes of transparent wrap in stock at one factory and 1000 boxes at his second factory.The manufacturer has order for this product from 3 different
WRITE the condition that should be fulfilled by two matrices A&B to get the product AB and BA
Find out the volume of the solid obtained by rotating the region bounded by y = (x -1) ( x - 3) 2 and the x-axis about the y-axis. Solution Let's first graph the bounded r
how do I solve 14/27 - 23/27 =
Difference between absolute and relative in the definition Now, let's talk a little bit regarding the subtle difference among the absolute & relative in the definition above.
0.875 of a number is 2282. What is the number ?
-255=-14t-t
3x^2+19x-14=0
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