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

TL;DR

This paper introduces new Turing machine models with external memory to analyze input/output complexity, exploring its relationship with other complexities and defining external access trace complexity for IO-efficient algorithms.

Contribution

It proposes three variants of Turing machines with external memory, providing a new computation model perspective on input/output complexity and its relation to other complexity measures.

Findings

Established relationships between I/O complexity and time/parameterized complexity.

Defined external access trace complexity to reflect physical disk behavior.

Provided theoretical foundations for IO-efficient algorithms.

Abstract

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