Class HyperBall
 All Implemented Interfaces:
SafelyCloseable
,Closeable
,Serializable
,AutoCloseable
Computes an approximation of the neighbourhood function, of the size of the reachable sets, and of (discounted) positive geometric centralities of a graph using HyperBall.
HyperBall is an algorithm computing by dynamic programming an approximation of the sizes of the balls of growing radius around the nodes of a graph. Starting from these data, it can approximate the neighbourhood function of a graph, that is, the function returning for each t the number of pairs of nodes at distance at most t, the number of nodes reachable from each node, Bavelas's closeness centrality, Lin's index, and harmonic centrality (studied by Paolo Boldi and Sebastiano Vigna in “Axioms for Centrality”, Internet Math., 2014). HyperBall can also compute discounted centralities, in which the weight assigned to a node is some specified function of its distance. All centralities are computed in their positive version (i.e., using distance from the source: see below how to compute the more usual, and useful, negative version).
HyperBall has been described by Paolo Boldi and Sebastiano Vigna in “InCore Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond”, Proc. of 2013 IEEE 13th International Conference on Data Mining Workshops (ICDMW 2013), IEEE, 2013, and it is a generalization of the method described in “HyperANF: Approximating the Neighbourhood Function of Very Large Graphs on a Budget”, by Paolo Boldi, Marco Rosa and Sebastiano Vigna, Proceedings of the 20th international conference on World Wide Web, pages 625−634, ACM, (2011).
Incidentally, HyperBall (actually, HyperANF) has been used to show that Facebook has just four degrees of separation.
At step t, for each node we (approximately) keep track (using HyperLogLog counters) of the set of nodes at distance at most t. At each iteration, the sets associated with the successors of each node are merged, thus obtaining the new sets. A crucial component in making this process efficient and scalable is the usage of broadword programming to implement the join (merge) phase, which requires maximising in parallel the list of registers associated with each successor (the implementation is geared towards 64bits processors).
Using the approximate sets, for each t we estimate the number of pairs of nodes (x,y) such that the distance from x to y is at most t. Since during the computation we are also in possession of the number of nodes at distance t − 1, we can also perform computations using the number of nodes at distance exactly t (e.g., centralities).
To use this class, you must first create an instance.
Then, you call init()
(once) and then iterate()
as much as needed (you can init/iterate several times, if you want so).
A commodity method will do everything for you.
Finally, you must close()
the instance. The method modified()
will tell you whether the internal state of
the algorithm has changed.
If you additionally pass to the constructor (or on the command line) the transpose of your graph (you can compute it using Transform.transposeOffline(ImmutableGraph,int)
or Transform.transposeOffline(ImmutableGraph, int)
), when three quarters of the nodes stop changing their value
HyperBall will switch to a systolic computation: using the transpose, when a node changes it will signal back
to its predecessors that at the next iteration they could change. At the next scan, only the successors of
signalled nodes will be scanned. In particular,
when a very small number of nodes is modified by an iteration, HyperBall will switch to a systolic local mode,
in which all information about modified nodes is kept in (traditional) dictionaries, rather than being represented as arrays of booleans.
This strategy makes the last phases of the computation orders of magnitude faster, and makes
in practice the running time of HyperBall proportional to the theoretical bound
O(m log n), where n
is the number of nodes and m is the number of the arcs of the graph. Note that
graphs with a large diameter require a correspondingly large number of iterations, and these iterations will have to
pass over all nodes if you do not provide the tranpose.
Deciding when to stop iterating is a rather delicate issue. The only safe way is to iterate until modified()
is zero,
and systolic (local) computation makes this goal easily attainable.
However, in some cases one can assume that the graph is not pathological, and stop when the relative increment of the number of pairs goes below
some threshold.
Computing Centralities
Note that usually one is interested in the negative version of a centrality measure, that is, the version that depends on the incoming arcs. HyperBall can compute only positive centralities: if you are interested (as it usually happens) in the negative version, you must pass to HyperBall the transpose of the graph (and if you want to run in systolic mode, the original graph, which is the transpose of the transpose). Note that the neighbourhood function of the transpose is identical to the neighbourhood function of the original graph, so the exchange does not alter its computation.
Configuring the JVM
HyperBall computations go against all basic assumptions of Java garbage collection. It is thus essential that you reconfigure your JVM properly. A good starting point is the following command line:
java server Xss256K Xms100G XX:PretenureSizeThreshold=512M XX:MaxNewSize=4G \ XX:+UseNUMA XX:+UseTLAB XX:+ResizeTLAB \ XX:+UseConcMarkSweepGC XX:CMSInitiatingOccupancyFraction=99 XX:+UseCMSInitiatingOccupancyOnly \ verbose:gc Xloggc:gc.log ...
Xss256K
reduces the stack memory used by each thread.Xms100G
size the heap: the more memory, the more counter per registers you can use (the amount, of course, depends on your hardware); please note that we set the starting heap size as expansion of large heaps is very expensive.XX:PretenureSizeThreshold=512M
forces the allocation of registers directly into the old generation.XX:MaxNewSize=4G
leaves almost all memory for the old generation.XX:+UseConcMarkSweepGC XX:CMSInitiatingOccupancyFraction=99 XX:+UseCMSInitiatingOccupancyOnly
set the concurrent garbage collector, and impose that no collection is performed until 99% of the permanent generation is filled.XX:+UseNUMA XX:+UseTLAB XX:+ResizeTLAB
usually improve performance, but your mileage may vary.
Check the garbage collector logs (gc.log
) to be sure that your
minor and major collections are very infrequent (as they should be).
Performance issues
To use HyperBall effectively, you should aim at filling a large percentage of the available core memory. This requires, of course, to size properly the heap, but also to configure some parameters.
Most of the memory goes into storing HyperLogLog registers. By tuning the number of registers per counter, you can modify the memory allocated for them. The amount of memory is logged, and you should check that the number of registers you chose almost fills up the heap memory you allocated, possibly leaving space for the graph(s) (but read below). Note that you can only choose a number of registers per counter that is a power of two, so your latitude in adjusting the memory used for registers is somewhat limited.
If you have little memory, this class can perform external computations: instead of keeping in core memory an old and a new copy of the counters, it can dump on disk an update list containing pairs <node, counter>. At the end of an iteration, the update list is loaded and applied to the counters in memory. The process is of course slower, but the core memory used is halved.
Then, some memory is necessary to load the graph (and possibly its tranpose). We suggest to check the offline option, which will map the graph into memory, rather than loading it. If you map the graph into memory, take care of leaving some free memory, beside that allocated for the heap, as the operating system will need some space to buffer the memorymapped graph(s).
If there are several available cores, the runs of iterate()
will be decomposed into relatively
small tasks (small blocks of nodes) and each task will be assigned to the first available core. Since all tasks are completely
independent, this behaviour ensures a very high degree of parallelism. Be careful, however, because this feature requires a graph with
a reasonably fast random access (e.g., in the case of a BVGraph
, short reference chains), as many
calls to ImmutableGraph.nodeIterator(long)
will be made. The granularity of the decomposition
is the number of nodes assigned to each task.
In any case, when attacking very large graphs (in particular, in external mode) some system tuning (e.g., increasing the filesystem commit time) is a good idea. Also experimenting with granularity and buffer sizes can be useful. Smaller buffers reduce the waits on I/O calls, but increase the time spent in disk seeks. Large buffers improve I/O, but they use a lot of memory. The best possible setup is the one in which the cores are 100% busy during the graph scan, and the I/O time logged at the end of a scan is roughly equal to the time that is necessary to reload the counters from disk: in such a case, essentially, you are computing as fast as possible.
 Author:
 Sebastiano Vigna, Paolo Boldi, Marco Rosa
 See Also:

