Monthly Archives: December 2013

Time and Space Complexity Class

Robust classes are those such that no reasonable changes to the model of computation should change the class; capable of classifying interesting problems. Examples \(\mathsf{L}\) (contains Formula Value, integer multiplication and division), \(\mathsf{P}\) (contains circuit value, linear programming, max flow),

Posted in Theory

Markov’s Inequality

Markov’s inequality provides a bound on the upper-tail probability of non-negative random variables. The bound is expressed with the expectation of the random variable. [Markov's Inequality] Let \(X\) be a non-negative random variable. Then, for any \(\lambda > 0\), \[

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Posted in Probability

Shuffle an Array or a List in Java

How can we rearrange an array of items in random order? A simple way is to manipulate the array by picking elements randomly. Or we can use Java Collections API. Shuffle an Array Write a loop to go through each

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Posted in Java

Pairwise Independence

A collection of random variables is pairwise independent if every pair of variables are independent. Given \(k\) independent bits, we define \(n = 2^k-1\) random variables each of which is a parity of a non-empty subset of the \(k\) bits.

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Posted in Theory