Class MinimalPerfectHashFunction<T>

  • All Implemented Interfaces:
    Function<T,​Long>, Object2LongFunction<T>, Size64, Serializable, Function<T,​Long>, ToLongFunction<T>

    public class MinimalPerfectHashFunction<T>
    extends AbstractHashFunction<T>
    implements Serializable
    A minimal perfect hash function.

    Given a list of keys without duplicates, the builder of this class finds a minimal perfect hash function for the list. Subsequent calls to the getLong(Object) method will return a distinct number for each key in the list. For keys out of the list, the resulting number is not specified. In some (rare) cases it might be possible to establish that a key was not in the original list, and in that case -1 will be returned; by signing the function (see below), you can guarantee with a prescribed probability that -1 will be returned on keys not in the original list. The class can then be saved by serialisation and reused later.

    This class uses a chunked hash store to provide highly scalable construction. Note that at construction time you can pass a ChunkedHashStore containing the keys (associated with any value); however, if the store is rebuilt because of a ChunkedHashStore.DuplicateException it will be rebuilt associating with each key its ordinal position.

    The theoretical memory requirements for the algorithm we use are 2γ=2.46 + o(n) bits per key, plus the bits for the random hashes (which are usually negligible). The o(n) part is due to an embedded ranking scheme that increases space occupancy by 6.25%, bringing the actual occupied space to around 2.68 bits per key.

    For convenience, this class provides a main method that reads from standard input a (possibly gzip'd) sequence of newline-separated strings, and writes a serialised minimal perfect hash function for the given list.


    Optionally, it is possible to sign the minimal perfect hash function. A w-bit signature will be associated with each key, so that getLong(Object) will return -1 on strings that are not in the original key set. As usual, false positives are possible with probability 2-w.

    How it Works

    The technique used is very similar (but developed independently) to that described by Fabiano C. Botelho, Rasmus Pagh and Nivio Ziviani in “Simple and Efficient Minimal Perfect Hashing Functions”, Algorithms and data structures: 10th international workshop, WADS 2007, number 4619 of Lecture Notes in Computer Science, pages 139−150, 2007. In turn, the mapping technique described therein was actually first proposed by Bernard Chazelle, Joe Kilian, Ronitt Rubinfeld and Ayellet Tal in “The Bloomier Filter: an Efficient Data Structure for Static Support Lookup Tables”, Proc. SODA 2004, pages 30−39, 2004, as one of the steps to implement a mutable table.

    The basic ingredient is the Majewski-Wormald-Havas-Czech 3-hypergraph technique. After generating a random 3-hypergraph, we sort its 3-hyperedges to that a distinguished vertex in each 3-hyperedge, the hinge, never appeared before. We then assign to each vertex a two-bit number in such a way that for each 3-hyperedge the sum of the values associated to its vertices modulo 3 gives the index of the hash function generating the hinge. As as a result we obtain a perfect hash of the original set (one just has to compute the three hash functions, collect the three two-bit values, add them modulo 3 and take the corresponding hash function value).

    To obtain a minimal perfect hash, we simply notice that we whenever we have to assign a value to a vertex, we can take care of using the number 3 instead of 0 if the vertex is actually the output value for some key. The final value of the minimal perfect hash function is the number of nonzero pairs of bits that precede the perfect hash value for the key. To compute this number, we use a simple table-free ranking scheme, recording the number of nonzero pairs each BITS_PER_BLOCK bits and using Long.bitCount(long) to count the number of nonzero pairs of bits in a word.

    Sebastiano Vigna
    See Also:
    Serialized Form
    • Field Detail

      • serialVersionUID

        public static final long serialVersionUID
        See Also:
        Constant Field Values

        public static final int BITS_PER_BLOCK
        The number of bits per block in the rank structure.
        See Also:
        Constant Field Values

        public static final int LOG2_CHUNK_SIZE
        The logarithm of the desired chunk size.
        See Also:
        Constant Field Values
      • n

        protected final long n
        The number of keys.
      • globalSeed

        protected final long globalSeed
        The seed used to generate the initial hash triple.
      • seed

        protected final long[] seed
        The seed of the underlying 3-hypergraphs.
      • offset

        protected final long[] offset
        The start offset of each chunk.
      • values

        protected final LongBigList values
        The final magick—the list of modulo-3 values that define the output of the minimal perfect hash function.
      • array

        protected transient long[] array
        The bit array supporting values.
      • signatureMask

        protected final long signatureMask
        The mask to compare signatures, or zero for no signatures.
      • signatures

        protected final LongBigList signatures
        The signatures.
      • count

        protected final long[] count
        The array of counts for blocks and superblocks.
    • Constructor Detail

      • MinimalPerfectHashFunction

        protected MinimalPerfectHashFunction​(Iterable<? extends T> keys,
                                             TransformationStrategy<? super T> transform,
                                             int signatureWidth,
                                             File tempDir,
                                             ChunkedHashStore<T> chunkedHashStore)
                                      throws IOException
        Creates a new minimal perfect hash function for the given keys.
        keys - the keys to hash, or null.
        transform - a transformation strategy for the keys.
        signatureWidth - a signature width, or 0 for no signature.
        tempDir - a temporary directory for the store files, or null for the standard temporary directory.
        chunkedHashStore - a chunked hash store containing the keys, or null; the store can be unchecked, but in this case keys and transform must be non-null.
    • Method Detail

      • countNonzeroPairs

        public static int countNonzeroPairs​(long x)
        Counts the number of nonzero pairs of bits in a long.
        x - a long.
        the number of nonzero bit pairs in x.
      • numBits

        public long numBits()
        Returns the number of bits used by this structure.
        the number of bits used by this structure.
      • getLongBySignature

        public long getLongBySignature​(long[] triple)
        Low-level access to the output of this minimal perfect hash function.

        This method makes it possible to build several kind of functions on the same ChunkedHashStore and then retrieve the resulting values by generating a single triple of hashes. The method TwoStepsMWHCFunction.getLong(Object) is a good example of this technique.

        triple - a triple generated as documented in ChunkedHashStore.
        the output of the function.