Field Summary
Modifier and TypeFieldDescriptionprotected long
The number of nodes per task (obtained by adaptinggranularity
to the current ratio of modified nodes).protected int
A variable used to wait for all threads to complete their iteration.protected final Condition
A condition that is notified when all iteration threads are waiting to be started.protected final AtomicLong
An atomic integer keeping track of the number of arcs processed so far.static final boolean
protected final int
The size of an I/O buffer, in counters.protected boolean
Whether this approximator has been already closed.protected boolean
True if the computation is over.protected final EliasFanoCumulativeOutdegreeList
The cumulative list of outdegrees.protected double
The value computed by the current iteration.static final int
The default size of a buffer in bytes.static final int
The default granularity of a task.final float[][][]
The overall discounted centrality, for everydiscountFunction
.final Int2DoubleFunction[]
A number of discounted centralities to be computed, possibly none.protected final boolean
Whether the sum of distances from each node (inverse of positive closeness centrality) should be computed; if false,sumOfDistances
isnull
.protected boolean
Whether the sum of inverse distances from each node (positive harmonic centrality) should be computed; if false,sumOfInverseDistances
isnull
.protected boolean
Whether we should used an update list on disk, instead of computing results in core memory.protected final FileChannel
Ifexternal
is true, a file channel used to write to the update list.protected final boolean
True if we have the transpose graph.protected final long
The number of actually scanned nodes per task in a multithreaded environment.protected int
The current iteration.protected double
The value computed by the last iteration.protected boolean
True if we started a local computation.protected long[]
Iflocal
is true, the sorted list of nodes that should be scanned.protected final LongSet
IfpreLocal
is true, the list of nodes that should be scanned on the next iteration.protected final ReentrantLock
The lock protecting all critical sections.protected final AtomicLong
The number of register modified by the last call toiterate()
.protected boolean[][]
For each counter, whether it has changed its value.protected boolean[][]
For each newly computed counter, whether it has changed its value.protected boolean[][]
For each newly computed counter, whether it has changed its value.final DoubleArrayList
The neighbourhood function, if requested.protected long
The number of arcs beforenextNode
.protected boolean[][]
For each counter, whether it has changed its value.protected long
The starting node of the next chunk of nodes to be processed.protected final AtomicLong
An atomic integer keeping track of the number of node processed so far.protected long
The number of arcs of the graph, cached.protected final int
The number of cores used in the computation.protected long
Total number of write operation performed onfileChannel
.protected final long
The number of nodes of the graph, cached.int
The current computation phase.protected final ProgressLogger
A progress logger, ornull
.protected boolean
True if we are preparing a local computation (we aresystolic
and less than 1% nodes were modified).protected RandomAccessFile
Ifexternal
is true, the randomaccess file underlyingfileChannel
.protected double
The relative increment of the neighbourhood function for the last iteration.protected final long[][]
Ifexternal
is false, the arrays where results are stored.protected final LongBigList[]
protected final double
The square ofnumNodes
, cached.protected final Condition
The condition on which all iteration threads wait before starting a new phase.final float[][]
The sum of the distances from every given node, if requested.final float[][]
The sum of inverse distances from each given node, if requested.protected boolean
True if we started a systolic computation.protected final it.unimi.dsi.big.webgraph.algo.HyperBall.IterationThread[]
The threads performing the computation.protected Throwable
One of the throwables thrown by some of the threads, if at least one thread has thrown a throwable.protected long
Total wait time in milliseconds of I/O activity onfileChannel
.protected final AtomicLong
Counts the number of unwritten entries whenexternal
is true, or the number of counters that did not change their value.protected final File
Ifexternal
is true, the name of the temporary file that will be used to write the update list.Fields inherited from class it.unimi.dsi.util.HyperLogLogCounterArray
bits, CHUNK_MASK, CHUNK_SHIFT, CHUNK_SIZE, counterLongwords, counterResidualMask, counterShift, counterSize, log2m, longwordAligned, lsbMask, m, mMinus1, msbMask, registers, registerSize, seed

