Relationship between the shortest path distances - tree, Mathematics

Assignment Help:

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.


Related Discussions:- Relationship between the shortest path distances - tree

MAT201, #There is a balance of $1,234 and this person receive a refund chec...

#There is a balance of $1,234 and this person receive a refund check in the amount of $25 with her paycheck that was deposited into her account for $1500 which made her balance $27

Calculate the number-average and weight-average molar mass, Three mixtures ...

Three mixtures were prepared with very narrow molar mass distribution polyisoprenesamples with molar masses of 8000, 25,000, and 100,000 as indicated below. (a) Equal numbers of

Arc length with polar coordinates, Arc Length with Polar Coordinates H...

Arc Length with Polar Coordinates Here we need to move into the applications of integrals and how we do them in terms of polar coordinates.  In this part we will look at the a

Define combined functions, Q. Define Combined Functions? Ans. We a...

Q. Define Combined Functions? Ans. We are often interested in functions which combine a trigonometric function with another type of function.  For example, y = x + sinx wi

Polynomials, In arithmetic, we deal with numbers. In contrast to this...

In arithmetic, we deal with numbers. In contrast to this, in algebra, we deal with symbols. These symbols are often represented by lower case alphabets. One of th

Describe the types of triangles, Describe the Types of triangles ? Tria...

Describe the Types of triangles ? Triangles can be classified according to the lengths of the sides or the measures of the angles. 1. Naming triangles by sides An

Complementary addition-word problems related to subtraction, Complementary ...

Complementary addition -what number how many things should be added to one number or group to get the other. (e.g., a classroom can seat 50 children, and 20 children are already s

Find the value of given equations in polynomial , If α & ß are the zeroes ...

If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2   b. 1/ α + 1/ ß  c. (α - ß) 2 d. 1/α 2 + 1/ß 2    e.  α 3 + ß 3 (Ans:-1, 4/5 ,-6,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd