Différences

Ci-dessous, les différences entre deux révisions de la page.

--- site:recherche:logiciels:rdfdist [11/05/2015 12:30]
amine [Hash-based approaches]
+++ site:recherche:logiciels:rdfdist [26/04/2017 13:06] (Version actuelle)
amann
@@ Ligne 1: / Ligne 1: @@
-===== RDFdist =====
+{{indexmenu_n>1}}
+===== RDFdist :  RDF distribution approaches using Spark =====
 This wiki page provides information about the experiments RDF distribution approaches using [[http://spark.apache.org/|Spark]].
-This information consists of i) the source code for both data preparation and query evaluation, ii) the query workload and iii) the  description of datasets used in the experiments.
+This information consists of i) the query workload ii) the source code for both data preparation and query evaluation, and iii) the  description of two datasets used in the experiments.
-For the sake of reproducibility, each source code is provied as a script which can be directly executed in the spark shell.
+For the sake of reproducibility, each source code is provided as a script which can be directly executed in the spark shell.
-=====Source Code=====
-====Hash-based approaches====
+=====Query workload====
+We picked three queries from the [[http://swat.cse.lehigh.edu/projects/lubm/|LUBM ]] dataset, namely #2, #9 and #12
+which are referred to as Query 2, Query 3 and Query 4, respectively.
+We have created an addirional one referred to as Query 1.
+We also created two queries for the [[https://www.wikidata.org/wiki/Wikidata:Main_Page|Wikidata]] dataset which are referred to as Query 5 and Query 6.
+===Query 1 (synthetic, LUBM)===
+<code>
+SELECT ?x ?y ?z
+WHERE
+{?x lubm:advisor ?y.
+ ?y lubm:worksFor ?z.
+ ?z lubm:subOrganisation ?t
+}
+</code>
-The following code presents the random hashing approach for the LUBM datasets, i.e., queries Q1, Q2, Q3 and Q4 are executed and evaluated.
+===Query 2 (#2 of LUBM)===
+<code>
+PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
+PREFIX ub: <http://www.lehigh.edu/~zhp2/2004/0401/univ-bench.owl#>
+SELECT ?X, ?Y, ?Z
+WHERE
+{?X rdf:type ub:GraduateStudent .
+  ?Y rdf:type ub:University .
+  ?Z rdf:type ub:Department .
+  ?X ub:memberOf ?Z .
+  ?Z ub:subOrganizationOf ?Y .
+  ?X ub:undergraduateDegreeFrom ?Y}
+</code>
+===Query 3 (#9 of LUBM)===
+<code>
+PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
+PREFIX ub: <http://www.lehigh.edu/~zhp2/2004/0401/univ-bench.owl#>
+SELECT ?X, ?Y, ?Z
+WHERE
+{?X rdf:type ub:Student .
+  ?Y rdf:type ub:Faculty .
+  ?Z rdf:type ub:Course .
+  ?X ub:advisor ?Y .
+  ?Y ub:teacherOf ?Z .
+  ?X ub:takesCourse ?Z}
+</code>
+===Query 4 (#12 of LUBM)===
+<code>
+PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
+PREFIX ub: <http://www.lehigh.edu/~zhp2/2004/0401/univ-bench.owl#>
+SELECT ?X, ?Y
+WHERE
+{?X rdf:type ub:Chair .
+  ?Y rdf:type ub:Department .
+  ?X ub:worksFor ?Y .
+  ?Y ub:subOrganizationOf <http://www.University0.edu>}
+</code>
+===Query 5 (synthetic, Wikidata)===
+<code>
+SELECT ?x ?y ?z
+WHERE
+{?x entity:P131s ?y.
+?y entity:P961v> ?z.
+?z entity:P704s ?w
+}
+</code>
+===Query 6 (synthetic, Wikidata) ===
+<code>
+SELECT ?x ?y ?z
+{?x entity:P39v ?y.
+?x entity:P580q ?z.
+?x rdf:type ?w
+}
+</code>
+=====Source Code=====
+====Hash-based approaches====
+The following code corresponds to the triple hashing and subject hashing approaches for the LUBM datasets.
+It consists of a data preparation part followd by a query evaluation part.