Constructor Summary
ConstructorDescriptionHyperBall
(ImmutableGraph g, int log2m) Creates a new HyperBall instance using default values and disabling systolic computation.HyperBall
(ImmutableGraph g, int log2m, long seed) Creates a new HyperBall instance using default values and disabling systolic computation.HyperBall
(ImmutableGraph g, int log2m, ProgressLogger pl) Creates a new HyperBall instance using default values and disabling systolic computation.HyperBall
(ImmutableGraph g, ImmutableGraph gt, int log2m) Creates a new HyperBall instance using default values.HyperBall
(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl) Creates a new HyperBall instance using default values.HyperBall
(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl, int numberOfThreads, int bufferSize, int granularity, boolean external) Creates a new HyperBall instance.HyperBall
(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl, int numberOfThreads, int bufferSize, int granularity, boolean external, boolean doSumOfDistances, boolean doSumOfInverseDistances, Int2DoubleFunction[] discountFunction, long seed) Creates a new HyperBall instance. 
Method Summary
Modifier and TypeMethodDescriptionvoid
close()
protected static final int
ensureRegisters
(int log2m) protected void
finalize()
void
init()
Initialises the approximator.void
init
(long seed) Initialises the approximator, providing a new seed to the underlyingHyperLogLogCounterArray
.void
iterate()
Performs a new iteration of HyperBall.static void
long
modified()
Returns the number of HyperLogLog counters that were modified by the last call toiterate()
.void
run()
Runs HyperBall.void
run
(long upperBound) Runs HyperBall.void
run
(long upperBound, double threshold) Runs HyperBall.void
run
(long upperBound, double threshold, long seed) Runs HyperBall.Methods inherited from class it.unimi.dsi.util.HyperLogLogCounterArray
add, chunk, clear, clear, count, count, getCounter, getCounter, log2NumberOfRegisters, max, max, offset, registers, registerSize, relativeStandardDeviation, setCounter, setCounter, transfer

