The Repetitive Nearest Neighbour Algorithm (RNNA) is a refinement of the Nearest Neighbour Algorithm. It uses the same greedy strategy of going to the nearest unvisited neighbour at each step, but instead of constructing just one tour, the RNNA constructs a tour starting from every vertex of the graph, and then selects the one with the lowest total length to return as the solution.

Here is the implementation in C:

#include <stdlib.h> typedef struct { unsigned int first; unsigned int second; unsigned int weight; } weighted_edge; /* Check if the tour already contains an edge */ static unsigned int tour_contains(const weighted_edge *tour, unsigned int t, const weighted_edge *edge) { unsigned int contains = 0; unsigned int i; for (i = 0; i < t && !contains; i++) { contains = tour[i].first == edge->first && tour[i].second == edge->second; } return contains; } /* Find the edge to v's nearest neighbour not in the tour already */ static unsigned int nearest_neighbour_edge(const weighted_edge *edges, unsigned int size, const weighted_edge *tour, unsigned int t, unsigned int v) { unsigned int min_distance = 0; unsigned int nearest_neighbour; unsigned int i; for (i = 0; i < size; i++) { if ((edges[i].first == v || edges[i].second == v) && (min_distance == 0 || edges[i].weight < min_distance) && !tour_contains(tour, t, &edges[i])) { min_distance = edges[i].weight; nearest_neighbour = i; } } return nearest_neighbour; } weighted_edge *repetitive_nearest_neighbour_tsp(const weighted_edge *edges, unsigned int size, unsigned int order) { unsigned int best_tour_distance = 0; weighted_edge *best_tour = NULL; unsigned int v; for (v = 0; v < order; v++) { unsigned int t; unsigned int distance = 0; weighted_edge *tour = malloc(order * sizeof(weighted_edge)); if (tour == NULL) { return NULL; } for (t = 0; t < order; t++) { unsigned int e = nearest_neighbour_edge(edges, size, tour, t, v); tour[t] = edges[e]; distance += edges[e].weight; v = edges[e].first == v ? edges[e].second : edges[e].first; } if (best_tour_distance == 0 || distance < best_tour_distance) { best_tour_distance = distance; free(best_tour); best_tour = tour; } else { free(tour); } } return best_tour; }

Here is an example program in C using the same graph as I used for the Nearest Neighbour and Cheapest-Link algorithms:

#include <stdio.h> #include <stdlib.h> void weighted_edge_connect(weighted_edge *edges, unsigned int first, unsigned int second, unsigned int weight, unsigned int *pos) { edges[*pos].first = first; edges[*pos].second = second; edges[*pos].weight = weight; (*pos)++; } void print_edges(const weighted_edge *edges, unsigned int n) { unsigned int e; for (e = 0; e < n; e++) { printf("(%u, %u, %u) ", edges[e].first, edges[e].second, edges[e].weight); } putchar('\n'); } int main(void) { unsigned int i = 0; const unsigned int size = 15; /* Edges */ const unsigned int order = 6; /* Vertices */ weighted_edge *edges = malloc(size * sizeof(weighted_edge)); weighted_edge *tour; weighted_edge_connect(edges, 0, 1, 25, &i); weighted_edge_connect(edges, 0, 2, 19, &i); weighted_edge_connect(edges, 0, 3, 19, &i); weighted_edge_connect(edges, 0, 4, 16, &i); weighted_edge_connect(edges, 0, 5, 28, &i); weighted_edge_connect(edges, 1, 2, 24, &i); weighted_edge_connect(edges, 1, 3, 30, &i); weighted_edge_connect(edges, 1, 4, 27, &i); weighted_edge_connect(edges, 1, 5, 17, &i); weighted_edge_connect(edges, 2, 3, 18, &i); weighted_edge_connect(edges, 2, 4, 20, &i); weighted_edge_connect(edges, 2, 5, 23, &i); weighted_edge_connect(edges, 3, 4, 19, &i); weighted_edge_connect(edges, 3, 5, 32, &i); weighted_edge_connect(edges, 4, 5, 41, &i); tour = repetitive_nearest_neighbour_tsp(edges, size, order); print_edges(tour, order); free(tour); free(edges); return 0; }

Here is the output:

(2, 3, 18) (0, 3, 19) (0, 4, 16) (3, 4, 19) (1, 3, 30) (1, 5, 17)