1. (1)Use dynamic programming technique to solve the all-pairs shortest paths problem in a directed graph. ( So called Floyd-Warshall algorithm ) (Define the object function; state the recursive formula, initial condition, and answer. Give the time complexity and space complexity without explanation.) (2)Suppose that some of the edge weights are negative, what can you say about the algorithm given in part (1)? Do you still get the all-pairs shortest simple path correct? How do you detect the existence of a negative weight directed cycle? How do you find one such cycle?
1. (1)Use dynamic programming technique to solve the all-pairs shortest paths problem in a directed graph. ( So called Floyd-Warshall algorithm ) (Define the object function; state the recursive formula, initial condition, and answer. Give the time complexity and space complexity without explanation.) (2)Suppose that some of the edge weights are negative, what can you say about the algorithm given in part (1)? Do you still get the all-pairs shortest simple path correct? How do you detect the existence of a negative weight directed cycle? How do you find one such cycle?
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
Section: Chapter Questions
Problem 1PE
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107_2_B_1
Dynamic

Transcribed Image Text:1.
(1)Use dynamic programming technique to solve the all-pairs shortest paths
problem in a directed graph. ( So called Floyd-Warshall algorithm )
(Define the object function; state the recursive formula, initial condition, and answer. Give the time
complexity and space complexity without explanation.)
(2)Suppose that some of the edge weights are negative, what can you say about the algorithm given in
part (1)? Do you still get the all-pairs shortest simple path correct? How do you detect the existence of
a negative weight directed cycle? How do you find one such cycle?
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