Graphs with negative edge costs, Data Structure & Algorithms

Assignment Help:

We have discussed that the above Dijkstra's single source shortest-path algorithm works for graphs along with non-negative edges (like road networks). Given two scenarios can emerge out of negative cost edges into a graph:

  • Negative edge along non- negative weight cycle reachable from the source.
  • Negative edge along non-negative weight cycle reachable from source.

529_Graphs with Negative Edge costs.png

Figure: A Graph with negative edge & non-negative weight cycle

The net weight of the cycle is 2(non-negative)

437_Graphs with Negative Edge costs1.png

 Figure: A graph with negative edge and negative weight cycle

The net weight of the cycle is 3(negative) (refer to above figure). The shortest path from A to B is not well defined as the shortest path to this vertex are infinite, that means , by traveling each cycle we can reduced the cost of the shortest path by 3, like (S, A, B) is path (S, A, B, A, B) is a path with less cost and so forth.

Dijkstra's Algorithm works only for directed graphs along non-negative weights (cost).


Related Discussions:- Graphs with negative edge costs

Four applications or implementation of the stack, Q. Write down any four ap...

Q. Write down any four applications or implementation of the stack.                                     Ans. (i)       The Conversion of infix to postfix form (ii)

Amortized algorithm analysis, In the amortized analysis, the time needed to...

In the amortized analysis, the time needed to perform a set of operations is the average of all operations performed. Amortized analysis considers as a long sequence of operations

Define dynamic programming, Define Dynamic Programming  Dynamic  progra...

Define Dynamic Programming  Dynamic  programming  is  a  method  for  solving  problems  with  overlapping  problems.  Typically, these sub problems arise from a recurrence rel

Find a minimum cost spanning arborescence rooted, Find a minimum cost spann...

Find a minimum cost spanning arborescence rooted at r for the digraph shown below, using the final algorithm shown in class. Please show your work, and also give a final diagram wh

Algorithms for push and pop operation, Q. Suggest a method of implementing ...

Q. Suggest a method of implementing two stacks in one array such that as long as space is there in an array, you should be capable to add an element in either stack. Using proposed

Linked list, write an algorithm for multiplication of two sparse matrices u...

write an algorithm for multiplication of two sparse matrices using Linked Lists

Algorithm to merge two sorted arrays with third array, Q. Write down an alg...

Q. Write down an algorithm to merge the two sorted arrays into the third array. Do  not perform the sort function in the third array.                           Ans: void m

Which data structure is used for implementing recursion, Which data structu...

Which data structure is used for implementing recursion Stack.

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