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My answer ended up being a bit more elaborated than I thought. While you might have luck by using the OpenMP implementation that comes with GCC (the paths of omp.h and libgomp.so can be found with the commands: gcc --print-file-name=include/omp.h and gcc --print-file-name=libgomp.so respectively), I'd suggest to do an out-of-tree build of the OpenMP subproject for the LLVM's exact version you use, as described here: http://openmp.llvm.org. The section "Status" of the same page says that since Clang 3.8, the OpenMP runtime is built as a normal part of the Clang build, so in theory we shouldn't need to do that manually. However, I didn't manage to enable OpenMP support just by installing the clang and llvm packages that come with Fedora. I've made a very small script (along the lines of the instructions in the page linked above), which allows you to install a local implementation of the OpenMP version compatible with Clang 3.9.1 (the one that comes with Fedora 25):

#!/bin/bash
cd ~ &&
rm -rf $HOME/BUILDS/CLANG391_OMP &&
mkdir -p $HOME/BUILDS/CLANG391_OMP &&
cd $HOME/BUILDS && 
svn co http://llvm.org/svn/llvm-project/openmp/tags/RELEASE_391/final openmp &&
cd openmp/runtime &&
cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=$HOME/BUILDS/CLANG391_OMP ../ &&
make -j4 && 
make install &&
cd ~ &&
rm -rf $HOME/BUILDS/openmp

you can just save it as build_clang391_omp.sh and make it executable with chmod +x build_clang391_omp.sh. Before launching the script (with ./build_clang391_omp.sh), make sure you have at least the packages svn, cmake, clang and the group "C Development Tools and Libraries" installed through dnf.

The building process is generally very fast and you will end up having the folder CLANG391_OMP inside $HOME/BUILDS. Now you can build your OpenMP-based test. Type in a terminal:

clang++ -fopenmp -I$HOME/BUILDS/CLANG391_OMP/include -L$HOME/BUILDS/CLANG391_OMP/lib dijkstra_openmp.cpp -o dijkstra_openmp

and then launch the executable:

LD_LIBRARY_PATH=$HOME/BUILDS/CLANG391_OMP/lib:$LD_LIBRARY_PATH ./dijkstra_openmp

which gives:

22 April 2017 03:18:01 PM

DIJKSTRA_OPENMP
  C++ version
  Use Dijkstra's algorithm to determine the minimum
  distance from node 0 to each node in a graph,
  given the distances between each pair of nodes.

  Although a very small example is considered, we
  demonstrate the use of OpenMP directives for
  parallel execution.

  Distance matrix:

    0   40   15  Inf  Inf  Inf
   40    0   20   10   25    6
   15   20    0  100  Inf  Inf
  Inf   10  100    0  Inf  Inf
  Inf   25  Inf  Inf    0    8
  Inf    6  Inf  Inf    8    0

  P0: Parallel region begins with 8 threads.

  P0  P  P  P  P24:  First=3:  First=  Last=0  Last=2-1

  P3:  First=2  Last=52
  P7:  First=5:  First=  Last=1  Last=51
  P6:  First=4  Last=4
:  First=3  Last=3

1:  First=0  Last=0
  P2: Connecting node 2
  P2: Connecting node 1
  P3: Connecting node 5
  P2: Connecting node 3
  P0: Connecting node 4

  P2: Exiting parallel region.

  Minimum distances from node 0:

   0   0
   1  35
   2  15
   3  45
   4  49
   5  41

DIJKSTRA_OPENMP
  Normal end of execution.

22 April 2017 03:18:01 PM

You could avoid setting up the variable LD_LIBRARY_PATH at every launch within the same terminal session with export LD_LIBRARY_PATH=$HOME/BUILDS/CLANG391_OMP/lib:$LD_LIBRARY_PATH. To make this permanent, you could add the same command to your ~/.bashrc, but I wouldn't recommend doing so, as polluting environment variables may cause you more subtle troubles, specially if you use different compilers at once.

