diff --git a/core/src/main/scala/org/apache/spark/Partitioner.scala b/core/src/main/scala/org/apache/spark/Partitioner.scala
index 52c018baa5f7b..37053bb6f37ad 100644
--- a/core/src/main/scala/org/apache/spark/Partitioner.scala
+++ b/core/src/main/scala/org/apache/spark/Partitioner.scala
@@ -19,11 +19,15 @@ package org.apache.spark
 
 import java.io.{IOException, ObjectInputStream, ObjectOutputStream}
 
-import scala.reflect.ClassTag
+import scala.collection.mutable
+import scala.collection.mutable.ArrayBuffer
+import scala.reflect.{ClassTag, classTag}
+import scala.util.hashing.byteswap32
 
-import org.apache.spark.rdd.RDD
+import org.apache.spark.rdd.{PartitionPruningRDD, RDD}
 import org.apache.spark.serializer.JavaSerializer
 import org.apache.spark.util.{CollectionsUtils, Utils}
+import org.apache.spark.util.random.{XORShiftRandom, SamplingUtils}
 
 /**
  * An object that defines how the elements in a key-value pair RDD are partitioned by key.
@@ -103,26 +107,49 @@ class RangePartitioner[K : Ordering : ClassTag, V](
     private var ascending: Boolean = true)
   extends Partitioner {
 
+  // We allow partitions = 0, which happens when sorting an empty RDD under the default settings.
+  require(partitions >= 0, s"Number of partitions cannot be negative but found $partitions.")
+
   private var ordering = implicitly[Ordering[K]]
 
   // An array of upper bounds for the first (partitions - 1) partitions
   private var rangeBounds: Array[K] = {
-    if (partitions == 1) {
-      Array()
+    if (partitions <= 1) {
+      Array.empty
     } else {
-      val rddSize = rdd.count()
-      val maxSampleSize = partitions * 20.0
-      val frac = math.min(maxSampleSize / math.max(rddSize, 1), 1.0)
-      val rddSample = rdd.sample(false, frac, 1).map(_._1).collect().sorted
-      if (rddSample.length == 0) {
-        Array()
+      // This is the sample size we need to have roughly balanced output partitions, capped at 1M.
+      val sampleSize = math.min(20.0 * partitions, 1e6)
+      // Assume the input partitions are roughly balanced and over-sample a little bit.
+      val sampleSizePerPartition = math.ceil(3.0 * sampleSize / rdd.partitions.size).toInt
+      val (numItems, sketched) = RangePartitioner.sketch(rdd.map(_._1), sampleSizePerPartition)
+      if (numItems == 0L) {
+        Array.empty
       } else {
-        val bounds = new Array[K](partitions - 1)
-        for (i <- 0 until partitions - 1) {
-          val index = (rddSample.length - 1) * (i + 1) / partitions
-          bounds(i) = rddSample(index)
+        // If a partition contains much more than the average number of items, we re-sample from it
+        // to ensure that enough items are collected from that partition.
+        val fraction = math.min(sampleSize / math.max(numItems, 1L), 1.0)
+        val candidates = ArrayBuffer.empty[(K, Float)]
+        val imbalancedPartitions = mutable.Set.empty[Int]
+        sketched.foreach { case (idx, n, sample) =>
+          if (fraction * n > sampleSizePerPartition) {
+            imbalancedPartitions += idx
+          } else {
+            // The weight is 1 over the sampling probability.
+            val weight = (n.toDouble / sample.size).toFloat
+            for (key <- sample) {
+              candidates += ((key, weight))
+            }
+          }
+        }
+        if (imbalancedPartitions.nonEmpty) {
+          // Re-sample imbalanced partitions with the desired sampling probability.
+          val imbalanced = new PartitionPruningRDD(rdd.map(_._1), imbalancedPartitions.contains)
+          val seed = byteswap32(-rdd.id - 1)
+          val reSampled = imbalanced.sample(withReplacement = false, fraction, seed).collect()
+          val weight = (1.0 / fraction).toFloat
+          candidates ++= reSampled.map(x => (x, weight))
         }
-        bounds
+        RangePartitioner.determineBounds(candidates, partitions)
       }
     }
   }
@@ -212,3 +239,67 @@ class RangePartitioner[K : Ordering : ClassTag, V](
     }
   }
 }
+
+private[spark] object RangePartitioner {
+
+  /**
+   * Sketches the input RDD via reservoir sampling on each partition.
+   *
+   * @param rdd the input RDD to sketch
+   * @param sampleSizePerPartition max sample size per partition
+   * @return (total number of items, an array of (partitionId, number of items, sample))
+   */
+  def sketch[K:ClassTag](
+      rdd: RDD[K],
+      sampleSizePerPartition: Int): (Long, Array[(Int, Int, Array[K])]) = {
+    val shift = rdd.id
+    // val classTagK = classTag[K] // to avoid serializing the entire partitioner object
+    val sketched = rdd.mapPartitionsWithIndex { (idx, iter) =>
+      val seed = byteswap32(idx ^ (shift << 16))
+      val (sample, n) = SamplingUtils.reservoirSampleAndCount(
+        iter, sampleSizePerPartition, seed)
+      Iterator((idx, n, sample))
+    }.collect()
+    val numItems = sketched.map(_._2.toLong).sum
+    (numItems, sketched)
+  }
+
+  /**
+   * Determines the bounds for range partitioning from candidates with weights indicating how many
+   * items each represents. Usually this is 1 over the probability used to sample this candidate.
+   *
+   * @param candidates unordered candidates with weights
+   * @param partitions number of partitions
+   * @return selected bounds
+   */
+  def determineBounds[K:Ordering:ClassTag](
+      candidates: ArrayBuffer[(K, Float)],
+      partitions: Int): Array[K] = {
+    val ordering = implicitly[Ordering[K]]
+    val ordered = candidates.sortBy(_._1)
+    val numCandidates = ordered.size
+    val sumWeights = ordered.map(_._2.toDouble).sum
+    val step = sumWeights / partitions
+    var cumWeight = 0.0
+    var target = step
+    val bounds = ArrayBuffer.empty[K]
+    var i = 0
+    var j = 0
+    var previousBound = Option.empty[K]
+    while ((i < numCandidates) && (j < partitions - 1)) {
+      val (key, weight) = ordered(i)
+      cumWeight += weight
+      if (cumWeight > target) {
+        // Skip duplicate values.
+        if (previousBound.isEmpty || ordering.gt(key, previousBound.get)) {
+          bounds += key
+          target += step
+          j += 1
+          previousBound = Some(key)
+        }
+      }
+      i += 1
+    }
+    bounds.toArray
+  }
+}
diff --git a/core/src/test/scala/org/apache/spark/PartitioningSuite.scala b/core/src/test/scala/org/apache/spark/PartitioningSuite.scala
index 4658a08064280..fc0cee3e8749d 100644
--- a/core/src/test/scala/org/apache/spark/PartitioningSuite.scala
+++ b/core/src/test/scala/org/apache/spark/PartitioningSuite.scala
@@ -17,6 +17,7 @@
 
 package org.apache.spark
 
+import scala.collection.mutable.ArrayBuffer
 import scala.math.abs
 
 import org.scalatest.{FunSuite, PrivateMethodTester}
@@ -52,14 +53,12 @@ class PartitioningSuite extends FunSuite with SharedSparkContext with PrivateMet
 
     assert(p2 === p2)
     assert(p4 === p4)
-    assert(p2 != p4)
-    assert(p4 != p2)
+    assert(p2 === p4)
     assert(p4 === anotherP4)
     assert(anotherP4 === p4)
     assert(descendingP2 === descendingP2)
     assert(descendingP4 === descendingP4)
-    assert(descendingP2 != descendingP4)
-    assert(descendingP4 != descendingP2)
+    assert(descendingP2 === descendingP4)
     assert(p2 != descendingP2)
     assert(p4 != descendingP4)
     assert(descendingP2 != p2)
@@ -102,6 +101,63 @@ class PartitioningSuite extends FunSuite with SharedSparkContext with PrivateMet
     partitioner.getPartition(Row(100))
   }
 
