Unique hashCodes is not enough to avoid collisions.

There is a common misconception that if you have unique hashCode() you won't have collisions.  While unique, or almost unique, hashCodes are good, this is not the end of the story.

The problem is that the size of a HashMap is not unlimited (or at least 2^32 in size)  This means the hashCode() number has to be reduced to a smaller number of bits.

The way HashMap, and thus HashSet and LinkedHashMap ,work is to mutate the bits in the following manner

    h ^= (h >>> 20) ^ (h >>> 12);
    return h ^ (h >>> 7) ^ (h >>> 4);

and then apply a mask for the lowest bits to select a bucket.  The problem is that even with unique hashCode()s as Integer does, there will be values with different hash code map to the same bucket. You can research how Integer.hashCode() works ;)

public static void main(String[] args) {
    Set integers = new HashSet<>();
    for (int i = 0; i <= 400; i++)
        if ((hash(i) & 0x1f) == 0)
            integers.add(i);
    Set integers2 = new HashSet<>();
    for (int i = 400; i >= 0; i--)
        if ((hash(i) & 0x1f) == 0)
            integers2.add(i);
    System.out.println(integers);
    System.out.println(integers2);

}

static int hash(int h) {
    // This function ensures that hashCodes that differ only by
    // constant multiples at each bit position have a bounded
    // number of collisions (approximately 8 at default load factor).
    h ^= (h >>> 20) ^ (h >>> 12);
    return h ^ (h >>> 7) ^ (h >>> 4);
}

this prints

[373, 343, 305, 275, 239, 205, 171, 137, 102, 68, 34, 0]
[0, 34, 68, 102, 137, 171, 205, 239, 275, 305, 343, 373]

The entries as in the reverse order they were added as the HashMap is acting as a linked list, placing all entries into the same bucket.

Solutions?

A simple solution is to have a bucket turn into a tree instead of a linked list.  In Java 8, it will do this for String keys, but this could be done for all Comparable types AFAIK.

Another approach is to allow custom hashing strategies to allow the developer to avoid such problems, or to randomize the mutation on a per collection basis, amortizing the cost to the application.

Other notes

I would favour supporting 64-bit hash codes, esp for complex objects.  This has a very low chance of collision in the hash code itself and supports very large data structures well. e.g. into the billions.


Comments

  1. Have you ever had problems with the way HashMap deals with HashCodes? Is the performance penalty noticeable? Is it likely that you have a HashMap collection containing a lot of elements that map to the same hash()?

    ReplyDelete
  2. Nice, Thanks for sharing. However, some of other scenarios which might be useful as well is,
    http://muhammadkhojaye.blogspot.co.uk/2010/02/java-hashing.html
    cheers,

    ReplyDelete
  3. There's no special handling for Strings in http://hg.openjdk.java.net/jdk8/jdk8/jdk/file/tip/src/share/classes/java/util/HashMap.java#l1959
    It uses the full hashCode first, and then the result of compareTo if applicable. Quite some magic there.

    ReplyDelete

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