Ranking
Ida Mele
Introduction
• The set of software components for the management of
large sets of data is made of:
–
–
–
–
–
–
MG4J,
Fastutil,
the DSI Utilities,
Sux4J,
WebGraph,
the LAW software.
• These software components have been developed by the
DSI of the University of Milan.
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Fastutil
• Fastutil 6 is a free software, developed in Java.
• Technical requirement:
– Java >= 6
• Useful links:
– http://fastutil.di.unimi.it/
– http://fastutil.di.unimi.it/docs/
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Fastutil
• Fastutil extends Java Collections, and it
provides:
– Type-specific maps, sets, and lists;
– Priority queues with a small memory footprint and
fast access and insertion;
– 64-bit arrays, sets, and lists;
– Fast I/O classes for text and binary files.
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Fastutil
• Advantages in using Fastutil:
– Classes of Fastutil are implemented in order to
work on huge collections of data in an efficient
way.
– Fastutil provides a new set of classes to deal
with collections whose size exceeds 231.
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Fastutil
• Advantages in using Fastutil:
– There are additional features (ex. bidirectional
iterators) that are not available in the standard
classes.
– Classes can be plugged into existing code,
because they implement their standard
counterpart (ex. Map for Maps).
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Fastutil: Big Arrays
• BigArrays: class that provides static methods and
objects for working with big arrays.
• Big arrays are arrays-of-arrays. For example, a big
array of integers has type int[][].
• Methods handle these arrays-of-arrays as if they are
monodimensional arrays with 64-bit indices.
• The length of a big array is bounded by
Long.MAX_VALUE rather than Integer.MAX_VALUE.
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Fastutil: Big Arrays
• Given a big array a, a[0], a[1], … a[n] are called segments.
Each one has length: SEGMENT_SIZE (the last segment can
have a smaller size).
• Each index i is associated with a segment and a displacement
into the segment.
– Methods segment/displacement compute the
segment/displacement associated with a given index.
– Method index receives the segment and the displacement
and returns the corresponding index.
– Methods get/set allow to return/set the value of a given
element in the big array.
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Fastutil Big Arrays - example
• We want to scan the big array a.
• First solution:
for( int s = 0; s < a.length; s++ ) {
final int[] t = a[ s ];
for( int d = 0; d < t.length; d++ ) {
//do something with t[ d ]
}
}
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Fastutil Big Arrays - example
• Second solution:
for( int s = a.length; s-- != 0; ) {
final int[] t = a[ s ];
for( int d = t.length; d-- != 0; ) {
//do something with t[ d ]
}
}
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Fastutil Big Arrays - example
• Third solution:
for( int s = a.length; s-- != 0; ) {
final long[] t = a[ s ];
for( int d = t.length; d-- != 0; )
t[d] = index( s, d );
}
We can use the index method, which returns the
index associated with a segment and displacement.
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Fastutil: Big data structures
• Fastutil provides classes also for other data
structures:
– BigList: a list with indices. The instances of this
class implement the same semantics of traditional
List.
– HashBigSet: the instances of this class use a hash
table to represent a big set. The number of
elements in the set is limited only by the amount
of core memory.
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Dsiutils
•
•
•
•
The DSI utilities are a mish mash of classes.
Free software.
Developed in Java.
Useful links:
– http://dsiutils.di.unimi.it/
– http://dsiutils.di.unimi.it/docs/
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Dsiutils: MultipleString
• In large-scale text indexing we want to use a
mutable string that, once frozen, can be used in
the same optimized way of an immutable string.
• In Java we have String and StringBuffer, which
can be used for immutable and mutable strings
respectively.
• The solution is MultipleString.
• MultipleString does not need synchronization.
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Dsiutils: packages
• Some important packages:
– it.unimi.dsi.bits contains main classes for
manipulating bits. Example: the class BitVectors
provides static methods and objects that do useful
things with bit vectors.
– it.unimi.dsi.compression provides word-based
compression/decompression classes.
– it.unimi.dsi.util offers implementations of
BloomFilters, PrefixMaps, StringMaps, BinaryTries
and others.
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WebGraph
• WebGraph is a framework for graph
compression.
• It exploits modern compression techniques to
manage very large graphs.
• Useful links:
– http://webgraph.di.unimi.it/
– http://webgraph.di.unimi.it/docs/
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WebGraph
• WebGraph provides:
– ζ-codes, which are suitable for storing web graphs.
– Algorithm for compressing the graph that exploit
gap compression as well as ζ-codes. The
parameters provide different tradeoffs between
access speed and compression ratio.
– Algorithms to access to compressed graphs
without decompression. The lazy techniques delay
the decompression until it is necessary.
