Memory optimisation: Custom Set


A few months ago I was confronted at work with the following use case: “data analysis of some selected clients”. It seems easy, but not if there are billions of data and there can be 10 million of clients to analyse and it needs to run as fast as possible!

In this post I’ll describe the solution I found but most importantly, how I came to this solution.


The problem

I have two files:

  • one with billions of data concerning clients (hundreds of Gigabytes to Terabytes)
  • another that contains the mobile numbers of the clients I am allowed to analyze. This file contains at max 10 million of numbers.

How can I efficiently filter the data in terms of CPU and memory consumption?


My first idea

I didn’t want to sort the files because the best sorting algorithm is in O(n *Log(n)) time complexity and (again) there are billions of data. This why a thought of using a Set<String> in memory and more precisely a HashSet<String> with the following idea:

  • Divide the data file into multi parts and give each part to a process
  • For each process, load the Set<String> in memory from the client file
  • For each process, read each line of the part file
    • If the mobile number of the data is in the Set, analyze it
    • else drop it

On paper that rocks because a HashSet has a time cost in O(1)  for checking the existence of an element. But here is another problem: what is the memory consumption for storing millions of strings ?

A (French) mobile number  looks like 33X XX XX XX XX and I needed to store 10 million of Strings with 11 caracteres. On a file in UTF8 encoding one number only takes 13 bytes (with the end of line caracteres) and 10 millions take less than 125 MegaBytes. But in java a String takes really more space. I found the following formula on a blog, I’m not sure if it’s true but from my tests it’s more true than the approximetly 13 bytes I was expecting:

Minimum String memory usage (bytes) = 8 * (int) ((((no chars) * 2) + 45) / 8)

I ended up with 1.4 Gigabytes  in memory. Instead of trying to optimize the memory usage of a string I tried another way.


My second idea

A French mobile number looks like 33X XX XX XX XX. Since it always begins with 33 there is need to keep it. So I had to find a way to store 9 digits while being still able to use them time efficiently. And the winner is … an integer:

The integer in java is a 32bit signed int so it can store up to 9 digits (the 10 th digit can only goes up to 2 but I don’t need it).

10 million integers take only 38 Mbytes, not bad? But using a HashSet<Integer> also comes at a price: with a default load factor of 0.75, the memory used by a HashSet only is approximately 900 Mbytes. Not that good anymore but I can live with that. The filtering with this HashSet worked well on my eclipse environment but there was a problem on the production environment (which is also used for testing): it was very slow!

The difference between my environment and the production was : the full program in production runs on a Hadoop cluster with an OpenJDK whereas my eclipse runs with Oracle’s Hotspot. I was suspecting three possibilities:

  • the mobile numbers were too skewed and it wasn’t good for the standard HashSet
  • the garbage collector was overworking because some parts of the heap were full or/and the JVM was badly configured (the only thing I was sure was that the heap space was 3 Gigabytes)
  • there was some side effect with hadoop

Since I couldn’t login on the production servers and I was just starting working with Hadoop, I tried to have a quick look at the implementation of the HashMap (an HashSet uses an HashMap). But instead of wasting time to resolve the problem, I look another way because I wasn’t happy with the memory consumption of this solution anyway.


My last idea

I wanted total control and comprehension of the data structure to use so I created a my own Set. My objectives where:

  • using the least possible memory,
  • insert() and get() as fast as possible.

I only needed to know if a mobile phone was present or not so a bit could do the trick. I thought of using a bits array where the indexes are the mobile numbers and the values their presence.

For example: array_of_bits[the number i’m looking for] == 0 means the mobile number is not present.

Without more optimizations:

  • it would have cost 799 999 999 (95 Megabytes) since the maximum possible number is(33)7 99 99 99 99
  • and the time costs of get() and insert() would have been immediat

But java doesn’t provide bits, I first used bytes which contains 8 bits. With the following formula one can used a bytes array like a bits array:

array_of_bytes[the number/8 + the mobile%8] == 0 means the mobile number is not present.

Bytes are signed numbers so the last bit is very difficult to handle. Char are the only unsigned “number”, this is why I decided to use chars instead of bytes. The only problem with chars is that whether you use 2 bits or 16 bits it will still costs you 16 bits in memory. Though I only needed a table of 799999999 bits for the set, using chars forced me to use 800000000 bits ((ceiling(799999999/16)*16)) which is not a big deal.
I optimized the space consumption using the following idea:

  • I only need to store number from 6 00 00 00 00 to 799 999 999 so I could transform those numbers inside the Set into 0 00 00 00 00 to 1 99 99 99 99.
  • ceiling(199999999/16)*16 = 200 000 000 bits

This Set using char only costs 24 Megabytes and has very fast insert() and get(). Sometimes it is worth reinventing the wheel.

Here is the resulting implementation the Set:

 * Set that stores mobile numbers between 6 00 00 00 00 to 7 99 99 99 99
public class MobileNumberSet {

	private static final int OFFSET_SCALE = 16;
	private static final int MAXIMUM_NUMBER = 2_00_00_00_00;
	private static final int SIZE_OF_HASH = MAXIMUM_NUMBER / OFFSET_SCALE;
	char[] hash = new char[SIZE_OF_HASH];

	 * pre computing of the powers of 2
	int[] power2 = new int[OFFSET_SCALE];
		for (int i = 0; i < OFFSET_SCALE; i++) {
			power2[i] = (int) Math.pow(2, i);

	public boolean contains(int mobileNumber) {
		try {
			mobileNumber = changeMobileNumberToHashableInteger(mobileNumber);
			int power = mobileNumber / OFFSET_SCALE;
			int offset = mobileNumber % OFFSET_SCALE;
			return (hash[power] & power2[offset]) == power2[offset];
		} catch (IllegalArgumentException e) {
			return false;

	public void add(int mobileNumber) {
		mobileNumber = changeMobileNumberToHashableInteger(mobileNumber);
		int offset = mobileNumber % OFFSET_SCALE;
		int power = mobileNumber / OFFSET_SCALE;
		hash[power] |= power2[offset];

	public void remove(int mobileNumber) {
		mobileNumber = changeMobileNumberToHashableInteger(mobileNumber);
		int offset = mobileNumber % OFFSET_SCALE;
		int power = mobileNumber / OFFSET_SCALE;
		hash[power] = (char) (hash[power] ^ power2[offset]);

	 * transforme a mobileNumber between 6 00 00 00 00 to 7 99 99 99 99 into a
	 * unique hash
	 * @param mobileNumber
	private int changeMobileNumberToHashableInteger(int mobileNumber) {
		if (mobileNumber >= 8_00_00_00_00 || mobileNumber < 6_00_00_00_00) {
			throw new IllegalArgumentException(
					"The given number is not a mobile number " + mobileNumber);
		return mobileNumber - 6_00_00_00_00;



2 Responses to“Memory optimisation: Custom Set”

  1. Marco
    July 11, 2015 at 8:34 pm #

    Could you not use a java.util.BitSet?

    • Li
      August 24, 2015 at 1:49 am #

      Yes, BitSet is good, and bloom filter can be used in extreme case.

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