(1) Describe the Bellman-Ford algorithm for solving the shortest path problem. (2) State the time complexity. Is it a polynomial time algorithm? Consider the graphs containing negative weight cycles. Can Bellman-Ford algorithm find a shortest path between two nodes? Explain or prove. (3)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Please refer to this textbook: “Cormen et al., Introduction to Algorithms, 3rd Edition”

 

And answer the following questions:

Question:23

3.
(1)
Describe the Bellman-Ford algorithm for solving the shortest path problem.
(2)
State the time complexity. Is it a polynomial time algorithm?
Consider the graphs containing negative weight cycles. Can Bellman-Ford algorithm find a
shortest path between two nodes? Explain or prove.
(3)
Is there a polynomial time algorithm to find a negative weight cycle? Explain or prove.
Is there a polynomial time algorithm to find the largest negative weight cycle? Explain or prove.
( A negative weight cycle such that the absolute value of its total weight is maximum..)
(4)
(5)
Transcribed Image Text:3. (1) Describe the Bellman-Ford algorithm for solving the shortest path problem. (2) State the time complexity. Is it a polynomial time algorithm? Consider the graphs containing negative weight cycles. Can Bellman-Ford algorithm find a shortest path between two nodes? Explain or prove. (3) Is there a polynomial time algorithm to find a negative weight cycle? Explain or prove. Is there a polynomial time algorithm to find the largest negative weight cycle? Explain or prove. ( A negative weight cycle such that the absolute value of its total weight is maximum..) (4) (5)
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