The asymptotic evolution of data structures
The evolution of certain pointer-based implementations of dictionaries, linear lists and priority queues is studied. Under the assumption of equiprobability of histories, i.e., of paths through the internal state space of the implementation, the n → ∞ asymptotics of the space and time costs of a sequence of n supported operations are computed.
For list implementations the mean integrated spatial cost is asymptotically proportional to n2, and its standard deviation to n3/2. For d-heap implementations of priority queues the mean integrated space cost grows only as n2/√log n, i.e. more slowly than the worst-case integrated cost. The standard deviation grows as n3/2.
These asymptotics reflect the convergence as n → ∞ of the normalized structure sizes to datatype-dependent deterministic functions of time, as earlier discovered by Louchard. This phenomenon is clarified with the aid of large deviation theory, and path integral techniques.
Keywordsdynamic data structures expected costs stochastic modelling large deviations
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