This book forms the much needed strong interface between
algorithmic complexity and computer experiments using a careful
blending of traditional ideas in algorithms with untraditional
research in computer experiments (esp. fitting stochastic models to
non-random data). While establishing the aforesaid interface, the
important role of statistical bounds and their empirical estimates
obtained over a finite range (called empirical O) is discovered as
a bonus. While these bounds are very valuable for the average case,
our research suggests in addition that there is no need to be
over-conservative in the worst case just as the statistical bounds
safeguard against making tall optimistic claims for the best cases.
In short the statistical bounds have a sense of "calculated
guarantee" that is neither too risky nor too conservative. In
parallel computing, with every change of the processor, it can be
argued that it is the weight of the operation that changes. Hence,
if the bound is itself based on weights, it should be deemed as the
ideal one.
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