Field Details

ASSERTS
public static final boolean ASSERTS See Also:

DEFAULT_GRANULARITY
public static final int DEFAULT_GRANULARITYThe default granularity of a task. See Also:

DEFAULT_BUFFER_SIZE
public static final int DEFAULT_BUFFER_SIZEThe default size of a buffer in bytes. See Also:

gotTranspose
protected final boolean gotTransposeTrue if we have the transpose graph. 
systolic
protected boolean systolicTrue if we started a systolic computation. 
preLocal
protected boolean preLocalTrue if we are preparing a local computation (we aresystolic
and less than 1% nodes were modified). 
local
protected boolean localTrue if we started a local computation. 
doSumOfDistances
protected final boolean doSumOfDistancesWhether the sum of distances from each node (inverse of positive closeness centrality) should be computed; if false,sumOfDistances
isnull
. 
doSumOfInverseDistances
protected boolean doSumOfInverseDistancesWhether the sum of inverse distances from each node (positive harmonic centrality) should be computed; if false,sumOfInverseDistances
isnull
. 
neighbourhoodFunction
The neighbourhood function, if requested. 
sumOfDistances
public final float[][] sumOfDistancesThe sum of the distances from every given node, if requested. 
sumOfInverseDistances
public final float[][] sumOfInverseDistancesThe sum of inverse distances from each given node, if requested. 
discountFunction
A number of discounted centralities to be computed, possibly none. 
discountedCentrality
public final float[][][] discountedCentralityThe overall discounted centrality, for everydiscountFunction
. 
numNodes
protected final long numNodesThe number of nodes of the graph, cached. 
numArcs
protected long numArcsThe number of arcs of the graph, cached. 
squareNumNodes
protected final double squareNumNodesThe square ofnumNodes
, cached. 
numberOfThreads
protected final int numberOfThreadsThe number of cores used in the computation. 
bufferSize
protected final int bufferSizeThe size of an I/O buffer, in counters. 
granularity
protected final long granularityThe number of actually scanned nodes per task in a multithreaded environment. Must be a multiple ofLong.SIZE
. 
adaptiveGranularity
protected long adaptiveGranularityThe number of nodes per task (obtained by adaptinggranularity
to the current ratio of modified nodes). Must be a multiple ofLong.SIZE
. 
last
protected double lastThe value computed by the last iteration. 
current
protected double currentThe value computed by the current iteration. 
iteration
protected int iterationThe current iteration. 
updateFile
Ifexternal
is true, the name of the temporary file that will be used to write the update list. 
fileChannel
Ifexternal
is true, a file channel used to write to the update list. 
randomAccessFile
Ifexternal
is true, the randomaccess file underlyingfileChannel
. 
cumulativeOutdegrees
The cumulative list of outdegrees. 
pl
A progress logger, ornull
. 
lock
The lock protecting all critical sections. 
allWaiting
A condition that is notified when all iteration threads are waiting to be started. 
start
The condition on which all iteration threads wait before starting a new phase. 
phase
public int phaseThe current computation phase. 
closed
protected boolean closedWhether this approximator has been already closed. 
thread
protected final it.unimi.dsi.big.webgraph.algo.HyperBall.IterationThread[] threadThe threads performing the computation. 
nodes
An atomic integer keeping track of the number of node processed so far. 
arcs
An atomic integer keeping track of the number of arcs processed so far. 
aliveThreads
protected volatile int aliveThreadsA variable used to wait for all threads to complete their iteration. 
completed
protected volatile boolean completedTrue if the computation is over. 
numberOfWrites
protected volatile long numberOfWritesTotal number of write operation performed onfileChannel
. 
totalIoMillis
protected volatile long totalIoMillisTotal wait time in milliseconds of I/O activity onfileChannel
. 
nextNode
protected long nextNodeThe starting node of the next chunk of nodes to be processed. 
nextArcs
protected long nextArcsThe number of arcs beforenextNode
. 
modified
The number of register modified by the last call toiterate()
. 
unwritten
Counts the number of unwritten entries whenexternal
is true, or the number of counters that did not change their value. 
relativeIncrement
protected double relativeIncrementThe relative increment of the neighbourhood function for the last iteration. 
external
protected boolean externalWhether we should used an update list on disk, instead of computing results in core memory. 
resultBits
protected final long[][] resultBitsIfexternal
is false, the arrays where results are stored. 
resultRegisters