@@ Ligne 28: / Ligne 110: @@
 val t1 = java.lang.System.currentTimeMillis();
+/**
+* set inputData with the path to the data encoded as quadruples (see Datasets excerpts)
+*/
 // loading and transformating the dataset
@@ Ligne 36: / Ligne 123: @@
 println("Loading time "+ (t2 - t1) +" msec for "+part+" partitions");
 // Partitioning the dataset
-val triples = triples0.map{case(f,(s,p,o))=>((s+p+o),(s,p,o))}.partitionBy(new HashPartitioner(part))
+/**
+* Uncomment one of the following lines depending on whether hashing is applied
+on the entire triple or only the subject
+*/
+// val triples = triples0.partitionBy(new HashPartitioner(part))
+// val triples = triples0.map{case(f,(s,p,o))=>((s+p+o),(s,p,o))}.partitionBy(new HashPartitioner(part))
 //triples.persist
@@ Ligne 63: / Ligne 156: @@
 val takco : Long = 1115684864
-def ajout(a : ListBuffer[(Long, Long, Long)], e: (Long, Long, Long) ) : ListBuffer[(Long, Long, Long)] = {
-  a += e
-  return a
-}
     // -----------------------------------------------------------
@@ Ligne 144: / Ligne 233: @@
 println("Processing LUBM #12 "+ (t2 - t1) +" msec for "+part+" partitions");
+// -----------------------------------------------------------
+// highly selective on wikidata :: 8 results
+    // QR5:  ?x <http://www.wikidata.org/entity/P131s> ?y.
+    ?y <http://www.wikidata.org/entity/P961v> ?z.
+    ?z <http://www.wikidata.org/entity/P704s> ?w.
+    // -----------------------------------------------------------
+val qr5 = triples.filter({case(s,p,o)=>p==P131s}).map({case(s,p,o)=>(o,(s,p))}).
+    join(triples.filter({case(s,p,o)=>p==P961v}).map({case(s,p,o)=>(s,(p,o))})).
+    map({case(k,((s1,p1),(p2,o2)))=>(o2,s1)}).
+    join(triples.filter({case(s,p,o)=>p==P704v}).map({case(s,p,o)=>(s,(p,o))}))
+qr5.persist
+qr5.collect
+// mid selectivity start shaped query : 10418 results
+// QR6: ?x <http://www.wikidata.org/entity/P39v> ?y. ?x <http://www.wikidata.org/entity/P580q> ?z. ?x <http://www.w3.org/1999/02/22-rdf-syntax-ns#type> ?w
+val qr6 = triples.filter({case(s,p,o)=>p==P39v}).map({case(s,p,o)=>(s,null)}).
+    join(triples.filter({case(s,p,o)=>p==P580q}).map({case(s,p,o)=>(s,null)})).
+    join(triples.filter({case(s,p,o)=>p==rdftype}))
+qr6.persist
+qr6.collect
 </code>
-==Hashing applied on the subject ==
-====Partitioning-based approaches====
-==nHop==
+====Graph partitioning-based approaches====
-==WARP==
+===Huang Approach ===
+<code>
+import org.apache.spark.HashPartitioner
+import scala.collection.mutable.ListBuffer
-==Hybrid==
+val folder=  "lubm" //"watdiv"
+val dataset= "univ" //"watdiv"
+val scale="1k"
+val part=20 //10, 20
+val folderName = folder +scale
+val fileName = dataset+scale+"_encoded_unique_quads.part."+part+".2hop"
+val t1 = java.lang.System.currentTimeMillis();
+val quads_I_SPO = sc.textFile(s"/user/olivier/${folderName}/${fileName}").coalesce(part).map(x=>x.split(",")).map(t=>(t(3).replace(")","").toLong, (t(0).replace("(","").toLong,t(1).toLong,t(2).toLong)))
+val quadsDist = quads_I_SPO.partitionBy(new HashPartitioner(part)).persist
+val t2 = java.lang.System.currentTimeMillis();
+print("Loading time of quads : "+(t2-t1)/1000 +" sec")
+    val advisor : Long = 1233125376
+    val worksFor : Long = 1136656384
+    val suborg : Long = 1224736768
+    val memof : Long = 113246208
+    val undeg : Long = 1101004800
+    val teaof : Long = 1199570944
+    val takco : Long = 1115684864
+    // -----------------------------------------------------------
+    // Query 1 : (not part of the benchmark)
+    // Pattern: (x advisor y) (y worksFor z) (z subOrganisation t)
+    // -----------------------------------------------------------
+var t1 = java.lang.System.currentTimeMillis();
+var pataws = quadsDist.filter({case(i,(s,p,o)) => p==advisor}).map({case(i,(s,p,o)) => (o,s)}).
+    join(quadsDist.filter({case(i,(s,p,o)) => p==worksFor}).map({case(i,(s,p,o)) => (s,o)}),part).
+    map({case (y,(x,z)) => (z,(x,y))}).
+    join(quadsDist.filter({case(i,(s,p,o)) => p==suborg}).map({case(i,(s,p,o)) => (s,o)}), part).
