A median computing algorithm based on multi-level space compressed measure-integral

Abstract

A new method for median computation was proposed based on a measure-integral model of median. At first the measure-integral model employs a step function to extend the array for median. Then the definition of function median is presented conforming to the definition of an array's median. The relationship between median and measure-integral is deduced and an algorithm is gained. To search the measure space fast we compress the measure space and get the compressed measure-integral. This is extended to multi-level compressing method at last. At last the start point to search is discussed to reduce the search distance. Experiments and analysis show that computing median with measure-integral has higher speed than known algorithms.