Relationship between the shortest path distances - tree, Mathematics

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.

Posted Date: 3/22/2013 3:59:36 AM | Location : United States







Related Discussions:- Relationship between the shortest path distances - tree, Assignment Help, Ask Question on Relationship between the shortest path distances - tree, Get Answer, Expert's Help, Relationship between the shortest path distances - tree Discussions

Write discussion on Relationship between the shortest path distances - tree
Your posts are moderated
Related Questions
angel 1 and angel 2 are what angels?

I cant figure out how to study for my math test

Graph  ( x + 1) 2 /9 -( y - 2) 2 /4 =1 Solution It is a hyperbola. There are in fact two standard forms for a hyperbola.  Following are the basics for each form. H

how much congruent sides does a trapezoid have

(a) Find an example of groups G, H, K with K  H and H G but K G. (b) A subgroup H of G is characteristic if σ(H) ⊆ H for every group automorphism σ of G. Show that eve

HOW CAN WE TAKE SUPPOSE THE VALUES OF X AND Y

An elevated cylindrical shaped water tower is in require of paint. If the radius of the tower is 10 ft and the tower is 40 ft tall, what is the net area to be painted? (π = 3.14)


What are the other differences between learners that a teacher needs to keep in mind, while teaching?  Let us see an example in which a teacher took the pupil's background into acc

Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini