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@@ -52,7 +52,8 @@ subsets of elements of the whole parallel collection. And similar to normal
 In general, collections are partitioned using `Splitter`s into subsets of
 roughly the same size. In cases where more arbitrarily-sized partions are
 required, in particular on parallel sequences, a `PreciseSplitter` is used,
-which inherits `Splitter`.
+which inherits `Splitter` and additionally implements a precise split method, 
+`psplit`.
 
 ### Combiners
 
@@ -86,12 +87,12 @@ regular collections framework's corresponding traits, as shown below.
 
 [<img src="{{ site.baseurl }}/resources/images/parallel-collections-hierarchy.png" width="550">]({{ site.baseurl }}/resources/images/parallel-collections-hierarchy.png)
 
-<center><b>Hierarchy of Scala's Collections and Parallel Collections Libraries<b></center>
-
+<center><b>Hierarchy of Scala's Collections and Parallel Collections Libraries</b></center>
+<br/>
 
 The goal is of course to integrate parallel collections as tightly as possible
 with sequential collections, so as to allow for straightforward substitution
-of sequntial and parallel collections. 
+of sequential and parallel collections. 
 
 In order to be able to have a reference to a collection which may be either
 sequential or parallel (such that it's possible to "toggle" between a parallel
 
@@ -10,22 +10,25 @@ num: 7
 
 ## Task support
 
-Parallel collections are modular in the way operations are scheduled. Each parallel
-collection is parametrized with a task support object which is responsible for
-scheduling and load-balancing tasks to processors.
-
-The task support object internally keeps a reference to a thread pool implementation
-and decides how and when tasks are split into smaller tasks.
-To learn more about the internals of how exactly this is done, see the tech report \[[1][1]\].
-
-There are currently a few task support implementations available for parallel collections.
-The `ForkJoinTaskSupport` uses a fork-join pool internally and is used by default on JVM 1.6 or greater.
-The less efficient `ThreadPoolTaskSupport` is a fallback for JVM 1.5 and JVMs that do not support
-the fork join pools. The `ExecutionContextTaskSupport` uses the default execution context implementation
-found in `scala.concurrent`, and it reuses the thread pool used in
-`scala.concurrent` (this is either a fork join pool or a thread pool executor, depending on the JVM version).
-The execution context task support is set to each parallel collection by default, so parallel collections
-reuse the same fork-join pool as the future API.
+Parallel collections are modular in the way operations are scheduled. Each
+parallel collection is parametrized with a task support object which is
+responsible for scheduling and load-balancing tasks to processors.
+
+The task support object internally keeps a reference to a thread pool
+implementation and decides how and when tasks are split into smaller tasks. To
+learn more about the internals of how exactly this is done, see the tech
+report \[[1][1]\].
+
+There are currently a few task support implementations available for parallel
+collections. The `ForkJoi
6D4E
nTaskSupport` uses a fork-join pool internally and is
+used by default on JVM 1.6 or greater. The less efficient
+`ThreadPoolTaskSupport` is a fallback for JVM 1.5 and JVMs that do not support
+the fork join pools. The `ExecutionContextTaskSupport` uses the default
+execution context implementation found in `scala.concurrent`, and it reuses
+the thread pool used in `scala.concurrent` (this is either a fork join pool or
+a thread pool executor, depending on the JVM version). The execution context
+task support is set to each parallel collection by default, so parallel
+collections reuse the same fork-join pool as the future API.
 
 Here is a way to change the task support of a parallel collection:
 
@@ -41,33 +44,34 @@ Here is a way to change the task support of a parallel collection:
     scala> pc map { _ + 1 }
     res0: scala.collection.parallel.mutable.ParArray[Int] = ParArray(2, 3, 4)
 
-The above sets the parallel collection to use a fork-join pool with parallelism level 2.
-To set the parallel collection to use a thread pool executor:
+The above sets the parallel collection to use a fork-join pool with
+parallelism level 2. To set the parallel collection to use a thread pool
+executor:
 
     scala> pc.tasksupport = new ThreadPoolTaskSupport()
     pc.tasksupport: scala.collection.parallel.TaskSupport = scala.collection.parallel.ThreadPoolTaskSupport@1d914a39
 
     scala> pc map { _ + 1 }
     res1: scala.collection.parallel.mutable.ParArray[Int] = ParArray(2, 3, 4)
 
-When a parallel collection is serialized, the task support field is omitted from serialization.
-When deserializing a parallel collection, the task support field is set to the default value - the execution context task support.
+When a parallel collection is serialized, the task support field is omitted
+from serialization. When deserializing a parallel collection, the task support
+field is set to the default value-- the execution context task support.
 
