An extrapolation on the interpolation search
Some new improvements on the Interpolation search are presented. They yield an average-case performance within an additive constant from optimal for uniformly distributed elements. The method is much less sensitive to non-uniform distributions than Interpolation search, and will have almost O(lg lgn) behavior for many distributions. Simulation results show, for example, that an element in a table of 30000 exponentially distributed elements can be found in less than 10 accesses on the average, without using any knowledge of the distribution.
There are two basic ideas that accomplish this improvement. One is to allow extrapolation over small intervals, and the other is to use the least-square method to approximate the first probe position in the table.
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