## Setup

To begin, we load a graph.

```
load ../graphs/clr-25-2.mat
```

Next, let's check the documentation to see which functions to implement for the visitor

```
help dijkstra_sp
```

DIJKSTRA_SP Compute the weighted single source shortest path problem. Dijkstra's algorithm for the single source shortest path problem only works on graphs without negative edge weights. This method works on weighted directed graphs without negative edge weights. The runtime is O(V log (V)). See the shortest_paths function for calling information. This function just calls shortest_paths(...,struct('algname','dijkstra')); The options structure can contain a visitor for the Dijkstra algorithm. See http://www.boost.org/libs/graph/doc/DijkstraVisitor.html for a description of the events. visitor is a struct with the following optional fields vis.initialize_vertex(u) vis.discover_vertex(u) vis.examine_vertex(u) vis.examine_edge(ei,u,v) vis.edge_relaxed(ei,u,v) vis.edge_not_relaxed(ei,u,v) vis.finish_vertex(u) Each visitor parameter should be a function pointer, which returns 0 if the shortest path search should stop. (If the function does not return anything, the algorithm continues.) Example: load graphs/clr-25-2.mat dijkstra_sp(A,1) See also SHORTEST_PATHS, BELLMAN_FORD_SP.

The help states that dijkstra_sp allows visitors functions for initialize_vertex, discover_vertex, examine_vertex, examine_edge, edge_relaxed, edge_not_relaxed, and finish_vertex.

Rather than implementing 7 functions ourselves, we define two helper functions. These helper functions return functions themselves. There is one helper that returns a vertex visitor function and one helper than returns an edge visitor function.

vertex_vis_print_func = @(str) @(u) ... fprintf('%s called on %s\n', str, char(labels{u})); edge_vis_print_func = @(str) @(ei,u,v) ... fprintf('%s called on (%s,%s)\n', str, char(labels{u}), char(labels{v}));

These anonymous functions return functions themselves.

```
ev_func = vertex_vis_print_func('examine_vertex');
ev_func(1)
```

examine_vertex called on s

I hope you see how these functions are useful in saving quite a bit of typing.

## Calling dijkstra_sp

We are almost done. Now, we just have to setup the visitor structure to pass to the dijkstra_sp call.

vis = struct(); vis.initialize_vertex = vertex_vis_print_func('initialize_vertex'); vis.discover_vertex = vertex_vis_print_func('discover_vertex'); vis.examine_vertex = vertex_vis_print_func('examine_vertex'); vis.finish_vertex = vertex_vis_print_func('finish_vertex'); vis.examine_edge = edge_vis_print_func('examine_edge'); vis.edge_relaxed = edge_vis_print_func('edge_relaxed'); vis.edge_not_relaxed = edge_vis_print_func('edge_not_relaxed');

With the visitor setup, there is hardly any work left.

```
dijkstra_sp(A,1,struct('visitor', vis));
```

initialize_vertex called on s initialize_vertex called on u initialize_vertex called on x initialize_vertex called on v initialize_vertex called on y discover_vertex called on s examine_vertex called on s examine_edge called on (s,u) edge_relaxed called on (s,u) discover_vertex called on u examine_edge called on (s,x) edge_relaxed called on (s,x) discover_vertex called on x finish_vertex called on s examine_vertex called on u examine_edge called on (u,x) edge_not_relaxed called on (u,x) examine_edge called on (u,v) edge_relaxed called on (u,v) discover_vertex called on v finish_vertex called on u examine_vertex called on x examine_edge called on (x,u) examine_edge called on (x,v) edge_not_relaxed called on (x,v) examine_edge called on (x,y) edge_relaxed called on (x,y) discover_vertex called on y finish_vertex called on x examine_vertex called on v examine_edge called on (v,y) edge_not_relaxed called on (v,y) finish_vertex called on v examine_vertex called on y examine_edge called on (y,s) examine_edge called on (y,v) finish_vertex called on y

## Understanding the output

To understand the output, we find it helpful to have a copy of Introduction to Algorithms by Cormen, Leiserson, and Rivest. The source for the graph is Figure 25-2 in that book and the authors use the graph to illustrate how Dijkstra's algorithm runs. In particular, Figure 25-5 shows a sample run of Dijkstra's algorithm.

Perhaps the first thing to notice is that the initialize vertex visitor is never called. This results from an error in the MatlabBGL and Boost documentation. Once it is resolved, we will update the MatlabBGL documentation to match the Boost graph library.

The results: discover_vertex is called before examine_vertex. For the edges, examine_edge is always called before either edge_relaxed or edge_not_relaxed. The edges that are relaxed are the shaded edges in Figure 25-5.

Finally, finish vertex is called on a vertex after all of its edges have been examined and possibly relaxed.