Package it.unimi.dsi.sux4j.mph

Class GV3CompressedFunction<T>

java.lang.Object
it.unimi.dsi.fastutil.objects.AbstractObject2LongFunction<T>
it.unimi.dsi.sux4j.mph.GV3CompressedFunction<T>
All Implemented Interfaces:
Function<T,Long>, Object2LongFunction<T>, Size64, Serializable, Function<T,Long>, ToLongFunction<T>
public class GV3CompressedFunction<T> extends AbstractObject2LongFunction<T> implements Serializable, Size64
An immutable function stored in a compressed form.

Instances of this class store a function from keys to values. Keys are provided by an iterable object (whose iterators must return elements in a consistent order), whereas values are provided by a LongIterable. If you do not specify values, each key will be assigned its rank (e.g., its position in iteration order starting from zero).

The values must have a skewed distribution: some values must be much more frequent than others. In that case, this data structure uses much less space than, say, a GOV3Function because it is able to use, for each key, a number of bits close to the empirical entropy of the value list (with an additional ≈10%). It is faster than a GV4CompressedFunction, and it can be built more quickly, but it uses more space.

In addition to the standard construction, which uses lazy Gaussian elimination to solve a number of random linear systems, this implementation has the option of enlarging slightly the space used by the structure (+12%) and use a peeling procedure (essentially, triangulation) to solve the systems. The construction time can be significantly shorter in this case.

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 function mapping each element of the list to its position, or to a given list of values.

Building a function

This class provides a great amount of flexibility when creating a new function; such flexibility is exposed through the builder. To exploit the various possibilities, you must understand some details of the construction.

In a first phase, we build a BucketedHashStore containing hashes of the keys. By default, the store will associate each hash with the rank of the key. If you specify values, the store will associate with each hash the corresponding value.

However, if you further require an indirect construction the store will associate again each hash with the rank of the corresponding key, and access randomly the values (which must be either a LongList or a LongBigList). Indirect construction is useful only in complex, multi-layer hashes (such as an LcpMonotoneMinimalPerfectHashFunction) in which we want to reuse a checked BucketedHashStore. Storing values in the BucketedHashStore is extremely scalable because the values must just be a LongIterable that will be scanned sequentially during the store construction. On the other hand, if you have already a store that associates ordinal positions, and you want to build a new function for which a LongList or LongBigList of values needs little space (e.g., because it is described implicitly), you can opt for an indirect construction using the already built store.

Note that if you specify a store it will be used before building a new one (possibly because of a DuplicateException), with obvious benefits in terms of performance. If the store is not checked, and a DuplicateException is thrown, the constructor will try to rebuild the store, but this requires, of course, that the keys, and possibly the values, are available. Note that it is your responsibility to pass a correct store.

Multithreading

This implementation is multithreaded: each bucket returned by the BucketedHashStore is processed independently. By default, this class uses Runtime.availableProcessors() parallel threads, but by default no more than 4. If you wish to set a specific number of threads, you can do so through the system property "it.unimi.dsi.sux4j.mph.threads".

Implementation Details

The detail of the data structure can be found in “Engineering Compressed Functions”, by Marco Genuzio and Sebastiano Vigna, 2017. The theoretical basis for the construction is described by Jóhannes B. Hreinsson, Morten Krøyer, and Rasmus Pagh in “Storing a compressed function with constant time access”, Algorithms - ESA 2009, 17th Annual European Symposium, 2009, pages 730−741. Each output value is represented by a codeword from a prefix-free code (by default, a length-limited Huffman code). We generate a random 3-regular linear system on F2, where the known term of the k-th equation is a bit in a bit array. When we read the bit array at three suitable positions depending on an input key, we can recover the codeword representing the output value.

Since:
4.2.0
Author:
Sebastiano Vigna, Marco Genuzio
See Also:

  • Field Details

    • SEED_BITS

      protected static final int SEED_BITS
      See Also:

    • OFFSET_BITS

      protected static final int OFFSET_BITS
      See Also:

    • NUMBER_OF_THREADS_PROPERTY

      public static final String NUMBER_OF_THREADS_PROPERTY
      The system property used to set the number of parallel threads.
      See Also:

    • DELTA_PEEL

      public static final double DELTA_PEEL
      See Also:

    • DELTA_GAUSSIAN

      public static final double DELTA_GAUSSIAN
      See Also:

    • BUCKET_SIZE

      public static final int BUCKET_SIZE
      The expected bucket size.
      See Also:

    • n

      protected final long n
      The number of keys.

    • globalMaxCodewordLength

      protected final int globalMaxCodewordLength
      Length of longest codeword

    • globalSeed

      protected long globalSeed
      The seed used to generate the initial signature.

    • offsetAndSeed

      protected final long[] offsetAndSeed
      A long containing three values per bucket:
      • the top SEED_BITS bits contain the seed (note that it must not be shifted right);
      • the remaining lower bits contain the starting position in data of the bits associated with the bucket.

    • data

      protected final BitVector data
      A bit vector storing the main data array.

    • transform

      protected final TransformationStrategy<? super T> transform
      The transformation strategy to turn objects of type T into bit vectors.

    • decoder

      protected final Codec.Decoder decoder
      The decoder that will be used to yield output values.

    • escapeLength

      protected final int escapeLength
      Codec.Decoder.escapeLength() from decoder, cached.

    • escapedSymbolLength

      protected final int escapedSymbolLength
      Codec.Decoder.escapedSymbolLength() from decoder, cached.

  • Constructor Details

    • GV3CompressedFunction

      protected GV3CompressedFunction(Iterable<? extends T> keys, TransformationStrategy<? super T> transform, LongIterable values, boolean indirect, File tempDir, BucketedHashStore<T> bucketedHashStore, Codec codec, boolean peeled) throws IOException
      Creates a new function for the given keys and values.
      Parameters:
      keys - the keys in the domain of the function, or null.
      transform - a transformation strategy for the keys.
      values - values to be assigned to each element, in the same order of the iterator returned by keys; if null, the assigned value will the ordinal number of each element.
      indirect - if true, bucketedHashStore contains ordinal positions, and values is a LongIterable that must be accessed to retrieve the actual values.
      tempDir - a temporary directory for the store files, or null for the standard temporary directory.
      bucketedHashStore - a bucketed hash store containing the keys associated with their values and counting value frequencies, or null; the store can be unchecked, but in this case keys and transform must be non-null.
      codec - the Codec used to encode values.
      peeled - whether to use peeling rather than lazy Gaussian elimination; the resulting structure uses +12% space, but it can be constructed much more quickly.
      Throws:
      IOException

  • Method Details