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

Illumination of wire frame, Illumination of wire frame The colour or sh...

Illumination of wire frame The colour or shade that a surface appears to the human eye depends primarily on three  factors : Colour and strength of incoming illumination

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

Acyclic graphs, Acyclic Graphs In a directed graph a path is said to fo...

Acyclic Graphs In a directed graph a path is said to form a cycle is there exists a path (A,B,C,.....P) such that A = P. A graph is called acyclic graph if there is no cycle in

Splaying procedure, For splaying, three trees are maintained, the central, ...

For splaying, three trees are maintained, the central, left & right sub trees. At first, the central subtree is the complete tree and left and right subtrees are empty. The target

Explain the interfaces in ruby, Explain the Interfaces in Ruby Recall...

Explain the Interfaces in Ruby Recall that in object-oriented programming, an interface is a collection of abstract operations that cannot be instantiated. Even though Ruby i

What is binary search, What is binary search?   Binary search is most ...

What is binary search?   Binary search is most useful when list is sorted. In binary search, element present in middle of the list is determined. If key (the number to search)

Define merge sort, Define Merge Sort  Merge sort is a perfect example ...

Define Merge Sort  Merge sort is a perfect example of a successful application of the divide and conquer method. It sorts a given array A[0...n-l] by separating it into two ha

Explain np-complete decision problem, a. Determine the result of inserting ...

a. Determine the result of inserting the keys 4,19, 17, 11, 3, 12, 8, 20, 22, 23, 13, 18, 14, 16, 1, 2, 24, 25, 26, 5 in order to an empty B-Tree of degree 3. Only draw the configu

Determine the algorithm for z-buffer method, Algorithm for Z-Buffer Method ...

Algorithm for Z-Buffer Method (a)  Initialize every pixel in the viewport to the smallest value of z, namely z0 the z-value of the rear clipping plane or "back-ground". Store a

Procedure of analysis of algorithm, Example 1:  Following are Simple sequen...

Example 1:  Following are Simple sequence of statements Statement 1;  Statement 2; ... ... Statement k; The entire time can be found out through adding the times for

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