Finding median of large set of numbers too big to fit into memory?

Have a look at the "Median of Medians" algorithm in this wikipedia article Related question: Median-of-medians in Java Explanation: ics.uci.edu/~eppstein/161/960130.html.

Have a look at the "Median of Medians" algorithm in this wikipedia article. Related question: Median-of-medians in Java. Explanation: ics.uci.edu/~eppstein/161/960130.html.

– garsh0p Oct 8 '10 at 6:06 Good question.Probably. You could of course also process each table 5 (or 7, ..) rows at a time... But then I suppose you may be violating the memory constraints. – aioobe Oct 8 '10 at 6:13 @aioobe, the number set is too large to fit into the memory, so even if we can find the median of medians, how can we do the quick select?

– Alcott Oct 11 at 2:25.

For the median of medians you still need to do pivoting. It is an in memory approach. In this case you need to use a streaming approach.In the first pass you find max and min of the sample.

Call that U and L for upper an lower bounds. Then set a candidate median at the average of U and L. With a second pass you count the probability of X Essentially it's binary search among possible medians.

If you can afford additional disk space, you can at each step filter all the elements between U and L and work only on those going forward, since the median is guaranteed to be included. This brings the complexity down to linear time, just as that of pivoting.

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