50 lines
1.7 KiB
Matlab
50 lines
1.7 KiB
Matlab
|
% Return all shortest paths from a start to an end node, given a graph.
|
||
|
|
%
|
||
|
|
% INPUTS: adjacency list, adjL (1xn), start node "s" (index between 1 and n),
|
||
|
|
% end node "t" (index between 1 and n)
|
||
|
|
% upperBound: max path length allowed in the search; best
|
||
|
|
% to set this to the graph diameter; if many shortest paths
|
||
|
|
% are sought at the same time, or the graph is very dense,
|
||
|
|
% upperBound can be set to the length of one pre-computed
|
||
|
|
% shortest path, using simpleDijkstra.m for example.
|
||
|
|
% OUTPUTS: list of all shortest paths between "s" and "t"
|
||
|
|
%
|
||
|
|
% Note 1: Works for a un/directed, unweighted graph.
|
||
|
|
% Note 2: This function uses recursion. It can be quite slow for
|
||
|
|
% dense graphs.
|
||
|
|
% Other routines used: findAllShortestPaths.m
|
||
|
|
% GB: last updated, July 15, 2015
|
||
|
|
|
||
|
|
function [allPaths, upperBound] = findAllShortestPaths(adjL,s,t,upperBound, allPaths={}, path = [])
|
||
|
|
|
||
|
|
|
||
|
|
path = [path s]; % add "s" to path
|
||
|
|
|
||
|
|
if s == t
|
||
|
|
if length(path)-1<=upperBound
|
||
|
|
upperBound = length(path)-1;
|
||
|
|
pathstr = '';
|
||
|
|
for i=1:length(path); pathstr = strcat(pathstr,'-',num2str(path(i))); end
|
||
|
|
allPaths{length(allPaths) + 1} = pathstr;
|
||
|
|
end
|
||
|
|
else
|
||
|
|
if length(path)-1<=upperBound
|
||
|
|
for node=1:length(adjL{s})
|
||
|
|
node = adjL{s}(node);
|
||
|
|
if length(find(node==path))==0 % avoid cycles
|
||
|
|
[allPaths,upperBound] = findAllShortestPaths(adjL, node, t, upperBound, allPaths, path);
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
|
||
|
|
path2remove = {};
|
||
|
|
for i=1:length(allPaths)
|
||
|
|
pathstr = allPaths{i};
|
||
|
|
if length(strsplit(pathstr,'-'))-2>upperBound
|
||
|
|
path2remove{length(path2remove)+1} = pathstr;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
allPaths = setdiff(allPaths,path2remove);
|