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Minimum Spanning Tree - Algorithm

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose a weighted connected graph G = (V,E) has n edges.
    Describe an algorithm to find a Minimum Spanning Tree of G in O(n) time. Prove the correctness of your answer. (Here n = |V |).


    2. Relevant equations
    I know about DFS, BFS, Prims algorithm


    3. The attempt at a solution
    I was thinking of running something similar to Breadth first search (BFS).
    Keep track of edges part of MST (call it EMST), and vertices part of MST (call it VMST)
    --
    -select a vertex
    -look at all adjacent edges and find the one with minimum weight (by keeping a variable 'min' and updating it as we loop)
    -put the min edge in EMST, so we don't look at it again
    -put the current vertex and the other vertex connected by the edge both in VMST
    -then for all vertices in VMST repeat the procedure (so look at all of their vertices and find min to add to the VMST)
    --

    I'm not sure if this procedure is O(n), i'm afraid it might be slower, but I can't think of a way to improve it. I'm also a bit unsure how to take advantage of n=|V|
     
  2. jcsd
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