53 lines
1.7 KiB
R
53 lines
1.7 KiB
R
minimum_spanning_tree <- function(C1, C2) {
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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) {
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C2 <- zeros(n)
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}
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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 in 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 in 1:length(NU)) {
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for (j in 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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}
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}
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}
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}
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return(A)
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}
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