+    map({case (z,((x,y),t)) => (x,y,z,t)})
+pataws.count
+var pataws2 = pataws.flatMap(x=>x).distinct
+var t2= java.lang.System.currentTimeMillis();
+println("Processing Q1 "+ (t2 - t1) +" msec for "+part+" partitions");
+    // -----------------------------------------------------------
+    // LUBM 2 : MSU
+    // Pattern: (x memberOf y) (y subOrg z) (x UndergraduateDegreeFrom z)
+    // -----------------------------------------------------------
+var t1 = java.lang.System.currentTimeMillis();
+//var pmemof = quadsDist.filter({case(i,(s,p,o)) => p==memof}).cache()
+var patmsu = quadsDist.filter({case(i,(s,p,o)) => p==memof}).map({case(i,(s,p,o)) => (o,s)}).
+             join(quadsDist.filter({case(i,(s,p,o)) => p==suborg}).map({case(i,(s,p,o)) => (s,o)}),part).
+             map({case (y,(x,z)) => (x+""+z,(x,y,z))}).
+             join(quadsDist.filter({case(i,(s,p,o)) => p==undeg}).map({case(i,(x,p,z))=> (x+""+z,null)}))
+patmsu.count
+var patmsu2 = patmsu.flatMap(identity).distinct
+var t2= java.lang.System.currentTimeMillis();
+println("Processing Q2 "+ (t2 - t1) +" msec for "+part+" partitions");
+    // -----------------------------------------------------------
+    // LUBM 9 : ATT
+    // Pattern: (x advisor y) (y teacherOf z) (x takesCourse z)
+    // -----------------------------------------------------------
+var t1 = java.lang.System.currentTimeMillis();
+var patatt = quadsDist.filter({case(i,(s,p,o)) => p==advisor}).map({case(i,(s,p,o)) => (o,s)}).
+              join(quadsDist.filter({case(i,(s,p,o)) => p==teaof}).map({case(i,(s,p,o)) => (s,o)}), part).
+              map({case (y,(x,z)) => (x+""+z,(x,y,z))}).
+              join(quadsDist.filter({case(i,(s,p,o)) => p==takco}).map({case(i,(s,p,o))=> (s+""+o,null)}), part)
+patatt.distinct.count
+var t2= java.lang.System.currentTimeMillis();
+println("Processing Q3 (LUBM #9) "+ (t2 - t1) +" msec for "+part+" partitions");
+    // -----------------------------------------------------------
+    // LUBM 12 : WS
+    // Pattern: (y worksFor z) (z subOrganisation t)
+    // -----------------------------------------------------------
+val t1 = java.lang.System.currentTimeMillis();
+val patws = quadsDist.filter({case(i,(s,p,o)) => p==worksFor}).map({case(i,(s,p,o)) => ((i,o),s)}).join(quadsDist.filter({case(i,(s,p,o)) => p==suborg}).map({case(i,(s,p,o)) => ((i,s),o)}),part).map({case ((i,k),(s,o)) => (s,o)})
+val ans_patws = patws.distinct.count
+val t2= java.lang.System.currentTimeMillis();
+println("Processing LUBM #12 "+ (t2 - t1) +" msec for "+part+" partitions");
+</code>
+===Warp===
+<code>
+// Spark implementation of WARP replication
+// usage: run this code into the spark-shell
+import scala.collection.mutable.ListBuffer
+import org.apache.spark.rdd.RDD
+import scala.reflect.ClassTag
+import org.apache.spark.SparkContext
+import org.apache.spark.SparkContext._
+import org.apache.spark.HashPartitioner
+import org.apache.spark.Partitioner
+import java.io.Serializable
+val folder= "lubm" //"watdiv"
+val dataset= "univ" //"watdiv"//
+val scale="1k"
+/* We have 15 cores per machine.
+   Each core is accessing a separate part in parallel.
+   The default parallelism = #machines * 15 cores
+   <=>   #machines = defaultParallelism / 15
+*/
+val machine = sc.defaultParallelism /15
+val part =  sc.defaultParallelism
+val folderName = folder + scale
+val fileName = dataset + scale
+/**
+* set inputData with the path to the data encoded as quadruples (see Datasets excerpts)
+*/
+val inputData = s"/user/olivier/${folderName}/${fileName}_encoded_unique_quads.part.${machine}"
+// Initial state, delete the storage
+sc.getPersistentRDDs.values.foreach(x => x.unpersist())
+sc.getPersistentRDDs.values.size
+var t1 = java.lang.System.currentTimeMillis();
+def affiche(s: String): Unit={
+println("#### ------------------------------- ####")
+println(s)
+println("#### ------------------------------- ####")
+}
+/*
+-----------------------
+STEP 1: read triples
+-----------------------
+*/
+/**
+  Function  lireTriples reads the input data
+  returns a quad (subject, property, object, partID)
+  with partID = hash(subject)
+**/
+def lireTriples(input: String): RDD[(Long, Long, Long, Int)] = {
+   return sc.textFile(input).
