FormationControlSimulation/SOURCE/networks-toolbox/findAllShortestPaths.m

50 lines
1.7 KiB
Matlab
Raw Normal View History

2019-06-17 14:31:50 +07:00
% 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);