Minimum Spanning Trees (MSTs)

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Presentation transcript:

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm Basic idea is: Start with a forest of n vertices and no edges. Add edges to the forest in non-decreasing order of weight. Only add an edge if it joins together two different sub-trees.

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 ? 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 5 3 ? 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 ? 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 b d e 2 4 ? 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 4 3 1 ? b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 ? 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g 3 ? 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c

Minimum Spanning Trees (MSTs) Kruskal’s Algorithm a g ? 3 4 3 1 b d e 2 4 5 3 2 f c