modifiedCounter
protected boolean[][] modifiedCounterFor each counter, whether it has changed its value. We use an array of boolean (instead of aLongArrayBitVector
) just for access speed. 
modifiedResultCounter
protected boolean[][] modifiedResultCounterFor each newly computed counter, whether it has changed its value.modifiedCounter
will be updated with the content of this bit vector by the end of the iteration. 
nextMustBeChecked
protected boolean[][] nextMustBeCheckedFor each counter, whether it has changed its value. We use an array of boolean (instead of aLongArrayBitVector
) just for access speed. 
mustBeChecked
protected boolean[][] mustBeCheckedFor each newly computed counter, whether it has changed its value.modifiedCounter
will be updated with the content of this bit vector by the end of the iteration. 
localCheckList
protected long[] localCheckListIflocal
is true, the sorted list of nodes that should be scanned. 
localNextMustBeChecked
IfpreLocal
is true, the list of nodes that should be scanned on the next iteration. Note that this set is synchronized. 
threadThrowable
One of the throwables thrown by some of the threads, if at least one thread has thrown a throwable.


Constructor Details

HyperBall
public HyperBall(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl, int numberOfThreads, int bufferSize, int granularity, boolean external) throws IOException Creates a new HyperBall instance. Parameters:
g
 the graph whose neighbourhood function you want to compute.gt
 the transpose ofg
in case you want to perform systolic computations, ornull
.log2m
 the logarithm of the number of registers per counter.pl
 a progress logger, ornull
.numberOfThreads
 the number of threads to be used (0 for automatic sizing).bufferSize
 the size of an I/O buffer in bytes (0 forDEFAULT_BUFFER_SIZE
).granularity
 the number of node per task in a multicore environment (it will be rounded to the next multiple of 64), or 0 forDEFAULT_GRANULARITY
.external
 if true, results of an iteration will be stored on disk. Throws:
IOException

HyperBall
Creates a new HyperBall instance using default values. Parameters:
g
 the graph whose neighbourhood function you want to compute.gt
 the transpose ofg
in case you want to perform systolic computations, ornull
.log2m
 the logarithm of the number of registers per counter. Throws:
IOException

