[10] | 1 | %DSPATH Single Shortest Path in a (Dissimilarity) Graph
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| 2 | %
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| 3 | % [D,P] = DSPATH (A,i,j)
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| 4 | %
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| 5 | % INPUT
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| 6 | % A NxN Weight / dissimilarity matrix or dataset
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| 7 | % i,j Vertices for which the shortest path should be found
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| 8 | %
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| 9 | % OUTPUT
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| 10 | % D Distance of the shortest path
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| 11 | % P List of edges of the shortest path
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| 12 | %
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| 13 | % DESCRIPTION
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| 14 | % Determines the shortest path between two vertices i and j. The Dijkstra's
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| 15 | % algorithm is used. Currently, it is not optimized fro speed in Matlab.
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| 16 | % A is a NxN matrix of weights (or a distance matrix) representing a graph
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| 17 | % G(V,E). V is a set of vertices, |V| = N, and E is a set of edges. If there
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| 18 | % is no edge between i and j then A(i,j) = INF. Use DSPATHS(A,'F') if all
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| 19 | % shortest paths should be computed.
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| 20 | %
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| 21 | % SEE ALSO
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| 22 | % DSPATHS
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| 23 | %
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| 24 | % LITERATURE
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| 25 | % Any book on graph algorithms or basic algorithms in computer science.
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| 26 |
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| 27 | % Elzbieta Pekalska, ela.pekalska@googlemail.com
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| 28 | % Faculty of EWI, Delft University of Technology, The Netherlands and
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| 29 | % School of Computer Science, University of Manchester
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| 30 |
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| 31 |
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| 32 | function [d, pt] = dspath(A,s,t)
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| 33 |
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| 34 | A = +A;
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| 35 | [n,m] = size(A);
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| 36 |
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| 37 | I = (1:n);
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| 38 | dmin(I) = 1e10;
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| 39 | final(I) = 0;
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| 40 | pred(I) = -1;
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| 41 |
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| 42 |
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| 43 | I(s) = [];
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| 44 | dmin(s) = 0;
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| 45 | final(s) = 1;
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| 46 | last = s;
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| 47 |
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| 48 | while ~final(t)
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| 49 | dminnew = dmin(last) + A(last,I);
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| 50 | Z = find(dminnew < dmin(I));
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| 51 | dmin(I(Z)) = dminnew(Z);
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| 52 | pred(I(Z)) = last;
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| 53 | [ss,last] = min(dmin(I));
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| 54 | last = I(last);
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| 55 | final(last) = 1;
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| 56 | I = setdiff(I,last);
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| 57 | end
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| 58 |
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| 59 | if nargout > 1,
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| 60 | if pred(t) ~= -1 % there is a path
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| 61 | k = t;
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| 62 | pt = t;
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| 63 | while k ~= s,
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| 64 | pt = [pred(k) pt];
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| 65 | k = pred(k);
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| 66 | end
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| 67 | else
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| 68 | pt = [];
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| 69 | end
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| 70 | end
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| 71 |
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| 72 | d = dmin(t);
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| 73 | return;
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