+    map(line => line.substring(1, line.length -1).split(",")).
+    map(tab => (tab(0).toLong, tab(1).toLong, tab(2).toLong, (tab(0).toInt).hashCode%machine))
+}
+val triples = lireTriples(inputData)
+triples.setName("triples")
+triples.persist
+//nombre total de nuplets
+//triples.count
+// stat: nb triplets par partition
+//triples.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b).collect.foreach(println)
+/*
+---------------------------------------------------------------------------
+STEP 2: COMPUTE REPLICATION TRIPLES
+Computes the triple to replicate in every partition, for each query
+---------------------------------------------------------------------------
+*/
+/*
+ Fonction filterProp : selects the triples a a given property
+ */
+def filterProp(input: RDD[(Long, Long, Long, Int)], prop: Long): RDD[(Long, Long, Int)] = {
+x  // on projette sur S et O car P est fixe
+  return input.filter(x => x._2 == prop).map{ case (s,p,o,f) => (s,o,f)}
+}
+def getOutsideTriple(seedF: Int, t: ListBuffer[(Long, Long, Int)], properties: Array[Long]): Seq[(Long, Long, Long, Int)] = {
+  var a = t.toArray
+  var res: ListBuffer[(Long, Long, Long, Int)] = ListBuffer()
+  for(i <-0 to (a.length - 1)) {
+    if( a(i)._3 != seedF) {
+      res.append( (a(i)._1,  properties(i), a(i)._2,  seedF))
+    }
+  }
+  return res
+}
+def getReplicaForQuery(query: RDD[ListBuffer[(Long, Long, Int)]], properties: Array[Long], nbCandidateSeed: Int): RDD[(Long, Long, Long, Int)] = {
+  var replica = sc.parallelize(List((0L,0L,0L,0)))
+  var min_nb = -1L
+  for (i <- 0 to (nbCandidateSeed-1)) {
+    var t1 = query.map(x => (x(i)._3, x))
+    //t1.take(5).foreach(println)
+    // lister les triplets a  repliquer = ceux qui ne sont pas dans la seed partition
+    var t2 = t1.flatMap{ case(seedF, tripleList) => getOutsideTriple(seedF, tripleList, properties)}.distinct
+    // count the triples to replicate
+    var nb = t2.count
+    if(min_nb == -1 || nb < min_nb){
+      min_nb=nb
+      replica=t2
+      println("current:")
+      println(s"seed $i, replica count: $nb ")
+    }
+    else {
+      println(s"-----ignore seed $i, replica count: $nb ")
+    }
+  }
+  return replica
+}
+// -------------------------------------------------------
+//  Compute replication for the folowing QUERIES
+// -------------------------------------------------------
+// based on dictionnary encoding
+val advisor : Long = 1233125376
+val worksFor : Long = 1136656384
+val suborg : Long = 1224736768
+val memof : Long = 1132462080
+val undeg : Long = 1101004800
+val teaof : Long = 1199570944
+val takco : Long = 1115684864
+// -----------------------------------------------------------
+// Query 1 : (not part of the benchmark)
+// Pattern: (x advisor y) (y worksFor z) (z subOrganisation t)
+// -----------------------------------------------------------
+val query1 = filterProp(triples, advisor).map{ case (x, y, f1) => ( y, (x, f1))}.
+  join(filterProp(triples, worksFor).map{ case (y, z, f2) => ( y, (z, f2) )}).
+  map{ case ( y, ((x,f1), (z, f2))) => (z, (x, f1, y, f2)) }.
+  join(filterProp(triples, suborg).map{ case ( z, t, f3) => (z, (t,f3))}).
+  map{ case ( z, ( (x,f1,y,f2), (t,f3) )) => ListBuffer( (x, y, f1), (y, z, f2) , (z, t, f3))}
+query1.setName("q1")
+//query1.persist()
+//query1.count
+// resultat: 4108791
+var t1 = java.lang.System.currentTimeMillis();
+val replica1 =  getReplicaForQuery(query1, Array(advisor, worksFor, suborg), 3)
+var t2= java.lang.System.currentTimeMillis();
+println("Processing Q1 "+ (t2 - t1) +" msec for "+part+" partitions");
+// stat: nb triples a repliquer dans chaque partition
+//replica1.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b).collect.foreach(println)
+// (0,15551) (1,15776) (2,17639) (3,201275) (4,46068)
+// -----------------------------------------------------------
+// LUBM 2 : MSU
+// Pattern: (x memberOf y) (y subOrg z) (x UndergraduateDegreeFrom z)
+// -----------------------------------------------------------
+val query2 = filterProp(triples, memof).map{ case (x, y, f1) => ( y, (x, f1))}.
