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

Sort the Sequence Using Merge Sort, Q. Sort the sequence written below of k...

Q. Sort the sequence written below of keys using merge sort. 66, 77, 11, 88, 99, 22, 33, 44, 55                                                                      Ans:

What is binary space partition, Binary Space Partition A binary space-p...

Binary Space Partition A binary space-partitioning (BSP) tree is an efficient method for determining object visibility by painting surfaces onto the screen from back to front,

Define chaining process of hashing, Chaining In this method, instead of...

Chaining In this method, instead of hashing function value as location we use it as an index into an array of pointers. Every pointer access a chain that holds the element havi

State the output of avaerage value of numbers, Draw trace table and determi...

Draw trace table and determine output from the subsequent flowchart using below data:  X = 5, -3, 0, -3, 7, 0, 6, -11, -7, 12

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

Algorithm that counts number of nodes in a linked list, Q. Write an algorit...

Q. Write an algorithm that counts number of nodes in a linked list.                                       A n s . Algo rithm to Count No. of Nodes in Linked List C

Operating system, discuss the operating system under the following: MONOLIT...

discuss the operating system under the following: MONOLITHIC SYSTEM,LAYER SYSTEM AND VIRTUAL MACHINES

Programs, Develop a program that accepts the car registration( hint: LEA 43...

Develop a program that accepts the car registration( hint: LEA 43242010)

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