-To implement a custom task support, extend the `TaskSupport` trait and implement the following methods:
+To implement a custom task support, extend the `TaskSupport` trait and
+implement the following methods:
 
     def execute[R, Tp](task: Task[R, Tp]): () => R
 
     def executeAndWaitResult[R, Tp](task: Task[R, Tp]): R
 
     def parallelismLevel: Int
 
-The `execute` method schedules a task asynchronously and returns a future to wait on the result of the computation.
-The `executeAndWait` method does the same, but only returns when the task is completed.
-The `parallelismLevel` simply returns the targeted number of cores that the task support uses to schedule tasks.
-
-
-
-
+The `execute` method schedules a task asynchronously and returns a future to
+wait on the result of the computation. The `executeAndWait` method does the
+same, but only returns when the task is completed. The `parallelismLevel`
+simply returns the targeted number of cores that the task support uses to
+schedule tasks.
 
 
 ## References
 
@@ -11,23 +11,23 @@ num: 3
 ## Converting between sequential and parallel collections
 
 Every sequential collection can be converted to its parallel variant
-using the `par` method. Certain sequential collections have their
-direct parallel counterparts. For these collections the conversion is
-efficient - it occurs in constant time, since both the sequential and
+using the `par` method. Certain sequential collections have a
+direct parallel counterpart. For these collections the conversion is
+efficient-- it occurs in constant time, since both the sequential and
 the parallel collection have the same data-structural representation
-(one exception are mutable hash maps and hash sets which are slightly
+(one exception is mutable hash maps and hash sets which are slightly
 more expensive to convert the first time `par` is called, but
 subsequent invocations of `par` take constant time). It should be
 noted that for mutable collections, changes in the sequential collection are
 visible in its parallel counterpart if they share the underlying data-structure.
 
-| sequential    | parallel       |
+| Sequential    | Parallel       |
 | ------------- | -------------- |
 | **mutable**   |                |
 | `Array`       | `ParArray`     |
 | `HashMap`     | `ParHashMap`   |
 | `HashSet`     | `ParHashSet`   |
-| `Ctrie`       | `ParCtrie`     |
+| `TrieMap`     | `ParTrieMap`   |
 | **immutable** |          
10000
      |
 | `Vector`      | `ParVector`    |
 | `Range`       | `ParRange`     |
@@ -43,9 +43,9 @@ vector.
 
 Every parallel collection can be converted to its sequential variant
 using the `seq` method. Converting a parallel collection to a
-sequential collection is always efficient - it takes constant
+sequential collection is always efficient-- it takes constant
 time. Calling `seq` on a mutable parallel collection yields a
-sequential collection which is backed by the same store - updates to
+sequential collection which is backed by the same store-- updates to
 one collection will be visible in the other one.
 
 
@@ -61,7 +61,7 @@ into a `ParX` collection.
 
 Here is a summary of all conversion methods:
 
-| method         | return type    |
+| Method         | Return Type    |
 | -------------- | -------------- |
 | `toArray`      | `Array`        |
 | `toList`       | `List`         |
 
@@ -18,17 +18,24 @@ parallel counterparts. The only difference between the two is that the
 former traverses its elements sequentially, whereas the latter does so in
 parallel.
 
-This is a nice property that allows you to write some algorithms more easily.
+This is a nice property that allows you to write some algorithms more
+easily. Typically, these are algorithms that process a dataset of elements
+iteratively, in which different elements need a different number of
+iterations to be processed.
+
 The following example computes the square roots of a set of numbers. Each iteration
 iteratively updates the square root value. Numbers whose square roots converged
 are removed from the map.
 
