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diff --git a/src/simple_example.cpp b/src/simple_example.cpp
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+/*  Copyright 2013 IST Austria
+    Contributed by: Ulrich Bauer, Michael Kerber, Jan Reininghaus
+
+    This file is part of PHAT.
+
+    PHAT is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    PHAT is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with PHAT.  If not, see <http://www.gnu.org/licenses/>. */
+
+// This file contains a simple example that demonstrates the usage of the library interface
+
+// wrapper algorithm that computes the persistence pairs of a given boundary matrix using a specified algorithm
+#include <phat/compute_persistence_pairs.h>
+
+// main data structure (choice affects performance)
+#include <phat/representations/vector_vector.h>
+
+// algorithm (choice affects performance)
+#include <phat/algorithms/standard_reduction.h>
+#include <phat/algorithms/chunk_reduction.h>
+#include <phat/algorithms/row_reduction.h>
+#include <phat/algorithms/twist_reduction.h>
+
+int main( int argc, char** argv ) 
+{
+    std::cout << "We will build an ordered boundary matrix of this simplicial complex consisting of a single triangle: " << std::endl;
+    std::cout << std::endl;
+    std::cout << " 3" << std::endl;
+    std::cout << " |\\" << std::endl;
+    std::cout << " | \\" << std::endl;
+    std::cout << " |  \\" << std::endl;
+    std::cout << " |   \\ 4" << std::endl;
+    std::cout << "5|    \\" << std::endl;
+    std::cout << " |     \\" << std::endl;
+    std::cout << " |  6   \\" << std::endl;
+    std::cout << " |       \\" << std::endl;
+    std::cout << " |________\\" << std::endl;
+    std::cout << " 0    2    1" << std::endl;
+
+
+    // first define a boundary matrix with the chosen internal representation
+    phat::boundary_matrix< phat::vector_vector > boundary_matrix;
+
+    // set the number of columns (has to be 7 since we have 7 simplices)
+    boundary_matrix.set_num_cols( 7 );
+    
+    // set the dimension of the cell that a column represents:
+    boundary_matrix.set_dim( 0, 0 );
+    boundary_matrix.set_dim( 1, 0 );
+    boundary_matrix.set_dim( 2, 1 );
+    boundary_matrix.set_dim( 3, 0 );
+    boundary_matrix.set_dim( 4, 1 );
+    boundary_matrix.set_dim( 5, 1 );
+    boundary_matrix.set_dim( 6, 2 );
+
+    // set the respective columns -- the columns entries have to be sorted
+    std::vector< phat::index > temp_col;
+
+    boundary_matrix.set_col( 0, temp_col );
+
+    boundary_matrix.set_col( 1, temp_col );
+
+    temp_col.push_back( 0 );
+    temp_col.push_back( 1 );
+    boundary_matrix.set_col( 2, temp_col );
+    temp_col.clear();
+
+    boundary_matrix.set_col( 3, temp_col );
+
+    temp_col.push_back( 1 );
+    temp_col.push_back( 3 );
+    boundary_matrix.set_col( 4, temp_col );
+    temp_col.clear();
+
+    temp_col.push_back( 0 );
+    temp_col.push_back( 3 );
+    boundary_matrix.set_col( 5, temp_col );
+    temp_col.clear();
+
+    temp_col.push_back( 2 );
+    temp_col.push_back( 4 );
+    temp_col.push_back( 5 );
+    boundary_matrix.set_col( 6, temp_col );
+    temp_col.clear();
+
+    // print some information of the boundary matrix:
+    std::cout << std::endl;
+    std::cout << "The boundary matrix has " << boundary_matrix.get_num_cols() << " columns: " << std::endl;
+    for( phat::index col_idx = 0; col_idx < boundary_matrix.get_num_cols(); col_idx++ ) {
+        std::cout << "Colum " << col_idx << " represents a cell of dimension " << (int)boundary_matrix.get_dim( col_idx ) << ". ";
+        if( !boundary_matrix.is_empty( col_idx ) ) {
+            std::vector< phat::index > temp_col;
+            boundary_matrix.get_col( col_idx, temp_col ); 
+            std::cout << "Its boundary consists of the cells";
+            for( phat::index idx = 0; idx < (phat::index)temp_col.size(); idx++ )
+                std::cout << " " << temp_col[ idx ];
+        }
+        std::cout << std::endl;
+    }
+    std::cout << "Overall, the boundary matrix has " << boundary_matrix.get_num_entries() << " entries." << std::endl;  
+    
+
+    // define the object to hold the resulting persistence pairs
+    phat::persistence_pairs pairs;
+
+    // choose an algorithm (choice affects performance) and compute the persistence pair
+    // (modifies boundary_matrix)
+    phat::compute_persistence_pairs< phat::twist_reduction >( pairs, boundary_matrix );
+    
+    // sort the persistence pairs by birth index 
+    pairs.sort();
+
+    // print the pairs:
+    std::cout << std::endl;
+    std::cout << "There are " << pairs.get_num_pairs() << " persistence pairs: " << std::endl;
+    for( phat::index idx = 0; idx < pairs.get_num_pairs(); idx++ )
+        std::cout << "Birth: " << pairs.get_pair( idx ).first << ", Death: " << pairs.get_pair( idx ).second << std::endl;
+}