[Solved]1 Approximate Median Tream M Elements Simplicity Assume Et S X1 T2 Xm Denote S Elements Q37289141

1 Approximate Median tream of m elements. For simplicity, assume et S – (x1, T2,. . . , Xm) denote a s that the elements in the stream are unique. Define the position of an element to be pos(r) – | {0€ S|y 〈 x}| . The e-approximate median is then defined to be an element x such that: 2 Provide an algorithm which returns a e-approximate median with high probability Provide a 3-part solution providing the algorithm, proof of correctness and the space complexity of the alg in space independent of the size of the stream. (Hint: Try to provide a sampling based algorithm and argue that less than 1/2 of the samples will be from the 1/2 -e and 1/2 + є percentile-use a Hoeffding bound for this argument). The following is a one-sided version of the Hoeffding bound which might be useful for this and other problems: solve the problem rithm. Note that the optimal algorithm can Show transcribed image text 1 Approximate Median tream of m elements. For simplicity, assume et S – (x1, T2,. . . , Xm) denote a s that the elements in the stream are unique. Define the position of an element to be pos(r) – | {0€ S|y 〈 x}| . The e-approximate median is then defined to be an element x such that: 2 Provide an algorithm which returns a e-approximate median with high probability Provide a 3-part solution providing the algorithm, proof of correctness and the space complexity of the alg in space independent of the size of the stream. (Hint: Try to provide a sampling based algorithm and argue that less than 1/2 of the samples will be from the 1/2 -e and 1/2 + є percentile-use a Hoeffding bound for this argument). The following is a one-sided version of the Hoeffding bound which might be useful for this and other problems: solve the problem rithm. Note that the optimal algorithm can

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Answer to 1 Approximate Median tream of m elements. For simplicity, assume et S – (x1, T2,. . . , Xm) denote a s that the elements… . . .