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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algorithm GenericSearch (G, s) pre-cond: G is a (directed or undirected) graph, and s is one of its nodes. post-cond: The output consists of all the nodes u that are reachable by a path in G from s.
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Algorithm GreedyIS (G=(V, E)) 1. n← VI 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 0} 4. 5. 6. 7. 8. 9. 10. 11. for u 0 to n - 1 12. 13. return IS u ← arg min{deg[v]; v € V, IS[v] = == 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,…
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