Don't need to solve question 1. Use the graph in question 1 to solve question 3 part (a). Thanks! 3. Let G = (V, E) be a directed graph with |V|=n. We say that an order vi < v2 < · ·…·< vnon V is a topological order for G if x precedes y in the order whenever (x, y) E E.(a) Remove the edges (b, a) and (a, d) from the graph in Question 1. List all possibletopological orders of the resulting graph.(b) What happens if you try to find a topological order for the graph from Question 2?With this in mind, what should we assume about a directed graph when considering itstopological orders?(c) Restricting to the type of graphs you answered in Part (b), come up with an algorithmthat finds a topological order for a given graph G. (You do not need to provide a runtime, but you should prove correctness of your algorithm.) Consider the following directed graph G. The numbers next to each edge denote the cost ofthe edge. (There are arrows; they're just tiny.)4324(a) Run Dijsktra's algorithm to find d(s, v) (the shortest distance from s to v) for allvertices v.(b) Change the cost of edge (b, a) to –2. What is the shortest distance from s to a now?(You can answer this by inspecting the graph.) Run Dijkstra’s algorithm until itcreates an error, and explain what went wrong (and why).

After removing (b,a) and (a,d) we will be left with the following edges - (s,b), (s,a), (b,d),…

Let G = (V, E) be a directed graph with |V| = n. We say that an order vi < v2 < ...< Un on V is a topological order for G if x precedes y in the order whenever (x, y) E E. (a) Remove the edges (b, a) and (a, d) from the graph in Question 1. List all possible topological orders of the resulting graph.

Let G = (V, E) be a directed graph with |V| = n. We say that an order vi < v2 < ...< Un on V is a topological order for G if x precedes y in the order whenever (x, y) E E. (a) Remove the edges (b, a) and (a, d) from the graph in Question 1. List all possible topological orders of the resulting graph.

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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