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<h1 class="topictitle1">Divide and Conquer</h1>
<div>
<div class="section"><h2 class="sectiontitle">Problem</h2>
<p>Parallelize a divide and conquer algorithm.
</p>
</div>
<div class="section"><h2 class="sectiontitle">Context</h2>
<p>Divide and conquer is widely used in serial algorithms. Common
examples are quicksort and mergesort.
</p>
</div>
<div class="section"><h2 class="sectiontitle">Forces</h2>
<ul type="disc">
<li>
<p>Problem can be transformed into subproblems that can be solved
independently.
</p>
</li>
<li>
<p>Splitting problem or merging solutions is relatively cheap
compared to cost of solving the subproblems.
</p>
</li>
</ul>
</div>
<div class="section"><h2 class="sectiontitle">Solution</h2>
<p>There are several ways to implement divide and conquer in Intel®
Threading Building Blocks (Intel® TBB). The best choice depends upon
circumstances.
</p>
<ul type="disc">
<li>
<p>If division always yields the same number of subproblems, use
recursion and
<samp class="codeph">tbb::parallel_invoke</samp>.
</p>
</li>
<li>
<p>If the number of subproblems varies, use recursion and
<samp class="codeph">tbb::task_group</samp>.
</p>
</li>
<li>
<p>If ultimate efficiency and scalability is important, use
<samp class="codeph">tbb::task</samp> and continuation passing style.
</p>
</li>
</ul>
</div>
<div class="section"><h2 class="sectiontitle">Example</h2>
<p>Quicksort is a classic divide-and-conquer algorithm. It divides a
sorting problem into two subsorts. A simple serial version looks
like:<a name="fnsrc_1" href="#fntarg_1"><sup>1</sup></a>
</p>
<pre>void SerialQuicksort( T* begin, T* end ) {
if( end-begin>1 ) {
using namespace std;
T* mid = partition( begin+1, end, bind2nd(less<T>(),*begin) );
swap( *begin, mid[-1] );
SerialQuicksort( begin, mid-1 );
SerialQuicksort( mid, end );
}
}</pre>
<p>The number of subsorts is fixed at two, so
<samp class="codeph">tbb::parallel_invoke</samp> provides a simple way to
parallelize it. The parallel code is shown below:
</p>
<pre>void ParallelQuicksort( T* begin, T* end ) {
if( end-begin>1 ) {
using namespace std;
T* mid = partition( begin+1, end, bind2nd(less<T>(),*begin) );
swap( *begin, mid[-1] );
tbb::parallel_invoke( [=]{ParallelQuicksort( begin, mid-1 );},
[=]{ParallelQuicksort( mid, end );} );
}
}</pre>
<p>Eventually the subsorts become small enough that serial execution is
more efficient. The following variation, with the change shown in
<samp class="codeph"><span style="color:blue"><strong>bold font</strong></span></samp>,
does sorts of less than 500 elements using the earlier serial code.
</p>
<pre>void ParallelQuicksort( T* begin, T* end ) {
if( end-begin>=<span style="color:blue"><strong>500</strong></span> ) {
using namespace std;
T* mid = partition( begin+1, end, bind2nd(less<T>(),*begin) );
swap( *begin, mid[-1] );
tbb::parallel_invoke( [=]{ParallelQuicksort( begin, mid-1 );},
[=]{ParallelQuicksort( mid, end );} );
} <span style="color:blue"><strong>else {
SerialQuicksort( begin, end );
}</strong></span>
}</pre>
<p>The change is an instance of the Agglomeration pattern.
</p>
<p>The next example considers a problem where there are a variable number
of subproblems. The problem involves a tree-like description of a mechanical
assembly. There are two kinds of nodes:
</p>
<ul type="disc">
<li>
<p>Leaf nodes represent individual parts.
</p>
</li>
<li>
<p>Internal nodes represent groups of parts.
</p>
</li>
</ul>
<p>The problem is to find all nodes that collide with a target node. The
following code shows a serial solution that walks the tree. It records in
<samp class="codeph">Hits</samp> any nodes that collide with
<samp class="codeph">Target</samp>.
</p>
<pre>std::list<Node*> Hits;
Node* Target;
void SerialFindCollisions( Node& x ) {
if( x.is_leaf() ) {
if( x.collides_with( *Target ) )
Hits.push_back(&x);
} else {
for( Node::const_iterator y=x.begin();y!=x.end(); ++y )
SerialFindCollisions(*y);
}
} </pre>
<p id="ParallelFindCollisions"><a name="ParallelFindCollisions"><!-- --></a>A parallel version is shown below.
</p>
<pre>typedef tbb::enumerable_thread_specific<std::list<Node*> > LocalList;
LocalList LocalHits;
Node* Target; // Target node
void ParallelWalk( Node& x ) {
if( x.is_leaf() ) {
if( x.collides_with( *Target ) )
LocalHits.local().push_back(&x);
} else {
// Recurse on each child y of x in parallel
tbb::task_group g;
for( Node::const_iterator y=x.begin(); y!=x.end(); ++y )
g.run( [=]{ParallelWalk(*y);} );
// Wait for recursive calls to complete
g.wait();
}
}
void ParallelFindCollisions( Node& x ) {
ParallelWalk(x);
for(LocalList::iterator i=LocalHits.begin();i!=LocalHits.end(); ++i)
Hits.splice( Hits.end(), *i );
} </pre>
<p>The recursive walk is parallelized using class
<samp class="codeph">task_group</samp> to do recursive calls in parallel.
</p>
<p>There is another significant change because of the parallelism that is
introduced. Because it would be unsafe to update
<samp class="codeph">Hits</samp> concurrently, the parallel walk uses variable
<samp class="codeph">LocalHits</samp> to accumulate results. Because it is of type
<samp class="codeph">enumerable_thread_specific</samp>, each thread accumulates
its own private result. The results are spliced together into Hits after the
walk completes.
</p>
<p>The results will
<em>not</em> be in the same order as the original serial code.
</p>
<p>If parallel overhead is high, use the agglomeration pattern. For
example, use the serial walk for subtrees under a certain threshold.
</p>
</div>
</div>
<div class="familylinks">
<div class="parentlink"><strong>Parent topic:</strong> <a href="../../tbb_userguide/Design_Patterns/Design_Patterns.htm">Design Patterns</a></div>
</div>
<div class="See Also">
<h2>See Also</h2>
<div class="linklist">
<div><a href="Agglomeration.htm#Agglomeration">Agglomeration
</a></div></div>
</div>
<p><a name="fntarg_1" href="#fnsrc_1"><sup>1</sup></a> Production quality quicksort implementations typically use more
sophisticated pivot selection, explicit stacks instead of recursion, and some
other sorting algorithm for small subsorts. The simple algorithm is used here
to focus on exposition of the parallel pattern.</p>
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