188 research outputs found
An Efficient Construction of Yao-Graph in Data-Distributed Settings
A sparse graph that preserves an approximation of the shortest paths between
all pairs of points in a plane is called a geometric spanner. Using range trees
of sublinear size, we design an algorithm in massively parallel computation
(MPC) model for constructing a geometric spanner known as Yao-graph. This
improves the total time and the total memory of existing algorithms for
geometric spanners from subquadratic to near-linear
A 2-Approximation Algorithm for Data-Distributed Metric k-Center
In a metric space, a set of point sets of roughly the same size and an
integer are given as the input and the goal of data-distributed
-center is to find a subset of size of the input points as the set of
centers to minimize the maximum distance from the input points to their closest
centers. Metric -center is known to be NP-hard which carries to the
data-distributed setting.
We give a -approximation algorithm of -center for sublinear in the
data-distributed setting, which is tight. This algorithm works in several
models, including the massively parallel computation model (MPC)
A Massively Parallel Dynamic Programming for Approximate Rectangle Escape Problem
Sublinear time complexity is required by the massively parallel computation
(MPC) model. Breaking dynamic programs into a set of sparse dynamic programs
that can be divided, solved, and merged in sublinear time.
The rectangle escape problem (REP) is defined as follows: For
axis-aligned rectangles inside an axis-aligned bounding box , extend each
rectangle in only one of the four directions: up, down, left, or right until it
reaches and the density is minimized, where is the maximum number
of extensions of rectangles to the boundary that pass through a point inside
bounding box . REP is NP-hard for . If the rectangles are points of a
grid (or unit squares of a grid), the problem is called the square escape
problem (SEP) and it is still NP-hard.
We give a -approximation algorithm for SEP with with time
complexity . This improves the time complexity of existing
algorithms which are at least quadratic. Also, the approximation ratio of our
algorithm for is which is tight. We also give a
-approximation algorithm for REP with time complexity and
give a MPC version of this algorithm for which is the first parallel
algorithm for this problem
Massively-Parallel Heat Map Sorting and Applications To Explainable Clustering
Given a set of points labeled with labels, we introduce the heat map
sorting problem as reordering and merging the points and dimensions while
preserving the clusters (labels). A cluster is preserved if it remains
connected, i.e., if it is not split into several clusters and no two clusters
are merged.
We prove the problem is NP-hard and we give a fixed-parameter algorithm with
a constant number of rounds in the massively parallel computation model, where
each machine has a sublinear memory and the total memory of the machines is
linear. We give an approximation algorithm for a NP-hard special case of the
problem. We empirically compare our algorithm with k-means and density-based
clustering (DBSCAN) using a dimensionality reduction via locality-sensitive
hashing on several directed and undirected graphs of email and computer
networks
The Effect of a Trans-theoretical model- based Education on Regular Consumption of Breakfast in Jiroft Students
Background: Breakfast has been known as the most important daily meal. The aim of this study was to determine the impact of using trans-theoretical model education on regular breakfast consumption in students of Jiroft, Iran.
Methods: This quasi-experimental study was performed on 290 students randomly divided into the control and experimental groups. The data collection instrument was a standard questionnaire. Educational intervention was conducted based on the Trans-theoretical model. Data were collected before the educational intervention and 3 months after that. Data analysis was done through SPSS 19.0 software and using Wilcoxon and Chi square tests.
Results: Before the educational program, 17% of students in the intervention group were at the action and maintenance stage; in which after the education, this rate increased to 87.7%. Results indicated significant increase in breakfast consumption and mean scores of process change (from 71.47 to 86.16), self- efficacy (from 27.84 to 33.57) and decision balance (from 34.97 to 43.74) (P<0.001). Mean scores of the change process and self- efficacy showed a slight meaningful increase in the control group (P<0.001).
Conclusion: Educational intervention based on the trans-theoretical model created adequate changes in nutritional behavior of the students over a 3 months period. Given the low cost and effectiveness of this educational model, generalization of such educational programs seems to be necessary
Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially.
Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular k-center variant which, given a set S of points from some metric space and a parameter k0, the algorithms yield solutions whose approximation ratios are a mere additive term \u3f5 away from those achievable by the best known polynomial-time sequential algorithms, a result that substantially improves upon the state of the art. Our algorithms are rather simple and adapt to the intrinsic complexity of the dataset, captured by the doubling dimension D of the metric space. Specifically, our analysis shows that the algorithms become very space-efficient for the important case of small (constant) D. These theoretical results are complemented with a set of experiments on real-world and synthetic datasets of up to over a billion points, which show that our algorithms yield better quality solutions over the state of the art while featuring excellent scalability, and that they also lend themselves to sequential implementations much faster than existing ones
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