51 lines
1.7 KiB
R
51 lines
1.7 KiB
R
minimum_spanning_tree <- function(C1, C2) stop("needs translation")
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# function A = minimum_spanning_tree(C1, C2)
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# %
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# % Find the minimum spanning tree using Prim's algorithm.
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# % C1(i,j) is the primary cost of connecting i to j.
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# % C2(i,j) is the (optional) secondary cost of connecting i to j, used to break ties.
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# % We assume that absent edges have 0 cost.
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# % To find the maximum spanning tree, used -1*C.
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# % See Aho, Hopcroft & Ullman 1983, "Data structures and algorithms", p 237.
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# % Prim's is O(V^2). Kruskal's algorithm is O(E log E) and hence is more efficient
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# % for sparse graphs, but is implemented in terms of a priority queue.
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# % We partition the nodes into those in U and those not in U.
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# % closest(i) is the vertex in U that is closest to i in V-U.
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# % lowcost(i) is the cost of the edge (i, closest(i)), or infinity is i has been used.
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# % In Aho, they say C(i,j) should be "some appropriate large value" if the edge is missing.
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# % We set it to infinity.
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# % However, since lowcost is initialized from C, we must distinguish absent edges from used nodes.
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# n = length(C1);
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# if nargin==1, C2 = zeros(n); end
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# A = zeros(n);
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# closest = ones(1,n);
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# used = zeros(1,n); % contains the members of U
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# used(1) = 1; % start with node 1
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# C1(find(C1==0))=inf;
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# C2(find(C2==0))=inf;
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# lowcost1 = C1(1,:);
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# lowcost2 = C2(1,:);
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# for i=2:n
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# ks = find(lowcost1==min(lowcost1));
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# k = ks(argmin(lowcost2(ks)));
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# A(k, closest(k)) = 1;
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# A(closest(k), k) = 1;
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# lowcost1(k) = inf;
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# lowcost2(k) = inf;
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# used(k) = 1;
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# NU = find(used==0);
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# for ji=1:length(NU)
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# for j=NU(ji)
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# if C1(k,j) < lowcost1(j)
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# lowcost1(j) = C1(k,j);
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# lowcost2(j) = C2(k,j);
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# closest(j) = k;
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# end
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# end
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# end
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# end
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