HyperBall
public HyperBall(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl) throws IOException Creates a new HyperBall instance using default values. Parameters:
g
 the graph whose neighbourhood function you want to compute.gt
 the transpose ofg
in case you want to perform systolic computations, ornull
.log2m
 the logarithm of the number of registers per counter.pl
 a progress logger, ornull
. Throws:
IOException

HyperBall
Creates a new HyperBall instance using default values and disabling systolic computation. Parameters:
g
 the graph whose neighbourhood function you want to compute.log2m
 the logarithm of the number of registers per counter. Throws:
IOException

HyperBall
Creates a new HyperBall instance using default values and disabling systolic computation. Parameters:
g
 the graph whose neighbourhood function you want to compute.log2m
 the logarithm of the number of registers per counter.seed
 the random seed passed toHyperLogLogCounterArray(long, long, int, long)
. Throws:
IOException

HyperBall
Creates a new HyperBall instance using default values and disabling systolic computation. Parameters:
g
 the graph whose neighbourhood function you want to compute.log2m
 the logarithm of the number of registers per counter.pl
 a progress logger, ornull
. Throws:
IOException

HyperBall
public HyperBall(ImmutableGraph g, ImmutableGraph gt, int log2m, ProgressLogger pl, int numberOfThreads, int bufferSize, int granularity, boolean external, boolean doSumOfDistances, boolean doSumOfInverseDistances, Int2DoubleFunction[] discountFunction, long seed) throws IOException Creates a new HyperBall instance. Parameters:
g
 the graph whose neighbourhood function you want to compute.gt
 the transpose ofg
, ornull
.log2m
 the logarithm of the number of registers per counter.pl
 a progress logger, ornull
.numberOfThreads
 the number of threads to be used (0 for automatic sizing).bufferSize
 the size of an I/O buffer in bytes (0 forDEFAULT_BUFFER_SIZE
).granularity
 the number of node per task in a multicore environment (it will be rounded to the next multiple of 64), or 0 forDEFAULT_GRANULARITY
.external
 if true, results of an iteration will be stored on disk.doSumOfDistances
 whether the sum of distances from each node should be computed.doSumOfInverseDistances
 whether the sum of inverse distances from each node should be computed.discountFunction
 an array (possiblynull
) of discount functions.seed
 the random seed passed toHyperLogLogCounterArray(long, long, int, long)
. Throws:
IOException


Method Details

ensureRegisters
protected static final int ensureRegisters(int log2m) 
init
public void init()Initialises the approximator.This method must be call before a series of iterations. Note that it will not change the seed used by the underlying
HyperLogLogCounterArray
. See Also:

init
public void init(long seed) Initialises the approximator, providing a new seed to the underlyingHyperLogLogCounterArray
.This method must be call before a series of iterations.
 Parameters:
seed
 passed toHyperLogLogCounterArray.clear(long)
.

close
 Specified by:
close
in interfaceAutoCloseable
 Specified by:
close
in interfaceCloseable
 Throws:
IOException

finalize

iterate
Performs a new iteration of HyperBall. Throws:
IOException

modified
public long modified()Returns the number of HyperLogLog counters that were modified by the last call toiterate()
. Returns:
 the number of HyperLogLog counters that were modified by the last call to
iterate()
.

run
Runs HyperBall. The computation will stop whenmodified()
returns false. Throws:
IOException

run
Runs HyperBall. Parameters:
upperBound
 an upper bound to the number of iterations. Throws:
IOException

run
Runs HyperBall. Parameters:
upperBound
 an upper bound to the number of iterations.threshold
 a value that will be used to stop the computation by relative increment if the neighbourhood function is being computed; if you specify 1, the computation will stop whenmodified()
returns false. Throws:
IOException

run
Runs HyperBall. Parameters:
upperBound
 an upper bound to the number of iterations.threshold
 a value that will be used to stop the computation by relative increment if the neighbourhood function is being computed; if you specify 1, the computation will stop whenmodified()
returns false.seed
 the random seed passed toHyperLogLogCounterArray(long, long, int, long)
. Throws:
IOException

main
public static void main(String[] arg) throws IOException, JSAPException, IllegalArgumentException, ClassNotFoundException, IllegalAccessException, InvocationTargetException, InstantiationException, NoSuchMethodException