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WebGraph: classes
• Some important classes:
– ImmutableGraph is an abstract class representing an
immutable graph.
– BVGraph allows to store and access web graphs in a
compressed form.
– ASCIIGraph is used to store the graph in a humanreadable ASCII format.
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WebGraph: classes
• Some important classes:
– ArcLabelledImmutableGraph is an abstract
implementation of a graph with labeled arcs.
– Transform returns the transformed version of an
immutable graph. We can use the transpose
method of this class if we want to create the
transpose graph.
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LAW
• Java software developed by the Laboratory for
Web Algorithms.
• It is free and contains several implementations
of the Pagerank algorithm.
• Useful links:
– http://law.di.unimi.it/software.php
– http://law.di.unimi.it/software/docs/index.html
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LAW: Pagerank
• PageRank of the package it.unimi.dis.law.rank is an
abstract class that defines methods and attributes
for Pagerank algorithm.
• Provided features:
– we can set the preference vectors;
– we can set the damping factor;
– we can program stopping criteria;
– step-by-step execution;
– reusability.
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Exercise
• Download the files:
– law-1.4.jar and webgraph-3.0.1.jar
– example
– Text2ASCII.class and PrintRanks.class
available at:
http://www.dis.uniroma1.it/~mele/teaching_20122013.ht
ml
• Add law-1.4.jar and webgraph-3.0.1.jar to the directory
containing all jar files (ex. lib_mg4j).
• Update file set-classpath.sh, and set the classpath:
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source set-classpath.sh Ranking
Build the graph: step1
• Create the file in the format ASCIIGraph:
java Text2ASCII example
• Output:
– example.graph-txt: the first line contains the number of
nodes, ex n. The following n lines contain the list of outneighbours of the nodes. In particular, the line i-th
contains the successors of the node i, sorted in an
increasing order and separated by a space.
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Build the graph: step1
• more example.graph-txt
Node id
.
.
.
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0
1
2
3
4
5
6
7
8
9
10
1 8
4 7
1 3
1 4
1
1
1
5
0
Num of nodes
9
9
4 5 6 7 8 9
5 6 9
Lists of successors
2
2 3 4 5
9
1 3 4 6
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Build the graph: step2
• We can use the main method of the BVGraph class to
load and compress an ImmutableGraph.
• The compressed graph is described by:
basename.graph: the graph file. It contains the
successor lists, one for each node. Each list is a
sequence of natural number that are coded as
sequence of bits in a efficient way.
basename.offsets: the offset file. It stores the offset for
each node of the graph.
basename.properties: the file with properties and
statistics.
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Build the graph: step2
• Step 2: Conversion from the ASCIIGraph to the
BVGraph:
java it.unimi.dsi.webgraph.BVGraph -g ASCIIGraph
example example
• Output:
• example.graph
• example.offsets
• example.properties
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Build the graph: step2
• more example.properties
#BVGraph properties
#Wed Nov 21 12:48:44 CET 2012
compratio=1,89
bitsforblocks=22
…
version=0
…
nodes=10
…
arcs=34
…
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Compute Pagerank
• To compute the Pagerank we can use the
implementations:
• PowerMethod
• GaussSeidel
• Jacobi
• The output is made of 2 files:
• basename.ranks: binary file with the results of
computation.
• basename.properties: text files with general info.
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Compute Pagerank: step1
• We use the main method of the class
PageRankPowerMethod by issuing the following
command:
java it.unimi.dsi.law.rank.PageRankPowerMethod
example examplePR
• Output:
• examplePR.ranks
• examplePR.properties
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Compute Pagerank: step1
• more examplePR.properties
rank.alpha = 0.85
rank.stronglyPreferential = false
method.numberOfIterations = 12
method.norm.type = INFTY
method.norm.value = 8.396275630317973E-7
graph.nodes = 10
graph.fileName = example
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Compute Pagerank: step2
• The file .ranks is a binary file with the scores of the
nodes.
• We can print these scores by using the class
PrintRanks:
java PrintRanks examplePR.ranks > ranks
• Output:
• ranks. This file has n lines, one for each node. The ith line contains the score of node number i.
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Compute Pagerank: step2
• more ranks
Node id
.
.
.
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1
2
3
4
5
6
7
8
9
0.0515659940361598
0.20197850631669495
0.07982657817906964
0.07587785830476211
0.14600457683651308
0.08608501191896127
0.07294688611466064
0.0931194920828582
0.05050241152172527
0.14209268468859523
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Homework
1) Repeat the exercise with the graphs:
• WikiIT
• WikiPT
available at:
http://www.dis.uniroma1.it/~mele/teaching_201
22013.html
2) Create a new graph by using synthetic or real data,
and repeat the exercise with this new graph.
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