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arXiv · 1309.0647

Unidirectional Input/Output Streaming Complexity of Reversal and Sorting

Nathanaël François·Rahul Jain·Frederic Magniez
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Abstract

We consider unidirectional data streams with restricted access, such as read-only and write-only streams. For read-write streams, we also introduce a new complexity measure called expansion, the ratio between the space used on the stream and the input size. We give tight bounds for the complexity of reversing a stream of length $n$ in several of the possible models. In the read-only and write-only model, we show that $p$-pass algorithms need memory space $Θ(n/p)$. But if either the output stream or the input stream is read-write, then the complexity falls to $Θ(n/p^2)$. It becomes $polylog(n)$ if $p = O(log n)$ and both streams are read-write. We also study the complexity of sorting a stream and give two algorithms with small expansion. Our main sorting algorithm is randomized and has $O(1)$ expansion, $O(log n)$ passes and $O(log n)$ memory.

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Nathanaël François, Rahul Jain, Frederic Magniez. 2014-07-18. Unidirectional Input/Output Streaming Complexity of Reversal and Sorting. https://arxiv.org/abs/1309.0647

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