1. Suppose that you have a graph G =may have negative cycles in it. We call a path P "simple" if it includes no repeated(V, E) with weight function w : E R. The graphvertices. Prove that either the shortest simple path P(s, t) exists for any s, t e V or thereis at least one edge e e E such that w(e) = -0.2. Provide an algorithm that finds the shortest simple path from s to t that works if nosimple path from s to t includes negative edges. Does your algorithm work when youallow non-simple paths?

Answer 2:- For a path from u to w passing through v, we just need to find paths from u to v and v to…

Answered: 2. Provide an algorithm that finds the…

2. Provide an algorithm that finds the shortest simple path from s to t that works if no simple path from s to t includes negative edges. Does your algorithm work when you allow non-simple paths?

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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Question

1. Suppose that you have a graph G =
may have negative cycles in it. We call a path P "simple" if it includes no repeated
(V, E) with weight function w : E R. The graph
vertices. Prove that either the shortest simple path P(s, t) exists for any s, t e V or there
is at least one edge e e E such that w(e) = -0.
2. Provide an algorithm that finds the shortest simple path from s to t that works if no
simple path from s to t includes negative edges. Does your algorithm work when you
allow non-simple paths?

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