MthSc 816 — Assignment #2 (Kruskal’s Algorithm)
Data Structures
from, to, cost: arrays for edge information O(3m)
heap: array of edge indices O(m)
pred, rank: node length arrays for union/find O(2n)
mst: indices of edges in MST [optional] O(n)
Space complexity is O(4m + 3n), if G has n nodes and m edges;
or O(4m + 2n), if don’t store the MST but print each edge as found.
Initialize using heap[k] = k; pred[j] = j, rank[j] = 0
Overall Design
readgraph O(m)
initialize O(n + m)
makeheap O(m)
while MSTedges < n – 1 (*)
edge = deletemin O(m d logd m)
root1 = findroot(from(edge)) O(mα)
root2 = findroot(to(edge)) O(mα)
if root1 ≠ root2
update mst, mincost, MSTedges O(n)
union(root1,root2) O(n)
output MST O(n)
[* Could also check that heapsize > 0, if G not connected.]
Time complexity is O(m d logd m), dominated by deletemin operation.
