The plans produced by each method are:

• SPARQL RDD:

val d1 = triples.filter{case(s,(p,o))=> p==P1}.map{case(x1,(p, x2)) => (x2, x1)}
val d2 = triples.filter{case(s,(p,o))=> p==P2}.mapValues{case(p,x3) => x3}
val d3 = triples.filter{case(s,(p,o))=> p==P3}.mapValues{case(p,x4) => x4}
val d4 = triples.filter{case(s,(p,o))=> p==P4}.mapValues{case(p,x5) => x5}
 
val j1 = d1.join(d2).map{case(x2,(x1, x3))=> (x3, (x1,x2))}
val j2 = j1.join(d3).map{case(x3,((x1,x2), x4))=> (x4, (x1,x2,x3))}
val j3 = j2.join(d4).map{case(x4,((x1,x2,x3), x5))=> (x5, (x1,x2,x3,x4))}
j3.count

• SPARQL DF:

val t1 = df.where(s"p=$P1").select("s","o").withColumnRenamed("s", "x1").withColumnRenamed("o", "x2")
val t2 = df.where(s"p=$P2").select("s","o").withColumnRenamed("s", "x2").withColumnRenamed("o", "x3")
val t3 = df.where(s"p=$P3").select("s","o").withColumnRenamed("s", "x3").withColumnRenamed("o", "x4")
val t4 = df.where(s"p=$P4").select("s","o").withColumnRenamed("s", "x4").withColumnRenamed("o", "x5")
val res = t1.join(t2,Seq("x2")).join(t3,Seq("x3")).join(t4,Seq("x4"))

• SPARQL Hybrid DF:

val subg = df.where(s"p in ($P2, $P3, $P4)")
subg.persist
subg.count
val st2 = subg.where(s"p= $P2").select("s","o").withColumnRenamed("s", "x2").withColumnRenamed("o", "x3")
val st3 = subg.where(s"p= $P3").select("s","o").withColumnRenamed("s", "x3").withColumnRenamed("o", "x4")
val st4 = subg.where(s"p= $P4").select("s","o").withColumnRenamed("s", "x4").withColumnRenamed("o", "x5")
val res = t1.join(st2,Seq("x2")).join(st3,Seq("x3")).join(st4,Seq("x4"))
res.count

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