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Note that mostly Ck[1,n] =
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C[1,k]+C[k,n]+D[1,k]+D[k,n]
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But
what about when k = 2?
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D[1,2]
appears in the
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formula,
but its not part of
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the
triangulation
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Trick:
Define C[1,2] = -D[1,2]
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In
general: C[i,i+1] = -D[i,i+1]
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Terms
cancel to provide
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correct
result
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With
this trick, formula
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above
holds for all k
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Note
that
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C[i,j]
= mink Ck[i,j]
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Agorithmic
idea:
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Determine
C[i,j] for all i and j
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Final
result is held in C[1,n]
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What
order should we use to
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fill
in C[i,j]?
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3
adjacent vertices, then
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4
adjacent vertices, then
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5
adjacent vertices, then...
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