Algorithm GreedyIS(G=(V, E)) 1. n← |V| 2. Adj is an adjacency list structure for E; IS and deg are initialised to all-Os 3. for u 0 ton - 1 do deg[u] = len(Adj[u]) while (some vertices remain in the graph) do u arg min{deg[v]; v € V, IS[v] 0} 4. 5. 6. 7. 8. 9. 10. 11. for u0 to n-1 12. 13. return IS IS[u] 1 for (w Nbd(u)) do // (set the initial deg values for all nodes) IS[u]max{0, IS[u]} == IS[w] -1 Update Adj, deg to reflect deletion of {u} U Nbd(u) // (node with min residual degree // gets added to the IS) Algorithm // (mark u's neighbours as disallowed) // (tidy: delete marks of disallowed vertices) A(iv) Assuming that the graph G = (V, E) is represented in Adjacency List format, justify in detail the fact GreedylS can be implemented in O(n² + m) worst-case running time, where n = |V|, m = |E|. note: this will require you to take real care in how the adjustment of Adj is done in line 10. The key is to only update/delete what is really necessary for the Algorithm, rather than being concerned with an accurate representation of the residual graph.

Algorithm GreedyIS(G=(V, E)) 1. n← |V| 2. Adj is an adjacency list structure for E; IS and deg are initialised to all-Os 3. for u 0 ton - 1 do deg[u] = len(Adj[u]) while (some vertices remain in the graph) do u arg min{deg[v]; v € V, IS[v] 0} 4. 5. 6. 7. 8. 9. 10. 11. for u0 to n-1 12. 13. return IS IS[u] 1 for (w Nbd(u)) do // (set the initial deg values for all nodes) IS[u]max{0, IS[u]} == IS[w] -1 Update Adj, deg to reflect deletion of {u} U Nbd(u) // (node with min residual degree // gets added to the IS) Algorithm // (mark u's neighbours as disallowed) // (tidy: delete marks of disallowed vertices) A(iv) Assuming that the graph G = (V, E) is represented in Adjacency List format, justify in detail the fact GreedylS can be implemented in O(n² + m) worst-case running time, where n = |V|, m = |E|. note: this will require you to take real care in how the adjustment of Adj is done in line 10. The key is to only update/delete what is really necessary for the Algorithm, rather than being concerned with an accurate representation of the residual 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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Question

Algorithm GreedyIS(G=(V, E))
1. n← |V|
2. Adj is an adjacency list structure for E; IS and deg are initialised to all-Os
3. for u
0 to n - 1 do
deg[u] = len (Adj[u])
while (some vertices remain in the graph) do
u arg min{deg[v]; v € V, IS[v]
0}
IS[u] ← 1
for (w Nbd(u)) do
4.
5.
6.
7.
8.
9.
10.
11. for u0 to n - 1
12.
13. return IS
// (set the initial deg values for all nodes)
IS[u]max{0, IS[u]}
==
IS[w] -1
Update Adj, deg to reflect deletion of {u} U Nbd(u)
// (node with min residual degree
// gets added to the IS)
Algorithm
// (mark u's neighbours as disallowed)
// (tidy: delete marks of disallowed vertices)
A(iv) Assuming that the graph G = (V, E) is represented in Adjacency List format, justify in detail the
fact GreedylS can be implemented in O(n² + m) worst-case running time, where n = |V], m = |E|.
note: this will require you to take real care in how the adjustment of Adj is done in line 10.
The key is to only update/delete what is really necessary for the Algorithm, rather than being
concerned with an accurate representation of the residual graph.

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With proper explanation else skip Proper explanation got thumbs-up