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

Insert an element after an element pointed by some pointer, Consider a link...

Consider a linked list of n elements. What is the time taken to insert an element after an element pointed by some pointer? O (1)

Which sorting algorithms not have running time of o (n2), Which sorting al...

Which sorting algorithms does not have a worst case running time of  O (n 2 ) ? Merge sort

Generate a single sorted list of all n elements, Q. Assume that we have sep...

Q. Assume that we have separated n elements in to m sorted lists. Explain how to generate a single sorted list of all n elements in time O (n log m )?

Big o notation, This notation gives an upper bound for a function to within...

This notation gives an upper bound for a function to within a constant factor. Given Figure illustrates the plot of f(n) = O(g(n)) depend on big O notation. We write f(n) = O(g(n))

Structure of an avl tree, Given is the structure of an AVL tree: struct ...

Given is the structure of an AVL tree: struct avl { struct node *left; int info; int bf; struct node *right; }; 2) A multiway tree of n order is an ord

#, if two relations R and S are joined, then the non matching tuples of bot...

if two relations R and S are joined, then the non matching tuples of both R and S are ignored in

Queues, Queue is a linear data structure utilized in several applications o...

Queue is a linear data structure utilized in several applications of computer science. Such as people stand in a queue to get a specific service, several processes will wait in a q

Write the algorithm to find input and output value, This algorithm inputs 5...

This algorithm inputs 5 values and outputs how many input numbers were positive and how many were negative. Data to be used: N = 1, -5, 2, -8, -7

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