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

Binary trees, A binary tree is a special tree where each non-leaf node can ...

A binary tree is a special tree where each non-leaf node can have atmost two child nodes. Most important types of trees which are used to model yes/no, on/off, higher/lower, i.e.,

What is class invariants assertion, What is Class invariants assertion ...

What is Class invariants assertion A class invariant is an assertion which should be true of any class instance before and after calls of its exported operations. Generally

Data type, Data type An implementation of an abstract data type on a...

Data type An implementation of an abstract data type on a computer. Therefore, for instance, Boolean ADT is implemented as the Boolean type in Java, and bool type in C++;

Define container in terms of object-oriented terms, Define container in te...

Define container in terms of  object-oriented terms A Container is a broad category whose instances are all more specific things; there is never anything which is just a Contai

Explain multidimensional array, Multidimensional array: Multidimensional a...

Multidimensional array: Multidimensional arrays can be defined as "arrays of arrays". For example, a bidimensional array can be imagined as a bidimensional table made of elements,

Inorder traversal, Inorder traversal: The left sub tree is visited, then t...

Inorder traversal: The left sub tree is visited, then the node and then right sub-tree. Algorithm for inorder traversal is following: traverse left sub-tree visit node

Representation of arrays, REPRESENTATION OF ARRAYS This is not uncommon...

REPRESENTATION OF ARRAYS This is not uncommon to determine a large number of programs which procedure the elements of an array in sequence. However, does it mean that the eleme

Flow chart, What is tha flow chart of algorithm

What is tha flow chart of algorithm

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