+  join(filterProp(triples, suborg).map{ case (y, z, f2) => ( y, (z, f2) )}).
+  map{ case ( y, ((x,f1), (z,f2) )) => ((x, z), (y, f1, f2)) }.
+  join(filterProp(triples, undeg).map{ case (x, z, f3) => ( (x, z), f3)}).
+  map{ case ((x, z), ((y, f1, f2), f3)) => ListBuffer((x, y, f1), (y, z, f2), (x, z, f3)) }
+query2.setName("q2")
+//query2.persist()
+//query2.count
+val replica2 =  getReplicaForQuery(query2, Array(memof, suborg, undeg), 2)
+//stat: nb triples a  repliquer dans chaque partition
+//replica2.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b).collect.foreach(println)
+//(0,1) (1,3) (3,4) (4,896)
+// -----------------------------------------------------------
+// LUBM 9 : ATT
+// Pattern: (x advisor y) (y teacherOf z) (x takesCourse z)
+// -----------------------------------------------------------
+val query9 = filterProp(triples, advisor).map{ case (x, y, f1) => ( y,(x, f1))}.
+  join(filterProp(triples, teaof).map{ case (y, z, f2) => ( y, (z, f2) )}).
+  map{ case ( y, ((x, f1), (z, f2) )) => ((x, z), (y, f1, f2)) }.
+  join(filterProp(triples, takco).map{ case (x, z, f3) => ( (x, z), f3)}).
+  map{ case ((x, z), ((y, f1, f2), f3)) => ListBuffer((x, y, f1), (y, z, f2), (x, z, f3)) }
+query9.setName("q9")
+//query9.persist()
+query9.count
+// 272982
+val replica9 =  getReplicaForQuery(query9, Array(advisor, teaof, takco) ,2)
+// stat : nb triples Ãƒ  repliquer dans chaque partition
+//replica9.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b).collect.foreach(println)
+//(0,3131) (1,3213) (2,3504) (3,44706) (4,2014)
+// -----------------------------------------------------------
+// LUBM 12 : WS
+// Pattern: (y worksFor z) (z subOrganisation t)
+// -----------------------------------------------------------
+val query12 = filterProp(triples, worksFor).map{ case (y, z, f1) => ( z, (y, f1))}.
+  join(filterProp(triples, suborg).map{ case (z, t, f2) => ( z, (t, f2))}).
+  map{ case ( z, ((y, f1), (t, f2) )) => ListBuffer((y, z, f1), (z, t, f2)) }
+query12.setName("q12")
+//query12.persist()
+query12.count
+//720628
+val replica12 =  getReplicaForQuery(query12, Array(worksFor, suborg), 2)
+//stat : nb triples Ãƒ  repliquer dans chaque partition
+//replica12.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b).collect.foreach(println)
+/*
+---------------------------------------------------------------------------
+STEP 3: UNION DES REPLICAS CALCULES POUR CHAQUE REQUETE
+---------------------------------------------------------------------------
+*/
+val allreplica = replica1.union(replica2).union(replica9).union(replica12).distinct
+val nbAjout = allreplica.count
+// 357 161 pour 5 part
+// 734 295 pour 10 part
+// 779 983 pour 20 part
+// replication rate
+affiche("N ajout:  " + nbAjout.toDouble)
+affiche("taux de replication: " + (nbAjout.toDouble / triples.count))
+var t2= java.lang.System.currentTimeMillis();
+affiche("Preparation time "+ (t2 - t1).toDouble/1000 +" sec for " + part + " partitions");
+val oDist = triples.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b)
+val oMean = oDist.map{case(f,c)=>c}.sum / machine
+val odevs = oDist.map{case(f,c)=>c}.map(score => (score - oMean) * (score - oMean))
+val ostddev = Math.sqrt(odevs.sum / machine)
+val nDist = oDist.join(allreplica.map{ case(s,p,o,f) => (f,1)}.reduceByKey( (a,b) => a+b)).map{case(f,(oc,on))=>(oc+on)}
+val nMean = nDist.sum / machine
+val ndevs = nDist.map(score => (score - nMean) * (score - nMean))
+val nstddev = Math.sqrt(ndevs.sum / machine)
+/*
+---------------------------------------------------------------------------
+STEP 4: LOCAL QUERY PROCESSING
+On the WARP replicated data
+---------------------------------------------------------------------------
+*/
+// Extends each partition with the WARP replicated triples.
