Relationship between shortest path distances of modified, Data Structure & Algorithms

Assignment Help:

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 shortest path distances of modified

Creation of a linked list, Program: Creation of a linked list In the ne...

Program: Creation of a linked list In the next example, wewill look to the process of addition of new nodes to the list with the function create_list(). #include #includ

Algorithms, Data array A has data series from 1,000,000 to 1 with step size...

Data array A has data series from 1,000,000 to 1 with step size 1, which is in perfect decreasing order. Data array B has data series from 1 to 1,000,000, which is in random order.

Dijkstras algorithm, Djikstra's algorithm (named after it is discovered by ...

Djikstra's algorithm (named after it is discovered by Dutch computer scientist E.W. Dijkstra) resolves the problem of finding the shortest path through a point in a graph (the sour

Algorithms, characteristics of a good algorithm

characteristics of a good algorithm

Recursive implementation of binary tree traversals, There are three typical...

There are three typical ways of recursively traversing a binary tree. In each of these, the left sub-trees & right sub-trees are visited recursively and the distinguishing feature

Data structures, Aa) Come up with an ERD from the following scenario, clear...

Aa) Come up with an ERD from the following scenario, clearly stating all entities, attributes, relationships before final sketch of the ERD: [50 m

Illustrate trivariate colour models, Illustrate Trivariate Colour Models ...

Illustrate Trivariate Colour Models Conventional colour models based on the tristimulus theory all contain three variables and so are called trivariate models. Let us now consi

Threaded Binary Tree, If a node in a binary tree is not containing left or ...

If a node in a binary tree is not containing left or right child or it is a leaf node then that absence of child node can be represented by the null pointers. The space engaged by

Find the optimal control, 1. Use the Weierstrass condition, find the (Stron...

1. Use the Weierstrass condition, find the (Strongly) minimizing curve and the value of J min for the cases where x(1) = 0, x(2) = 3. 2. The system = x 1 + 2u; where

Determine the output of vehicles algorithm, Draw trace table and determine ...

Draw trace table and determine the output from the below flowchart using following data (NOTE: input of the word "end" stops program and outputs results of survey):  Vehicle = c

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