## Overview

Example that uses parallel_do to do parallel preorder traversal of a sparse graph.

Each vertex in the graph is called a "cell". Each cell has a value. The value is a matrix. Some of the cells have operators that compute the cell's value, using other cell's values as input. A cell that uses the value of cell x is called a successor of x.

The algorithm works as follows.

1. Compute the set of cells that have no inputs. This set is called `root_set`.
2. Each cell has an associated field `ref_count` that is an atomic integer. Initialize `ref_count` to the number of inputs for the Cell.
3. Update each cell in `root_set`, by applying a `parallel_do` to a `root_set`
4. After updating a cell, for each of its successors
   1. Atomically decrement the successor's `ref_count`
   2. If the count became zero, add the cell to the set of cells to be updated, by calling `parallel_do_feeder_impl::add`.

The times printed are for the traversal and update, and do not include time for computing the root_set.

The example is using custom synchronization via `ref_count` atomic variable. Correctness checking tools might not take this into account, and report data races between different tasks that are actually synchronized.

NOTE: It is important to understand that this example is unlikely to show speedup if the cell values are changed to type "float". The reason is twofold.

- The smaller value type causes each Cell to be significantly smaller than a cache line, which leads to false sharing conflicts.
- The time to update the cells becomes very small, and consequently the overhead of parallel_do swamps the useful work.

## Files

main.cpp
  Main program which parses command line options and runs the algorithm with different numbers of threads.
parallel_preorder.cpp
  Implementation of the parallel preorder traversal algorithm.
Graph.h
  Interfaces of the Graph and Cell classes.
Graph.cpp
  Implementations of the Graph and Cell classes.
Matrix.h
  The Matrix class definition.
Makefile
  Makefile for building example.

## Directories

msvs
  Contains Microsoft* Visual Studio* 2010 workspace for building and running the example (Windows* systems only).
xcode
  Contains Xcode* IDE workspace for building and running the example (OS X* systems only).

## To Build

General build directions can be found here.

## Usage

`parallel_preorder -h`
  Prints the help for command line options
`parallel_preorder [n-of-threads=value] [n-of-nodes=value] [n-of-traversals=value] [silent]`
`parallel_preorder [n-of-threads [n-of-nodes [n-of-traversals]]] [silent]`
  n-of-threads is the number of threads to use; a range of the form low[:high], where low and optional high are non-negative integers or 'auto' for the TBB default.
  n-of-nodes is a number of nodes in the graph. Default value is 1000.
  n-of-traversals is the number of times to evaluate the graph. Default value is 500.
  silent - no output except elapsed time.
To run a short version of this example, e.g., for use with Intel® Parallel Inspector:
  Build a debug version of the example (see the build directions).
  Run it with the desired number of threads and smaller number of traversals, e.g., `parallel_preorder 4 1000 5`.

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