7,893 research outputs found
Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space
For a set of points in , and parameters and \eps, we present
a data structure that answers (1+\eps,k)-\ANN queries in logarithmic time.
Surprisingly, the space used by the data-structure is \Otilde (n /k); that
is, the space used is sublinear in the input size if is sufficiently large.
Our approach provides a novel way to summarize geometric data, such that
meaningful proximity queries on the data can be carried out using this sketch.
Using this, we provide a sublinear space data-structure that can estimate the
density of a point set under various measures, including:
\begin{inparaenum}[(i)]
\item sum of distances of closest points to the query point, and
\item sum of squared distances of closest points to the query point.
\end{inparaenum}
Our approach generalizes to other distance based estimation of densities of
similar flavor. We also study the problem of approximating some of these
quantities when using sampling. In particular, we show that a sample of size
\Otilde (n /k) is sufficient, in some restricted cases, to estimate the above
quantities. Remarkably, the sample size has only linear dependency on the
dimension
Reverse k Nearest Neighbor Search over Trajectories
GPS enables mobile devices to continuously provide new opportunities to
improve our daily lives. For example, the data collected in applications
created by Uber or Public Transport Authorities can be used to plan
transportation routes, estimate capacities, and proactively identify low
coverage areas. In this paper, we study a new kind of query-Reverse k Nearest
Neighbor Search over Trajectories (RkNNT), which can be used for route planning
and capacity estimation. Given a set of existing routes DR, a set of passenger
transitions DT, and a query route Q, a RkNNT query returns all transitions that
take Q as one of its k nearest travel routes. To solve the problem, we first
develop an index to handle dynamic trajectory updates, so that the most
up-to-date transition data are available for answering a RkNNT query. Then we
introduce a filter refinement framework for processing RkNNT queries using the
proposed indexes. Next, we show how to use RkNNT to solve the optimal route
planning problem MaxRkNNT (MinRkNNT), which is to search for the optimal route
from a start location to an end location that could attract the maximum (or
minimum) number of passengers based on a pre-defined travel distance threshold.
Experiments on real datasets demonstrate the efficiency and scalability of our
approaches. To the best of our best knowledge, this is the first work to study
the RkNNT problem for route planning.Comment: 12 page
Modeling spatial social complex networks for dynamical processes
The study of social networks --- where people are located, geographically,
and how they might be connected to one another --- is a current hot topic of
interest, because of its immediate relevance to important applications, from
devising efficient immunization techniques for the arrest of epidemics, to the
design of better transportation and city planning paradigms, to the
understanding of how rumors and opinions spread and take shape over time. We
develop a spatial social complex network (SSCN) model that captures not only
essential connectivity features of real-life social networks, including a
heavy-tailed degree distribution and high clustering, but also the spatial
location of individuals, reproducing Zipf's law for the distribution of city
populations as well as other observed hallmarks. We then simulate Milgram's
Small-World experiment on our SSCN model, obtaining good qualitative agreement
with the known results and shedding light on the role played by various network
attributes and the strategies used by the players in the game. This
demonstrates the potential of the SSCN model for the simulation and study of
the many social processes mentioned above, where both connectivity and
geography play a role in the dynamics.Comment: 10 pages, 6 figure
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