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The input/output complexity, which is the complexity of data exchange betweenthe main memory and the external memory, has been elaborately studied by a lotof former researchers. However, the existing works failed to consider theinput/output complexity in a computation model point of view. In this paper weremedy this by proposing three variants of Turing machine that include externalmemory and the mechanism of exchanging data between main memory and externalmemory. Based on these new models, the input/output complexity is deeplystudied. We discussed the relationship between input/output complexity and theother complexity measures such as time complexity and parameterized complexity,which is not considered by former researchers. We also define the externalaccess trace complexity, which reflects the physical behavior of magnetic disksand gives a theoretical evidence of IO-efficient algorithms.

Turing Machines with Two-level Memory: A Deep Look into the Input/Output Complexity