+// Each machine stores one partition
+val triplesWARP = triples.union(allreplica).
+  map{ case (s,p,o,f) => (f, (s,p,o))}.
+  partitionBy(new HashPartitioner(machine)).map{ case (f, (s,p,o)) => (s,p,o,f)}
+triplesWARP.setName("triples WARP")
+triplesWARP.persist()
+triplesWARP.count
+var t2= java.lang.System.currentTimeMillis();
+affiche("Preparation time "+ (t2 - t1).toDouble/1000 +" sec for " + part + " partitions");
+// -------------------
+//  Q1 LOCAL
+// -------------------
+t1= java.lang.System.currentTimeMillis();
+// Query1 locale avec projection sur les variables (x,y,z,t)
+val localQuery1 = filterProp(triplesWARP, advisor).map{ case (x, y, f) => ( (y, f), x)}.
+  join(filterProp(triplesWARP, worksFor).map{ case (y, z, f) => ( (y, f), z )}).
+  map{ case ( (y, f), (x, z)) => ((z, f), (x, y)) }.
+  join(filterProp(triplesWARP, suborg).map{ case ( z, t, f) => ((z, f), t)}).
+  map{ case ( (z, f), ( (x,y), t)) => (x, y, z, t)}
+localQuery1.count
+//4108791  OK idem sans replication
+t2= java.lang.System.currentTimeMillis();
+affiche("DurÃƒÂ©ee de la requÃƒÂªte Q1 : "+ (t2 - t1) +" msec pour " + part + " partitions");
+// -----------------------------------------------------------
+// Q2 LOCAL:
+// Pattern: (x memberOf y) (y subOrg z) (x UndergraduateDegreeFrom z)
+// -----------------------------------------------------------
+t1= java.lang.System.currentTimeMillis();
+val localQuery2 = filterProp(triplesWARP, memof).map{ case (x, y, f) => ( (y, f), x)}.
+  join(filterProp(triplesWARP, suborg).map{ case (y, z, f) => ( (y, f), z )}).
+  map{ case ( (y, f), (x, z)) => ((x, z, f), y) }.
+  join(filterProp(triplesWARP, undeg).map{ case (x, z, f) => ( (x, z, f), 1)}).
+  map{ case ((x, z, f), (y, 1)) => (x, y, z) }
+localQuery2.count
+//2528
+t2= java.lang.System.currentTimeMillis();
+affiche("Duree de la requete Q2 : "+ (t2 - t1) +" msec pour " + part + " partitions");
+// -----------------------------------------------------------
+// Q9 LOCAL
+// Pattern: (x advisor y) (y teacherOf z) (x takesCourse z)
+// -----------------------------------------------------------
+t1= java.lang.System.currentTimeMillis();
+val localQuery9 = filterProp(triplesWARP, advisor).map{ case (x, y, f) => ( (y, f), x)}.
+  join(filterProp(triplesWARP, teaof).map{ case (y, z, f) => ( (y, f), z )}).
+  map{ case ( (y, f), (x, z)) => ((x, z, f), y) }.
+  join(filterProp(triplesWARP, takco).map{ case (x, z, f) => ( (x, z, f), 1)}).
+  map{ case ((x, z, f), (y, 1)) => (x, y, z) }
+localQuery9.count
+//272982
+t2= java.lang.System.currentTimeMillis();
+affiche("Duree de la requete Q9 : "+ (t2 - t1) +" msec pour " + part + " partitions");
+// -----------------------------------------------------------
+// Q12 LOCAL
+// Pattern: (y worksFor z) (z subOrganisation t)
+// -----------------------------------------------------------
+t1= java.lang.System.currentTimeMillis();
+val localQuery12 = filterProp(triplesWARP, worksFor).map{ case (y, z, f) => ( (z, f), y)}.
+  join(filterProp(triplesWARP, suborg).map{ case (z, t, f) => ( (z, f), t)}).
