## Azuma’s Inequality

The Chernoff bound gives the concentration of sums of independent random variables. The concentration result can be generalized to martingales. Martingales and Azuma’s Inequality A sequence of random variables $$X_0, X_1, \ldots, X_n$$ is called a martingale if \[ {\bf

Tagged with: ,
Posted in Probability

## Read and Write Text Files in Java

An I/O Stream represents an input source or an output destination. A stream can represent many different kinds of sources and destinations, including disk files, devices, other programs, and memory arrays. A file is identified by its path through the

Tagged with: , ,
Posted in Java

## Debugging in Java

A software bug is a mistake in a program. Debugging is to find and correct the mistakes (introduced by yourself). Programmers usually spend 20% of time for coding, and 80% of time for debugging. In 1996, the European Space Agency’s

Tagged with: ,
Posted in Java

## Randomness

Randomness is an important computational resource, just as running time and memory space. Randomness sometimes is essential for designing algorithms. Randomness is useful! Quick Select In quick sort, a random pivot selection has the property that, for any input data,

Tagged with: , , ,
Posted in Algorithm, Java