1 research outputs found
Tight Static Lower Bounds for Non-Adaptive Data Structures
In this paper, we study the static cell probe complexity of non-adaptive data
structures that maintain a subset of points from a universe consisting of
points. A data structure is defined to be non-adaptive when
the memory locations that are chosen to be accessed during a query depend only
on the query inputs and not on the contents of memory. We prove an static cell probe complexity lower bound for
non-adaptive data structures that solve the fundamental dictionary problem
where denotes the space of the data structure in the number of cells and
is the cell size in bits. Our lower bounds hold for all word sizes
including the bit probe model () and are matched by the upper bounds of
Boninger et al. [FSTTCS'17].
Our results imply a sharp dichotomy between dictionary data structures with
one round of adaptive and at least two rounds of adaptivity. We show that
, or , overhead dictionary constructions are
only achievable with at least two rounds of adaptivity. In particular, we show
that many dictionary constructions with two rounds of adaptivity such as
cuckoo hashing are optimal in terms of adaptivity. On the other hand,
non-adaptive dictionaries must use significantly more overhead.
Finally, our results also imply static lower bounds for the non-adaptive
predecessor problem. Our static lower bounds peak higher than the previous,
best known lower bounds of for the dynamic
predecessor problem by Boninger et al. [FSTTCS'17] and Ramamoorthy and Rao
[CCC'18] in the natural setting of linear space where each
point can fit in a single cell . Furthermore, our results
are stronger as they apply to the static setting unlike the previous lower
bounds that only applied in the dynamic setting.Comment: 15 page