| Closest Pair £ EMST |
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| Claim:
Closest Pair £ EMST |
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| Proof: |
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| • | Given the set of
input points, form the EMST |
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| • | We know the EMST
is the MST of the compete graph |
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| on the set of
input points and we know from Kruskal’s |
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| Algorithm that
the shortest edge in the graph is a |
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| member of the MST |
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| • | Thus we can check
each edge of the EMST to find |
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| the shortest;
this will tell us the closest pair |
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| Conclusion:
EMST requires W(n log n) time |
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| CS409 - Spring
2000 |
| 8 |