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

If else, design algorithm and flow chart that computes the absolute differe...

design algorithm and flow chart that computes the absolute difference of two values x and y

Inorder and preorder traversal to reconstruct a binary tree, Q. Using the f...

Q. Using the following given inorder and preorder traversal reconstruct a binary tree Inorder sequence is D, G, B, H, E, A, F, I, C

Algorithm of binary search, Step 1: Declare array 'k' of size 'n' i.e. k(n)...

Step 1: Declare array 'k' of size 'n' i.e. k(n) is an array which stores all the keys of a file containing 'n' records Step 2: i←0 Step 3: low←0, high←n-1 Step 4: while (l

Splaying steps - splay trees, Readjusting for tree modification calls for r...

Readjusting for tree modification calls for rotations in the binary search tree. Single rotations are possible in the left or right direction for moving a node to the root position

Implementation of tree, The most common way to insert nodes to a general tr...

The most common way to insert nodes to a general tree is to first discover the desired parent of the node you desire to insert, and then insert the node to the parent's child list.

Multiple queue, #questionalgorithm for implementing multiple\e queues in a ...

#questionalgorithm for implementing multiple\e queues in a single dimensional array

SORTING ALGORIthm, the deference between insertion,selection and bubble sor...

the deference between insertion,selection and bubble sort

What are the properties of colour, Properties of colour Colour descript...

Properties of colour Colour descriptions and specifications generally include three properties: hue; saturation and brightness. Hue associates a colour with some position in th

Threads in main method, Create main method or a test class that creates 2 E...

Create main method or a test class that creates 2 Element objects that are neighbours of each other, the first element temperature set at 100, the 2nd at 0 and use an appropriate h

Characteristics of good algorithms, What do we mean by algorithm? What are ...

What do we mean by algorithm? What are the characteristics of a good and relevant algorithm? An algorithm is "a step-by-step procedure for finishing some task'' An algorithm 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