+    case class Entry(num: Double) {
+      var sqrt = num
+    }
 
     val length = 50000
 
 	// prepare the list
     val entries = (1 until length) map { num => Entry(num.toDouble) }
-    val results = ParConcurrentTrieMap()
+    val results = ParTrieMap()
     for (e <- entries) results += ((e.num, e))
 
 	// compute square roots
@@ -41,8 +48,25 @@ are removed from the map.
       }
     }
 
+Note that in the above Babylonian method square root computation
+(\[[3][3]\]) some numbers may converge much faster than the others. For
+this reason, we want to remove them from `results` so that only those
+elements that need to be worked on are traversed.
+
 Another example is the breadth-first search algorithm, which iteratively expands the nodefront
-until either it finds some path to the target or there are no more nodes to expand.
+until either it finds some path to the target or there are no more
+nodes to expand. We define a node on a 2D map as a tuple of
+`Int`s. We define the `map` as a 2D array of booleans which denote is
+the respective slot occupied or not. We then declare 2 concurrent trie
+maps-- `open` which contains all the nodes which have to be
+expanded (the nodefront), and `closed` which contains all the nodes which have already
+been expanded. We want to start the search from the corners of the map and
+find a path to the center of the map-- we initialize the `open` map
+with appropriate nodes. Then we iteratively expand all the nodes in
+the `open` map in parallel until there are no more nodes to expand.
+Each time a node is expanded, it is removed from the `open` map and
+placed in the `closed` map.
+Once done, we output the path from the target to the initial node.
 
 	val length = 1000
 
@@ -63,8 +87,8 @@ until either it finds some path to the target or there are no more nodes to expa
 
     // open list - the nodefront
     // closed list - nodes already processed
-    val open = ParConcurrentTrieMap[Node, Parent]()
-    val closed = ParConcurrentTrieMap[Node, Parent]()
+    val open = ParTrieMap[Node, Parent]()
+    val closed = ParTrieMap[Node, Parent]()
 
     // add a couple of starting positions
     open((0, 0)) = null
@@ -97,13 +121,22 @@ until either it finds some path to the target or there are no more nodes to expa
     }
     println()
 
-The concurrent trie data structure supports a linearizable, lock-free, constant
-time, lazily evaluated snapshot operation. The snapshot operation merely creates
+
+The concurrent tries also support a linearizable, lock-free, constant
+time `snapshot` operation. This operation creates a new concurrent
+trie with all the elements at a specific point in time, thus in effect
+capturing the state of the trie at a specific point.
+The `snapshot` operation merely creates
 a new root for the concurrent trie. Subsequent updates lazily rebuild the part of
 the concurrent trie relevant to the update and leave the rest of the concurrent trie
 intact. First of all, this means that the snapshot operation by itself is not expensive
 since it does not copy the elements. Second, since the copy-on-write optimization copies
 only parts of the concurrent trie, subsequent modifications scale horizontally.
+The `readOnlySnapshot` method is slightly more efficient than the
+`snapshot` method, but returns a read-only map which cannot be
+modified. Concurrent tries also support a linearizable, constant-time
+`clear` operation based on the snapshot mechanism.
+To learn more about how concurrent tries and snapshots work, see \[[1][1]\] and \[[2][2]\].
 
 The iterators for concurrent tries are based on snapshots. Before the iterator
 object gets created, a snapshot of the concurrent trie is taken, so the iterator
@@ -119,7 +152,14 @@ of the `size` method to amortized logarithmic time. In effect, this means that a
 the size only for those branches of the trie which have been modified since the last `size` call.
 Additionally, size computation for parallel concurrent tries is performed in parallel.
 
-The concurrent tries also support a linearizable, lock-free, constant time `clear` operation.
 
 
+## References
+
+1. [Cache-Aware Lock-Free Concurrent Hash Tries][1]
+2. [Concurrent Tries with Efficient Non-Blocking Snapshots][2]
+3. [Methods of computing square roots][3]
 
+  [1]: http://infoscience.epfl.ch/record/166908/files/ctries-techreport.pdf "Ctries-techreport"
+  [2]: http://lampwww.epfl.ch/~prokopec/ctries-snapshot.pdf "Ctries-snapshot"
+  [3]: http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method "babylonian-method"