+  test("RangPartitioner.sketch") {
+    val rdd = sc.makeRDD(0 until 20, 20).flatMap { i =>
+      val random = new java.util.Random(i)
+      Iterator.fill(i)(random.nextDouble())
+    }.cache()
+    val sampleSizePerPartition = 10
+    val (count, sketched) = RangePartitioner.sketch(rdd, sampleSizePerPartition)
+    assert(count === rdd.count())
+    sketched.foreach { case (idx, n, sample) =>
+      assert(n === idx)
+      assert(sample.size === math.min(n, sampleSizePerPartition))
+    }
+  }
+
+  test("RangePartitioner.determineBounds") {
+    assert(RangePartitioner.determineBounds(ArrayBuffer.empty[(Int, Float)], 10).isEmpty,
+      "Bounds on an empty candidates set should be empty.")
+    val candidates = ArrayBuffer(
+      (0.7, 2.0f), (0.1, 1.0f), (0.4, 1.0f), (0.3, 1.0f), (0.2, 1.0f), (0.5, 1.0f), (1.0, 3.0f))
+    assert(RangePartitioner.determineBounds(candidates, 3) === Array(0.4, 0.7))
+  }
+
+  test("RangePartitioner should run only one job if data is roughly balanced") {
+    val rdd = sc.makeRDD(0 until 20, 20).flatMap { i =>
+      val random = new java.util.Random(i)
+      Iterator.fill(5000 * i)((random.nextDouble() + i, i))
+    }.cache()
+    for (numPartitions <- Seq(10, 20, 40)) {
+      val partitioner = new RangePartitioner(numPartitions, rdd)
+      assert(partitioner.numPartitions === numPartitions)
+      val counts = rdd.keys.map(key => partitioner.getPartition(key)).countByValue().values
+      assert(counts.max < 3.0 * counts.min)
+    }
+  }
+
+  test("RangePartitioner should work well on unbalanced data") {
+    val rdd = sc.makeRDD(0 until 20, 20).flatMap { i =>
+      val random = new java.util.Random(i)
+      Iterator.fill(20 * i * i * i)((random.nextDouble() + i, i))
+    }.cache()
+    for (numPartitions <- Seq(2, 4, 8)) {
+      val partitioner = new RangePartitioner(numPartitions, rdd)
+      assert(partitioner.numPartitions === numPartitions)
+      val counts = rdd.keys.map(key => partitioner.getPartition(key)).countByValue().values
+      assert(counts.max < 3.0 * counts.min)
+    }
+  }
+
+  test("RangePartitioner should return a single partition for empty RDDs") {
+    val empty1 = sc.emptyRDD[(Int, Double)]
+    val partitioner1 = new RangePartitioner(0, empty1)
+    assert(partitioner1.numPartitions === 1)
+    val empty2 = sc.makeRDD(0 until 2, 2).flatMap(i => Seq.empty[(Int, Double)])
+    val partitioner2 = new RangePartitioner(2, empty2)
+    assert(partitioner2.numPartitions === 1)
+  }
+
   test("HashPartitioner not equal to RangePartitioner") {
     val rdd = sc.parallelize(1 to 10).map(x => (x, x))
     val rangeP2 = new RangePartitioner(2, rdd)
diff --git a/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala b/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
index 6654ec2d7c656..fdc83bc0a5f8e 100644
--- a/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
+++ b/core/src/test/scala/org/apache/spark/rdd/RDDSuite.scala
@@ -613,6 +613,11 @@ class RDDSuite extends FunSuite with SharedSparkContext {
     }
   }
 
+  test("sort an empty RDD") {
+    val data = sc.emptyRDD[Int]
+    assert(data.sortBy(x => x).collect() === Array.empty)
+  }
+
   test("sortByKey") {
     val data = sc.parallelize(Seq("5|50|A","4|60|C", "6|40|B"))