10,850 research outputs found
Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls
We consider space-bounded computations on a random-access machine (RAM) where
the input is given on a read-only random-access medium, the output is to be
produced to a write-only sequential-access medium, and the available workspace
allows random reads and writes but is of limited capacity. The length of the
input is elements, the length of the output is limited by the computation,
and the capacity of the workspace is bits for some predetermined
parameter . We present a state-of-the-art priority queue---called an
adjustable navigation pile---for this restricted RAM model. Under some
reasonable assumptions, our priority queue supports and
in worst-case time and in worst-case time for any . We show how to use this
data structure to sort elements and to compute the convex hull of
points in the two-dimensional Euclidean space in
worst-case time for any . Following a known lower bound for the
space-time product of any branching program for finding unique elements, both
our sorting and convex-hull algorithms are optimal. The adjustable navigation
pile has turned out to be useful when designing other space-efficient
algorithms, and we expect that it will find its way to yet other applications.Comment: 21 page
Structure and Dynamics of Information Pathways in Online Media
Diffusion of information, spread of rumors and infectious diseases are all
instances of stochastic processes that occur over the edges of an underlying
network. Many times networks over which contagions spread are unobserved, and
such networks are often dynamic and change over time. In this paper, we
investigate the problem of inferring dynamic networks based on information
diffusion data. We assume there is an unobserved dynamic network that changes
over time, while we observe the results of a dynamic process spreading over the
edges of the network. The task then is to infer the edges and the dynamics of
the underlying network.
We develop an on-line algorithm that relies on stochastic convex optimization
to efficiently solve the dynamic network inference problem. We apply our
algorithm to information diffusion among 3.3 million mainstream media and blog
sites and experiment with more than 179 million different pieces of information
spreading over the network in a one year period. We study the evolution of
information pathways in the online media space and find interesting insights.
Information pathways for general recurrent topics are more stable across time
than for on-going news events. Clusters of news media sites and blogs often
emerge and vanish in matter of days for on-going news events. Major social
movements and events involving civil population, such as the Libyan's civil war
or Syria's uprise, lead to an increased amount of information pathways among
blogs as well as in the overall increase in the network centrality of blogs and
social media sites.Comment: To Appear at the 6th International Conference on Web Search and Data
Mining (WSDM '13
Analytical modelling in Dynamo
BIM is applied as modern database for civil
engineering. Its recent development allows to preserve
both structure geometrical and analytical information. The
analytical model described in the paper is derived directly
from BIM model of a structure automatically but in most
cases it requires manual improvements before being sent
to FEM software. Dynamo visual programming language
was used to handle the analytical data. Authors developed
a program which corrects faulty analytical model obtained
from BIM geometry, thus providing better automation for
preparing FEM model. Program logic is explained and test
cases shown
On the complexity of range searching among curves
Modern tracking technology has made the collection of large numbers of
densely sampled trajectories of moving objects widely available. We consider a
fundamental problem encountered when analysing such data: Given polygonal
curves in , preprocess into a data structure that answers
queries with a query curve and radius for the curves of that
have \Frechet distance at most to .
We initiate a comprehensive analysis of the space/query-time trade-off for
this data structuring problem. Our lower bounds imply that any data structure
in the pointer model model that achieves query time, where is
the output size, has to use roughly space in
the worst case, even if queries are mere points (for the discrete \Frechet
distance) or line segments (for the continuous \Frechet distance). More
importantly, we show that more complex queries and input curves lead to
additional logarithmic factors in the lower bound. Roughly speaking, the number
of logarithmic factors added is linear in the number of edges added to the
query and input curve complexity. This means that the space/query time
trade-off worsens by an exponential factor of input and query complexity. This
behaviour addresses an open question in the range searching literature: whether
it is possible to avoid the additional logarithmic factors in the space and
query time of a multilevel partition tree. We answer this question negatively.
On the positive side, we show we can build data structures for the \Frechet
distance by using semialgebraic range searching. Our solution for the discrete
\Frechet distance is in line with the lower bound, as the number of levels in
the data structure is , where denotes the maximal number of vertices
of a curve. For the continuous \Frechet distance, the number of levels
increases to
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