如何改善短弦的散列以避免碰撞？

Question

I am having a problem with hash collisions using short strings in .NET4.
EDIT: I am using the built-in string hashing function in .NET.

I'm implementing a cache using objects that store the direction of a conversion like this

public class MyClass
{
    private string _from;
    private string _to;

   // More code here....

    public MyClass(string from, string to)
    {
        this._from = from;
        this._to = to;
    }

    public override int GetHashCode()
    {
        return string.Concat(this._from, this._to).GetHashCode();
    }

    public bool Equals(MyClass other)
    {
        return this.To == other.To && this.From == other.From;
    }

    public override bool Equals(object obj)
    {
        if (obj == null) return false;
        if (this.GetType() != obj.GetType()) return false;
        return Equals(obj as MyClass);
    }
}

This is direction dependent and the from and to are represented by short strings like "AAB" and "ABA".

I am getting sparse hash collisions with these small strings, I have tried something simple like adding a salt (did not work).

The problem is that too many of my small strings like "AABABA" collides its hash with the reverse of "ABAAAB" (Note that these are not real examples, I have no idea if AAB and ABA actually cause collisions!)

and I have gone heavy duty like implementing MD5 (which works, but is MUCH slower)

I have also implemented the suggestion from Jon Skeet here:
Should I use a concatenation of my string fields as a hash code? This works but I don't know how dependable it is with my various 3-character strings.

How can I improve and stabilize the hashing of small strings without adding too much overhead like MD5?

EDIT: In response to a few of the answers posted... the cache is implemented using concurrent dictionaries keyed from MyClass as stubbed out above. If I replace the GetHashCode in the code above with something simple like @JonSkeet 's code from the link I posted:

int hash = 17;
hash = hash * 23 + this._from.GetHashCode();
hash = hash * 23 + this._to.GetHashCode();        
return hash;

Everything functions as expected. It's also worth noting that in this particular use-case the cache is not used in a multi-threaded environment so there is no race condition.

EDIT: I should also note that this misbehavior is platform dependant. It works as intended on my fully updated Win7x64 machine but does not behave properly on a non-updated Win7x64 machine. I don't know the extend of what updates are missing but I know it doesn't have Win7 SP1... so I would assume there may also be a framework SP or update it's missing as well.

EDIT: As susggested, my issue was not caused by a problem with the hashing function. I had an elusive race condition, which is why it worked on some computers but not others and also why a "slower" hashing method made things work properly. The answer I selected was the most useful in understanding why my problem was not hash collisions in the dictionary.

Answer 1

Are you sure that collisions are who causes problems? When you say

I finally discovered what was causing this bug

You mean some slowness of your code or something else? If not I'm curious what kind of problem is that? Because any hash function (except "perfect" hash functions on limited domains) would cause collisions.

I put a quick piece of code to check for collisions for 3-letter words. And this code doesn't report a single collision for them. You see what I mean? Looks like buid-in hash algorithm is not so bad.

Dictionary<int, bool> set = new Dictionary<int, bool>();
char[] buffer = new char[3];
int count = 0;
for (int c1 = (int)'A'; c1 <= (int)'z'; c1++)
{
    buffer[0] = (char)c1;
    for (int c2 = (int)'A'; c2 <= (int)'z'; c2++)
    {
        buffer[1] = (char)c2;
        for (int c3 = (int)'A'; c3 <= (int)'z'; c3++)
        {
            buffer[2] = (char)c3;
            string str = new string(buffer);
            count++;
            int hash = str.GetHashCode();
            if (set.ContainsKey(hash))
            {
                Console.WriteLine("Collision for {0}", str);
            }
            set[hash] = false;
        }
    }
}

Console.WriteLine("Generated {0} of {1} hashes", set.Count, count);

While you could pick almost any of well-known hash functions (as David mentioned) or even choose a "perfect" hash since it looks like your domain is limited (like minimum perfect hash)... It would be great to understand if the source of problems are really collisions.

Update

What I want to say is that .NET build-in hash function for string is not so bad. It doesn't give so many collisions that you would need to write your own algorithm in regular scenarios. And this doesn't depend on the lenght of strings. If you have a lot of 6-symbol strings that doesn't imply that your chances to see a collision are highier than with 1000-symbol strings. This is one of the basic properties of hash functions.

And again, another question is what kind of problems do you experience because of collisions? All build-in hashtables and dictionaries support collision resolution. So I would say all you can see is just... probably some slowness. Is this your problem?

As for your code

return string.Concat(this._from, this._to).GetHashCode(); 

This can cause problems. Because on every hash code calculation you create a new string. Maybe this is what causes your issues?

int hash = 17; 
hash = hash * 23 + this._from.GetHashCode(); 
hash = hash * 23 + this._to.GetHashCode();         
return hash; 

This would be much better approach - just because you don't create new objects on the heap. Actually it's one of the main points of this approach - get a good hash code of an object with a complex "key" without creating new objects. So if you don't have a single value key then this should work for you. BTW, this is not a new hash function, this is just a way to combine existing hash values without compromising main properties of hash functions.

Answer 2

Any common hash function should be suitable for this purpose. If you're getting collisions on short strings like that, I'd say you're using an unusually bad hash function. You can use Jenkins or Knuth's with no issues.

Here's a very simple hash function that should be adequate. (Implemented in C, but should easily port to any similar language.)

unsigned int hash(const char *it)
{
 unsigned hval=0;
 while(*it!=0)
 {
  hval+=*it++;
  hval+=(hval<<10);
  hval^=(hval>>6);
  hval+=(hval<<3);
  hval^=(hval>>11);
  hval+=(hval<<15);
 }
 return hval;
}

Note that if you want to trim the bits of the output of this function, you must use the least significant bits. You can also use mod to reduce the output range. The last character of the string tends to only affect the low-order bits. If you need a more even distribution, change return hval; to return hval * 2654435761U; .

Update :

public override int GetHashCode()
{
    return string.Concat(this._from, this._to).GetHashCode();
}

This is broken. It treats from="foot",to="ar" as the same as from="foo",to="tar". Since your Equals function doesn't consider those equal, your hash function should not. Possible fixes include:

1) Form the string from,"XXX",to and hash that. (This assumes the string "XXX" almost never appears in your input strings.

2) Combine the hash of 'from' with the hash of 'to'. You'll have to use a clever combining function. For example, XOR or sum will cause from="foo",to="bar" to hash the same as from="bar",to="foo". Unfortunately, choosing the right combining function is not easy without knowing the internals of the hashing function. You can try:

int hc1=from.GetHashCode();
int hc2=to.GetHashCode();
return (hc1<<7)^(hc2>>25)^(hc1>>21)^(hc2<<11);