+  map{ case ( (z, f), (y, t)) => (y, z, t) }
+localQuery12.count
+//938356
+t2= java.lang.System.currentTimeMillis();
+affiche("Duree de la requete Q12: "+ (t2 - t1) +" msec pour " + part + " partitions");
+</code>
+===2-hop based approach===
+<code>
+val folder=  "lubm"
+val dataset= "univ"
+val scale="10k"
+val folderName = folder +scale
+val part = Array(5,10,20)
+for (p <- part)
+{
+val fileName = dataset+scale+"_encoded_unique_quads.part."+p
+val fileNamewatdiv2k_encoded_unique_quads.partNew.5
+val t1 = java.lang.System.currentTimeMillis();
+val quads = sc.textFile(s"/user/olivier/${folderName}/${fileName}").map(x=>x.split(",")).map(t=>(t(0).replace("(","").toLong,t(1).toLong,t(2).toLong,t(3).replace(")","").toLong))
+var addOneHop = quads.map({case(s,p,o,i)=>(o,i)}).join(quads.map({case(s,p,o,i)=>(s,(p,o,i))})).filter({case(termS,(i1,(p,o,i2)))=>i1!=i2}).distinct.map({case(termS,(i1,(p,o,i2)))=>(termS,p,o,i1)})
+val newQuads = quads.union(addOneHop).distinct
+val newQuadsSize = newQuads.count
+val t2 = java.lang.System.currentTimeMillis();
+val hopSize = addOneHop.count
+println(s"Time to compute one more hop on $folderName for $p partitions is ${t2-t1}")
+println(s" new size = $newQuadsSize , added $hopSize")
+newQuads.saveAsTextFile(s"/user/olivier/${folderName}/${fileName}.2hop")
+}
+</code>
 ====Datasets excerpts====
+===Encoding of LUBM concepts and properties===
+<code>
+Properties:
+<http://www.w3.org/1999/02/22-rdf-syntax-ns#type>
+603979776 <http://www.univ-mlv.fr/~ocure/lubm.owl#officeNumber>
+671088640 <http://www.univ-mlv.fr/~ocure/lubm.owl#name>
+738197504 <http://www.univ-mlv.fr/~ocure/lubm.owl#title>
+805306368 <http://www.univ-mlv.fr/~ocure/lubm.owl#age>
+872415232 <http://www.univ-mlv.fr/~ocure/lubm.owl#telephone>
+939524096 <http://www.univ-mlv.fr/~ocure/lubm.owl#emailAddress>
+1006632960 <http://www.univ-mlv.fr/~ocure/lubm.owl#researchInterest>
+1082130432 <http://www.univ-mlv.fr/~ocure/lubm.owl#researchProject>
+1090519040 <http://www.univ-mlv.fr/~ocure/lubm.owl#hasAlumnus>
+1098907648 <http://www.univ-mlv.fr/~ocure/lubm.owl#degreeFrom>
+1101004800 <http://www.univ-mlv.fr/~ocure/lubm.owl#undergraduateDegreeFrom>
+1103101952 <http://www.univ-mlv.fr/~ocure/lubm.owl#mastersDegreeFrom>
+1105199104 <http://www.univ-mlv.fr/~ocure/lubm.owl#doctoralDegreeFrom>
+1107296256 <http://www.univ-mlv.fr/~ocure/lubm.owl#orgPublication>
+1115684864 <http://www.univ-mlv.fr/~ocure/lubm.owl#takesCourse>
+1124073472 <http://www.univ-mlv.fr/~ocure/lubm.owl#member>
+1132462080 <http://www.univ-mlv.fr/~ocure/lubm.owl#memberOf>
+1136656384 <http://www.univ-mlv.fr/~ocure/lubm.owl#worksFor>
+1138753536 <http://www.univ-mlv.fr/~ocure/lubm.owl#headOf>
+1140850688 <http://www.univ-mlv.fr/~ocure/lubm.owl#teachingAssistantOf>
+1149239296 <http://www.univ-mlv.fr/~ocure/lubm.owl#listedCourse>
+1157627904 <http://www.univ-mlv.fr/~ocure/lubm.owl#softwareDocumentation>
+1166016512 <http://www.univ-mlv.fr/~ocure/lubm.owl#publicationAuthor>
+1174405120 <http://www.univ-mlv.fr/~ocure/lubm.owl#softwareVersion>
+1182793728 <http://www.univ-mlv.fr/~ocure/lubm.owl#affiliateOf>
+1191182336 <http://www.univ-mlv.fr/~ocure/lubm.owl#tenured>
+1199570944 <http://www.univ-mlv.fr/~ocure/lubm.owl#teacherOf>
+1207959552 <http://www.univ-mlv.fr/~ocure/lubm.owl#publicationDate>
+1216348160 <http://www.univ-mlv.fr/~ocure/lubm.owl#affiliatedOrganizationOf>
+1224736768 <http://www.univ-mlv.fr/~ocure/lubm.owl#subOrganizationOf>
