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java.lang.Objectit.unimi.dsi.sux4j.mph.HypergraphSorter<T>
public class HypergraphSorter<T>
A class implementing the 3-hypergraph edge sorting procedure that is necessary for the Majewski-Wormald-Havas-Czech technique.
Bohdan S. Majewski, Nicholas C. Wormald, George Havas, and Zbigniew J. Czech have described in “A family of perfect hashing methods”, Comput. J., 39(6):547−554, 1996, a 3-hypergraph based technique to store functions (actually, the paper uses the technique just to store a permutation of the key set, but it is clear it can be used to store any function). More generally, the procedure first generates a random 3-hypergraph whose edges correspond to elements of the function domain. The, it sorts the edges of the random 3-hypergraph so that for each edge at least one vertex, the hinge, never appeared before in the sorted edge list (this happens with high probability if the number of vertices is at least γ times the number of edges).
Instances of this class contain the data necessary to generate the random hypergraph
and apply the sorting procedure. At construction time, you provide just the desired number
of edges; then, each call to generateAndSort()
will generate a new 3-hypergraph using a 64-bit seed, an iterator returning the key set,
and a corresponding TransformationStrategy
. If the method returns true, the sorting was
successful and in the public field stack
you can retrieve the opposite
of the desired order (so enumerating edges starting from the last in stack
you
are guaranteed to find each time a vertex that never appeared before). The public fields
edge
, numEdges
and numVertices
expose the structure of the generated
3-hypergraph. For m edges, the number of vertices will be &lceil γm ⌉ + 1,
unless m is zero, in which case the number of vertices will be zero, too.
To guarantee the same results when reading a Majewski-Wormald-Havas-Czech-like structure,
the method bitVectorToEdge()
can be used to retrieve, starting from
a bit vector, the corresponding edge. While having a function returning the edge starting
from a key would be more object-oriented and avoid hidden dependencies, it would also require
storing the transformation provided at construction time, which would make this class non-thread-safe.
Just be careful to transform the keys into bit vectors using
the same TransformationStrategy
used to generate the random 3-hypergraph.
This class provides two special access points for classes that have pre-digested their keys. The methods
generateAndSort(Iterator, long)
and tripleToEdge(long[], long, int, int[])
use
fixed-length 192-bit keys under the form of triples of longs. The intended usage is that of
turning the keys into such a triple using Jenkins's hash and
then operating directly on the hash codes. This is particularly useful in chunked constructions, where
the keys are replaced by their 192-bit hashes in the first place. Note that the hashes are actually
rehashed using Hashes.jenkins(long[], long, long[])
—this is necessary to vary the associated edges whenever
the generated 3-hypergraph is not acyclic.
Warning: you cannot mix the bitvector-based and the triple-based constructors and static methods. It is your responsibility to pair them correctly.
We use Jenkin's hash in its 64-bit incarnation: beside providing an excellent hash function, it actually computes three 64-bit hash values, which is exactly what we need.
Building and sorting a large 3-hypergraph may take hours. As it happens with all probabilistic algorithms, one can just give estimates of the expected time.
There are two probabilistic sources of problems: duplicate edges and non-acyclic hypergraphs. However, the probability of duplicate edges is vanishing when n approaches infinity, and once the hypergraph has been generated, the stripping procedure succeeds in an expected number of trials that tends to 1 as n approaches infinity.
To help diagnosing problem with the generation process
class, this class will log at DEBUG
level
what's happening.
Note that if during the generation process the log warns more than once about duplicate edges (this happens
at INFO
level), you should
suspect that there are duplicates in the string list, as duplicate edges are extremely unlikely.
Nested Class Summary | |
---|---|
static class |
HypergraphSorter.Result
|
Field Summary | |
---|---|
int[][] |
edge
An 3×n array recording the triple of vertices involved in each edge. |
static double |
GAMMA
The mythical threshold (or better, a very closed upper bound of): random 3-hypergraphs are acyclic with high probability if the ratio vertices/edges exceeds this constant. |
int |
numEdges
The number of edges in the hypergraph. |
int |
numVertices
The number of vertices in the hypergraph ( ⌈ GAMMA * numEdges ⌉ + 1 ). |
int[] |
stack
The edge stack. |
Constructor Summary | |
---|---|
HypergraphSorter(int numEdges)
Creates a hypergraph sorter for a given number of edges. |
Method Summary | |
---|---|
static void |
bitVectorToEdge(BitVector bv,
long seed,
int numVertices,
int[] e)
Turns a bit vector into an edge. |
HypergraphSorter.Result |
generateAndSort(Iterator<? extends T> iterator,
TransformationStrategy<? super T> transform,
long seed)
Generates a random 3-hypergraph and tries to sort its edges. |
HypergraphSorter.Result |
generateAndSort(Iterator<long[]> iterator,
long seed)
Generates a random 3-hypergraph and tries to sort its edges. |
static void |
tripleToEdge(long[] triple,
long seed,
int numVertices,
int[] e)
Turns a triple of longs into an edge. |
Methods inherited from class java.lang.Object |
---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
---|
public static final double GAMMA
public final int numVertices
GAMMA
* numEdges
⌉ + 1 ).
public final int numEdges
public final int[][] edge
public final int[] stack
Constructor Detail |
---|
public HypergraphSorter(int numEdges)
numEdges
- the number of edges of this hypergraph sorter.Method Detail |
---|
public static void bitVectorToEdge(BitVector bv, long seed, int numVertices, int[] e)
This method will never return a degenerate edge. However, if there are no edges
the vector e
will be filled with -1.
bv
- a bit vector.seed
- the seed for the hash function.numVertices
- the number of vertices in the underlying hypergraph.e
- an array to store the resulting edge.public static void tripleToEdge(long[] triple, long seed, int numVertices, int[] e)
This method will never return a degenerate edge. However, if there are no edges
the vector e
will be filled with -1.
triple
- a triple of intermediate hashes.seed
- the seed for the hash function.numVertices
- the number of vertices in the underlying hypergraph.e
- an array to store the resulting edge.public HypergraphSorter.Result generateAndSort(Iterator<? extends T> iterator, TransformationStrategy<? super T> transform, long seed)
iterator
- an iterator returning numEdges
keys.transform
- a transformation from keys to bit vectors.seed
- a 64-bit random seed.
public HypergraphSorter.Result generateAndSort(Iterator<long[]> iterator, long seed)
iterator
- an iterator returning numEdges
triples of longs.seed
- a 64-bit random seed.
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