$30.00

## Description

1 Introduction

The Hamiltonian Path Problem is a classic computer science problem: Given a graph and two vertices i and j, determine whether there is a path from i to j in the graph that visits each vertex in the graph exactly once. Now, this problem is well–known to be NP–complete.

I have written a solution to this problem (Hamiltonian_Path.cc) that uses the

next_permutation function in C++ to generate all of the permutations (tours) of the ver– tices that start at vertex i and end in vertex j. This program will find a Hamiltonian Path, if it exists. Otheriwse, it will say that no such path exists. However, this program is painfully slow. On a small graph (small_graph.dat) with 5 vertices, it finds the the tour 2 0 1 3 4 from 2 to 4 in much less than a second. But, on a bigger graph (big.dat) with 13 vertices, it takes over one minute to find a solution. On bigger graphs (bigger.dat and biggest.dat), it takes much longer to solve.

For example, on input

5 |
2 |
4 |
||

0 |
: |
1 |
2 |
4 |

1 |
: |
0 |
2 |
3 4 |

2 |
: |
0 |
1 |
3 |

3 |
: |
1 |
2 |
4 |

4 |
: |
0 |
1 |
3 |

The output of the program should be “Tour = 2 0 1 3 4”.

Your task is to make this code faster using parallel computing. Modify Hamiltonian_Path.cc using OpenMP so that

1. Your modified program still produces the correct results, and

2. It is at least 75% efficient on bigger.dat on a machine with 4 cores/processors.