My answer ended up being a bit more elaborated than I thought. While you might have luck by using the OpenMP implementation that comes with GCC (the paths of omp.h and libgomp.so can be found with the commands: gcc --print-file-name=include/omp.h and gcc --print-file-name=libgomp.so respectively), I'd suggest to do an out-of-tree build of the OpenMP subproject for the LLVM's exact version you use, as described here: http://openmp.llvm.org. The section "Status" of the same page says that since Clang 3.8, the OpenMP runtime is built as a normal part of the Clang build, so in theory we shouldn't need to do that manually. However, I didn't manage to enable OpenMP support just by installing the clang and llvm packages that come with Fedora. I've made a very small script (along the lines of the instructions in the page linked above), which allows you to locally install a local implementation of the OpenMP version compatible with Clang 3.9.1 (the one that comes with Fedora 25):

#!/bin/bash
cd ~ &&
rm -rf $HOME/BUILDS/CLANG391_OMP &&
mkdir -p $HOME/BUILDS/CLANG391_OMP &&
cd $HOME/BUILDS && 
svn co http://llvm.org/svn/llvm-project/openmp/tags/RELEASE_391/final openmp &&
cd openmp/runtime &&
cmake -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=$HOME/BUILDS/CLANG391_OMP ../ &&
make -j4 && 
make install &&
cd ~ &&
rm -rf $HOME/BUILDS/openmp

you can just save it as build_clang391_omp.sh and make it executable with chmod +x build_clang391_omp.sh. Before launching the script (with ./build_clang391_omp.sh), , as normal user), make sure you have at least the packages svn, cmake, clang and the group "C Development Tools and Libraries" installed through dnf.

The building process is generally very fast and you will end up having the folder CLANG391_OMP inside $HOME/BUILDS. Now you can build your OpenMP-based test. Type in a terminal:

clang++ -fopenmp -I$HOME/BUILDS/CLANG391_OMP/include -L$HOME/BUILDS/CLANG391_OMP/lib dijkstra_openmp.cpp test-openmp.cpp -o dijkstra_openmp
test-openmp

and then launch the executable:

LD_LIBRARY_PATH=$HOME/BUILDS/CLANG391_OMP/lib:$LD_LIBRARY_PATH ./dijkstra_openmp
./test-openmp

which gives:

22 April 2017 03:18:01 PM

DIJKSTRA_OPENMP
  C++ version
  Use Dijkstra's algorithm to determine the minimum
  distance from node 0 to each node in a graph,
  given the distances between each pair of nodes.

  Although a very small example is considered, we
  demonstrate the use of OpenMP directives for
  parallel execution.

  Distance matrix:

    0   40   15  Inf  Inf  Inf
   40    0   20   10   25    6
   15   20    0  100  Inf  Inf
  Inf   10  100    0  Inf  Inf
  Inf   25  Inf  Inf    0    8
  Inf    6  Inf  Inf    8    0

  P0: Parallel region begins with 8 threads.

  P0  P  P  P  P24:  First=3:  First=  Last=0  Last=2-1

  P3:  First=2  Last=52
  P7:  First=5:  First=  Last=1  Last=51
  P6:  First=4  Last=4
:  First=3  Last=3

1:  First=0  Last=0
  P2: Connecting node 2
  P2: Connecting node 1
  P3: Connecting node 5
  P2: Connecting node 3
  P0: Connecting node 4

  P2: Exiting parallel region.

  Minimum distances from node 0:

   0   0
   1  35
   2  15
   3  45
   4  49
   5  41

DIJKSTRA_OPENMP
  Normal end of execution.

22 April 2017 03:18:01 PM

You could avoid setting up the variable LD_LIBRARY_PATH at every launch within the same terminal session with export LD_LIBRARY_PATH=$HOME/BUILDS/CLANG391_OMP/lib:$LD_LIBRARY_PATH. To make this permanent, you could add the same command to your ~/.bashrc, but I wouldn't recommend doing so, as polluting environment variables may cause you more subtle troubles, specially if you use different compilers at once.