Luby’s Algorithm: 1. Input: G = (V, E) 2. Output: MIS I of G 3. I ← ∅ 4. V ← V 5. while V = ∅ 6. assign a random number r(v) to each vertex v ∈ V 7. for all v ∈ V in parallel 8. if r(v) is minimum amongst all neighbors 9. I ← I ∪ {v} 10. V ← V \ {v ∪ N(v)} Make Implementation of this algorithm in sequential form in Python

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A: Algorithm: Input: a graph G represented as a dictionary with vertices as keys and neighboring…

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A: Given:

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A: Lets see the solution.

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A: Algorithm: Initialize an empty set I to represent the maximal independent set. While the set of…

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A: Create a program that will do the following:• Displays whether all nodes are connected to the graph…

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A:

Q: Algorithm 7.3 Dijkstra’s Algorithm 1: Input : G = (V, E, w)  connected, weighted graph G and a…

A: Given Dijkstra’s Algorithm Algorithm: 1: Input : G = (V, E, w)  connected, weighted graph G and a…

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A: Given:

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A: Consider the given graph :

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A: Below i have answered:

Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.