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TR17-050 | 15th March 2017 20:15

#### Non-Adaptive Data Structure Bounds for Dynamic Predecessor Search

TR17-050
Authors: Joe Boninger, Joshua Brody, Owen Kephart
Publication: 16th March 2017 06:27
Downloads: 314
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Abstract:

In this work, we continue the examination of the role non-adaptivity} plays in maintaining dynamic data structures, initiated by Brody and Larsen [BL15].. We consider nonadaptive data structures for predecessor search in the w-bit cell probe model. Predecessor search is one of the most well-studied data structure problems. For this problem, using non-adaptivity comes at a steep price. We provide exponential cell probe complexity separations between (i) adaptive and non-adaptive data structures and (ii) non-adaptive and memoryless data structures for predecessor search.

A classic data structure of van Emde Boas [vEB75] solves dynamic predecessor search in $O(\log \log m)$ probes; this data structure is adaptive. For dynamic data structures which make nonadaptive updates, we show the cell probe complexity is $O\left(\min\{\frac{\log m}{\log(w/\log m)}, \frac{n\log m}{w}\}\right)$. We also give a nearly-matching $\Omega\left(\min\{\frac{\log m}{\log w}, \frac{n \log m}{w \log w}\}\right)$ lower bound. We also give an $\Omega(m)$ lower bound for memoryless data structures.
Our lower bound technique is tailored to nonadaptive (as opposed to memoryless) updates and should be of independent interest.

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