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