9,531 research outputs found
Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds
This paper proves the first super-logarithmic lower bounds on the cell probe
complexity of dynamic boolean (a.k.a. decision) data structure problems, a
long-standing milestone in data structure lower bounds.
We introduce a new method for proving dynamic cell probe lower bounds and use
it to prove a lower bound on the operational
time of a wide range of boolean data structure problems, most notably, on the
query time of dynamic range counting over ([Pat07]). Proving an
lower bound for this problem was explicitly posed as one of
five important open problems in the late Mihai P\v{a}tra\c{s}cu's obituary
[Tho13]. This result also implies the first lower bound for the
classical 2D range counting problem, one of the most fundamental data structure
problems in computational geometry and spatial databases. We derive similar
lower bounds for boolean versions of dynamic polynomial evaluation and 2D
rectangle stabbing, and for the (non-boolean) problems of range selection and
range median.
Our technical centerpiece is a new way of "weakly" simulating dynamic data
structures using efficient one-way communication protocols with small advantage
over random guessing. This simulation involves a surprising excursion to
low-degree (Chebychev) polynomials which may be of independent interest, and
offers an entirely new algorithmic angle on the "cell sampling" method of
Panigrahy et al. [PTW10]
Parallel Batch-Dynamic Graph Connectivity
In this paper, we study batch parallel algorithms for the dynamic
connectivity problem, a fundamental problem that has received considerable
attention in the sequential setting. The most well known sequential algorithm
for dynamic connectivity is the elegant level-set algorithm of Holm, de
Lichtenberg and Thorup (HDT), which achieves amortized time per
edge insertion or deletion, and time per query. We
design a parallel batch-dynamic connectivity algorithm that is work-efficient
with respect to the HDT algorithm for small batch sizes, and is asymptotically
faster when the average batch size is sufficiently large. Given a sequence of
batched updates, where is the average batch size of all deletions, our
algorithm achieves expected amortized work per
edge insertion and deletion and depth w.h.p. Our algorithm
answers a batch of connectivity queries in expected
work and depth w.h.p. To the best of our knowledge, our algorithm
is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium
on Parallelism in Algorithms and Architectures (SPAA), 201
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