this is for holding javascript data
Xavier Holt edited CST_Monopolar_Consider_every_point__1.md
almost 8 years ago
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* \(L_r \leftarrow |i,p|\); \(L_p \leftarrow p\)
* d \(\leftarrow \min \{d, R_r + L_r\}\)
* Return d + |i,j|
Correctedness (of the sub-routine) follows from above -- we consider all radii which could potentially be diameter-defining, and simply return the minimum of all of these. Runtime is \(O(n)\)
### Main Algorithm
* For all points i:
* \(P_s \leftarrow\) `P-{i}` sorted in increasing distance WRT `i`: \(O(n \log n)\)
* For all points j:
* Remove `j` from \(P_s\): O(n)
* \(d = \min\{ d, \text{diameter}(i,j,P_s) \}\)