In that are you assuming that there will only be one area of specialization? - because we can't assume that.
No, he said it passes through all the points.
There are two situations where I believe the benefits of interpolation will outweight the cpu cost.
First one is of new to young nodes who have little to medium information about the rest of the network. If experimental data shows that the response times generally resemble a wave accross the key spectrum for those types of nodes, running FFT may yield _significantly_ better hit ratios. FFT gets very expensive when the number of reference points grows too much, but between 5 to 50 reference points its doable on current cpus. (not sure about those numbers, could be a lot more/less)
The second situation is that of well integrated nodes, most of whose reference points are clustered closely together, representing a specialization of sort. Suppose a request arrives that is close to the cluster, but outside of its farthest reference point. In this case, the values of the points in the cluster will affect the curve and it will be very different than a straight line from the outter reference point that is part of the cluster and the non-clustered outlier. This may seem like a cosmetic difference, but its really cheap computationally and could extend the "efficiency" part of the keyspace for the node (we won't be taking all reference points in account in this case, just 3 or 4).
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