57,662 research outputs found
Optimal Color Range Reporting in One Dimension
Color (or categorical) range reporting is a variant of the orthogonal range
reporting problem in which every point in the input is assigned a \emph{color}.
While the answer to an orthogonal point reporting query contains all points in
the query range , the answer to a color reporting query contains only
distinct colors of points in . In this paper we describe an O(N)-space data
structure that answers one-dimensional color reporting queries in optimal
time, where is the number of colors in the answer and is the
number of points in the data structure. Our result can be also dynamized and
extended to the external memory model
Towards Tight Lower Bounds for Range Reporting on the RAM
In the orthogonal range reporting problem, we are to preprocess a set of
points with integer coordinates on a grid. The goal is to support
reporting all points inside an axis-aligned query rectangle. This is one of
the most fundamental data structure problems in databases and computational
geometry. Despite the importance of the problem its complexity remains
unresolved in the word-RAM. On the upper bound side, three best tradeoffs
exists: (1.) Query time with words
of space for any constant . (2.) Query time with words of space. (3.) Query time
with optimal words of space. However, the
only known query time lower bound is , even for linear
space data structures.
All three current best upper bound tradeoffs are derived by reducing range
reporting to a ball-inheritance problem. Ball-inheritance is a problem that
essentially encapsulates all previous attempts at solving range reporting in
the word-RAM. In this paper we make progress towards closing the gap between
the upper and lower bounds for range reporting by proving cell probe lower
bounds for ball-inheritance. Our lower bounds are tight for a large range of
parameters, excluding any further progress for range reporting using the
ball-inheritance reduction
I/O-Efficient Planar Range Skyline and Attrition Priority Queues
In the planar range skyline reporting problem, we store a set P of n 2D
points in a structure such that, given a query rectangle Q = [a_1, a_2] x [b_1,
b_2], the maxima (a.k.a. skyline) of P \cap Q can be reported efficiently. The
query is 3-sided if an edge of Q is grounded, giving rise to two variants:
top-open (b_2 = \infty) and left-open (a_1 = -\infty) queries.
All our results are in external memory under the O(n/B) space budget, for
both the static and dynamic settings:
* For static P, we give structures that answer top-open queries in O(log_B n
+ k/B), O(loglog_B U + k/B), and O(1 + k/B) I/Os when the universe is R^2, a U
x U grid, and a rank space grid [O(n)]^2, respectively (where k is the number
of reported points). The query complexity is optimal in all cases.
* We show that the left-open case is harder, such that any linear-size
structure must incur \Omega((n/B)^e + k/B) I/Os for a query. We show that this
case is as difficult as the general 4-sided queries, for which we give a static
structure with the optimal query cost O((n/B)^e + k/B).
* We give a dynamic structure that supports top-open queries in O(log_2B^e
(n/B) + k/B^1-e) I/Os, and updates in O(log_2B^e (n/B)) I/Os, for any e
satisfying 0 \le e \le 1. This leads to a dynamic structure for 4-sided queries
with optimal query cost O((n/B)^e + k/B), and amortized update cost O(log
(n/B)).
As a contribution of independent interest, we propose an I/O-efficient
version of the fundamental structure priority queue with attrition (PQA). Our
PQA supports FindMin, DeleteMin, and InsertAndAttrite all in O(1) worst case
I/Os, and O(1/B) amortized I/Os per operation.
We also add the new CatenateAndAttrite operation that catenates two PQAs in
O(1) worst case and O(1/B) amortized I/Os. This operation is a non-trivial
extension to the classic PQA of Sundar, even in internal memory.Comment: Appeared at PODS 2013, New York, 19 pages, 10 figures. arXiv admin
note: text overlap with arXiv:1208.4511, arXiv:1207.234
The Hosting Environment of the Advanced Resource Connector middleware
The central component of AR
Empirical Evaluation of the Parallel Distribution Sweeping Framework on Multicore Architectures
In this paper, we perform an empirical evaluation of the Parallel External
Memory (PEM) model in the context of geometric problems. In particular, we
implement the parallel distribution sweeping framework of Ajwani, Sitchinava
and Zeh to solve batched 1-dimensional stabbing max problem. While modern
processors consist of sophisticated memory systems (multiple levels of caches,
set associativity, TLB, prefetching), we empirically show that algorithms
designed in simple models, that focus on minimizing the I/O transfers between
shared memory and single level cache, can lead to efficient software on current
multicore architectures. Our implementation exhibits significantly fewer
accesses to slow DRAM and, therefore, outperforms traditional approaches based
on plane sweep and two-way divide and conquer.Comment: Longer version of ESA'13 pape
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