36,940 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
Differences in health symptoms among residents living near illegal dump sites in Los Laureles Canyon, Tijuana, Mexico: a cross sectional survey.
Living near landfills is a known health hazard prompting recognition of environmental injustice. The study aim was to compare self-reported symptoms of ill health among residents of four neighborhoods, living in haphazardly constructed settlements surrounded by illegal dumpsites in Tijuana, Mexico. One adult from each of 388 households located in Los Laureles Canyon were interviewed about demographics, health status, and symptoms. Distance from each residence to both the nearest dumpsite and the canyon bottom was assessed. The neighborhoods were selected from locations within the canyon, and varied with respect to proximity to dump sites. Residents of San Bernardo reported significantly higher frequencies of ill-health symptoms than the other neighborhoods, including extreme fatigue (OR 3.01 (95% CI 1.6-5.5)), skin problems/irritations (OR 2.73 (95% CI 1.3-5.9)), stomach discomfort (OR 2.47 (1.3-4.8)), eye irritation/tears (OR 2.02 (1.2-3.6)), and confusion/difficulty concentrating (OR 2.39 (1.2-4.8)). Proximity to dumpsites did not explain these results, that varied only slightly when adjusted for distance to nearest dumpsite or distance to the canyon bottom. Because San Bernardo has no paved roads, we hypothesize that dust and the toxicants it carries is a possible explanation for this difference. Studies are needed to further document this association and sources of toxicants
Connectivity Oracles for Graphs Subject to Vertex Failures
We introduce new data structures for answering connectivity queries in graphs
subject to batched vertex failures. A deterministic structure processes a batch
of failed vertices in time and thereafter
answers connectivity queries in time. It occupies space . We develop a randomized Monte Carlo version of our data structure
with update time , query time , and space
for any failure bound . This is the first connectivity oracle for
general graphs that can efficiently deal with an unbounded number of vertex
failures.
We also develop a more efficient Monte Carlo edge-failure connectivity
oracle. Using space , edge failures are processed in time and thereafter, connectivity queries are answered in
time, which are correct w.h.p.
Our data structures are based on a new decomposition theorem for an
undirected graph , which is of independent interest. It states that
for any terminal set we can remove a set of
vertices such that the remaining graph contains a Steiner forest for with
maximum degree
Categorical Range Reporting with Frequencies
In this paper, we consider a variant of the color range reporting problem called color reporting with frequencies. Our goal is to pre-process a set of colored points into a data structure, so that given a query range Q, we can report all colors that appear in Q, along with their respective frequencies. In other words, for each reported color, we also output the number of times it occurs in Q. We describe an external-memory data structure that uses O(N(1+log^2D/log N)) words and answers one-dimensional queries in O(1 +K/B) I/Os, where N is the total number of points in the data structure, D is the total number of colors in the data structure, K is the number of reported colors, and B is the block size.
Next we turn to an approximate version of this problem: report all colors sigma that appear in the query range; for every reported color, we provide a constant-factor approximation on its frequency. We consider color reporting with approximate frequencies in two dimensions. Our data structure uses O(N) space and answers two-dimensional queries in O(log_B N +log^*B + K/B) I/Os in the special case when the query range is bounded on two sides. As a corollary, we can also answer one-dimensional approximate queries within the same time and space bounds
Funding Student Learning: How to Align Education Resources With Student Learning Goals
Identifies factors preventing the education finance system from supporting high-level student learning. Recommends transparent, flexible, and strategic funding mechanisms and practices, including student-based funding and school-linked accounts
On Optimal Top-K String Retrieval
Let = be a given set of
(string) documents of total length . The top- document retrieval problem
is to index such that when a pattern of length , and a
parameter come as a query, the index returns the most relevant
documents to the pattern . Hon et. al. \cite{HSV09} gave the first linear
space framework to solve this problem in time. This was
improved by Navarro and Nekrich \cite{NN12} to . These results are
powerful enough to support arbitrary relevance functions like frequency,
proximity, PageRank, etc. In many applications like desktop or email search,
the data resides on disk and hence disk-bound indexes are needed. Despite of
continued progress on this problem in terms of theoretical, practical and
compression aspects, any non-trivial bounds in external memory model have so
far been elusive. Internal memory (or RAM) solution to this problem decomposes
the problem into subproblems and thus incurs the additive factor of
. In external memory, these approaches will lead to I/Os instead
of optimal I/O term where is the block-size. We re-interpret the
problem independent of , as interval stabbing with priority over tree-shaped
structure. This leads us to a linear space index in external memory supporting
top- queries (with unsorted outputs) in near optimal I/Os for any constant { and
}. Then we get space index
with optimal I/Os.Comment: 3 figure
Dynamic Colored Orthogonal Range Searching
In the colored orthogonal range reporting problem, we want a data structure for storing n colored points so that given a query axis-aligned rectangle, we can report the distinct colors among the points inside the rectangle. This natural problem has been studied in a series of papers, but most prior work focused on the static case. In this paper, we give a dynamic data structure in the 2D case which can answer queries in O(log^{1+o(1)} n + klog^{1/2+o(1)}n) time, where k denotes the output size (the number of distinct colors in the query range), and which can support insertions and deletions in O(log^{2+o(1)}n) time (amortized) in the standard RAM model. This is the first fully dynamic structure with polylogarithmic update time whose query cost per color reported is sublogarithmic (near ?{log n}). We also give an alternative data structure with O(log^{1+o(1)} n + klog^{3/4+o(1)}n) query time and O(log^{3/2+o(1)}n) update time (amortized). We also mention extensions to higher constant dimensions
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