+1233125376 <http://www.univ-mlv.fr/~ocure/lubm.owl#advisor>
+1241513984 <http://www.univ-mlv.fr/~ocure/lubm.owl#publicationResearch>
+Concepts:
+<http://www.univ-mlv.fr/~ocure/lubm.owl#Schedule>
+268435456 <http://www.univ-mlv.fr/~ocure/lubm.owl#Organization>
+301989888 <http://www.univ-mlv.fr/~ocure/lubm.owl#College>
+335544320 <http://www.univ-mlv.fr/~ocure/lubm.owl#Department>
+369098752 <http://www.univ-mlv.fr/~ocure/lubm.owl#Institute>
+402653184 <http://www.univ-mlv.fr/~ocure/lubm.owl#ResearchGroup>
+436207616 <http://www.univ-mlv.fr/~ocure/lubm.owl#Program>
+469762048 <http://www.univ-mlv.fr/~ocure/lubm.owl#University>
+536870912 <http://www.univ-mlv.fr/~ocure/lubm.owl#Publication>
+570425344 <http://www.univ-mlv.fr/~ocure/lubm.owl#Software>
+603979776 <http://www.univ-mlv.fr/~ocure/lubm.owl#Book>
+637534208 <http://www.univ-mlv.fr/~ocure/lubm.owl#Specification>
+671088640 <http://www.univ-mlv.fr/~ocure/lubm.owl#Manual>
+704643072 <http://www.univ-mlv.fr/~ocure/lubm.owl#Article>
+713031680 <http://www.univ-mlv.fr/~ocure/lubm.owl#TechnicalReport>
+721420288 <http://www.univ-mlv.fr/~ocure/lubm.owl#ConferencePaper>
+729808896 <http://www.univ-mlv.fr/~ocure/lubm.owl#JournalArticle>
+738197504 <http://www.univ-mlv.fr/~ocure/lubm.owl#UnofficialPublication>
+805306368 <http://www.univ-mlv.fr/~ocure/lubm.owl#Person>
+872415232 <http://www.univ-mlv.fr/~ocure/lubm.owl#TeachingAssistant>
+939524096 <http://www.univ-mlv.fr/~ocure/lubm.owl#Student>
+956301312 <http://www.univ-mlv.fr/~ocure/lubm.owl#GraduateStudent>
+973078528 <http://www.univ-mlv.fr/~ocure/lubm.owl#UndergraduateStudent>
+1006632960 <http://www.univ-mlv.fr/~ocure/lubm.owl#Employee>
+1015021568 <http://www.univ-mlv.fr/~ocure/lubm.owl#ResearchAssistant>
+1023410176 <http://www.univ-mlv.fr/~ocure/lubm.owl#Director>
+1031798784 <http://www.univ-mlv.fr/~ocure/lubm.owl#AdministrativeStaff>
+1033895936 <http://www.univ-mlv.fr/~ocure/lubm.owl#SystemsStaff>
+1035993088 <http://www.univ-mlv.fr/~ocure/lubm.owl#ClericalStaff>
+1040187392 <http://www.univ-mlv.fr/~ocure/lubm.owl#Faculty>
+1042284544 <http://www.univ-mlv.fr/~ocure/lubm.owl#PostDoc>
+1044381696 <http://www.univ-mlv.fr/~ocure/lubm.owl#Professor>
+1044643840 <http://www.univ-mlv.fr/~ocure/lubm.owl#Chair>
+1044905984 <http://www.univ-mlv.fr/~ocure/lubm.owl#VisitingProfessor>
+1045168128 <http://www.univ-mlv.fr/~ocure/lubm.owl#AssociateProfessor>
+1045430272 <http://www.univ-mlv.fr/~ocure/lubm.owl#Dean>
+1045692416 <http://www.univ-mlv.fr/~ocure/lubm.owl#FullProfessor>
+1045954560 <http://www.univ-mlv.fr/~ocure/lubm.owl#AssistantProfessor>
+1046478848 <http://www.univ-mlv.fr/~ocure/lubm.owl#Lecturer>
+1073741824 <http://www.univ-mlv.fr/~ocure/lubm.owl#Work>
+1140850688 <http://www.univ-mlv.fr/~ocure/lubm.owl#Course>
+1174405120 <http://www.univ-mlv.fr/~ocure/lubm.owl#GraduateCourse>
+1207959552 <http://www.univ-mlv.fr/~ocure/lubm.owl#Research>
+</code>
+===LUBM Univ1  ===
+-[[http://webia.lip6.fr/~baazizi/research/iswc2015eval/sources/univ1_encoded_unique.id|encoded triples]](2.1MB)
+-[[http://webia.lip6.fr/~baazizi/research/iswc2015eval/sources/quads_plus_replicas.id|encoded quaruples with replication]](2.3MB)
+-[[http://webia.lip6.fr/~baazizi/research/iswc2015eval/sources/quads.id|replicated quaruples]](0.3MB)
+-[[http://webia.lip6.fr/~baazizi/research/iswc2015eval/sources/univ1.nt|univ1.nt]] (16.3MB)

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