Suppose we have the following undirected graph, and we know that the two bolded edges (B-E and G-E) constitute the global minimum cut of the graph. 1. If we run the Karger’s algorithm for just one time to find the global minimum cut, what is the probability for the algorithm to find the minimum cut correctly? Please show your reasoning process. 2. How many times do we need to run the Karger’s algorithm if we want to guarantee that the probability of success is greater than or equal to 0.95, by “success” we mean that there is at least one time the Karger’s algorithm correctly found the minimum cut. Please show your reasoning process. [You do not have to work out the exact value of a logarithm]

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
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Suppose we have the following undirected graph, and we know that the two bolded edges (B-E and G-E) constitute the global minimum cut of the graph. 1. If we run the Karger’s algorithm for just one time to find the global minimum cut, what is the probability for the algorithm to find the minimum cut correctly? Please show your reasoning process. 2. How many times do we need to run the Karger’s algorithm if we want to guarantee that the probability of success is greater than or equal to 0.95, by “success” we mean that there is at least one time the Karger’s algorithm correctly found the minimum cut. Please show your reasoning process. [You do not have to work out the exact value of a logarithm]
A
F
B
G
E
C
D
Transcribed Image Text:A F B G E C D
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