Input/Output Streaming Complexity of Reversal and Sorting

This work revisits the study of streaming algorithms where both input and output are data streams. While streaming algorithms with multiple streams have been studied before, such as in the context of sorting, most assumed very nonrestrictive models and thus had weak lower bounds. We consider data streams with restricted access, such as read-only and write-only streams, as opposed to read-write streams. We also require streams to be processed in one direction only when multiple passes are allowed. Last, we forbid the use of any other external streams. Reversing a stream has been demonstrated to allow exponential speed-up for several decision problems. Therefore, it naturally arises as the bottleneck problem of our model. We give several tight bounds for reversing the input stream depending on the model. We also study the problem of sorting, and improve previously known algorithms in terms of space used on the two streams. ∗Partially supported by the French ANR Blanc project ANR-12-BS02-005 (RDAM) †[email protected] ‡[email protected]