20,365 research outputs found
Optimal Base Station Placement: A Stochastic Method Using Interference Gradient In Downlink Case
In this paper, we study the optimal placement and optimal number of base
stations added to an existing wireless data network through the interference
gradient method. This proposed method considers a sub-region of the existing
wireless data network, hereafter called region of interest. In this region, the
provider wants to increase the network coverage and the users throughput. In
this aim, the provider needs to determine the optimal number of base stations
to be added and their optimal placement. The proposed approach is based on the
Delaunay triangulation of the region of interest and the gradient descent
method in each triangle to compute the minimum interference locations. We
quantify the increase of coverage and throughput.Comment: This work has been presented in the 5th International ICST Conference
on Performance Evaluation Methodologies and Tools (Valuetools 2011
On a Linear Program for Minimum-Weight Triangulation
Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time
constant-factor approximation algorithm, and a variety of effective polynomial-
time heuristics that, for many instances, can find the exact MWT. Linear
programs (LPs) for MWT are well-studied, but previously no connection was known
between any LP and any approximation algorithm or heuristic for MWT. Here we
show the first such connections: for an LP formulation due to Dantzig et al.
(1985): (i) the integrality gap is bounded by a constant; (ii) given any
instance, if the aforementioned heuristics find the MWT, then so does the LP.Comment: To appear in SICOMP. Extended abstract appeared in SODA 201
Optimizing the double description method for normal surface enumeration
Many key algorithms in 3-manifold topology involve the enumeration of normal
surfaces, which is based upon the double description method for finding the
vertices of a convex polytope. Typically we are only interested in a small
subset of these vertices, thus opening the way for substantial optimization.
Here we give an account of the vertex enumeration problem as it applies to
normal surfaces, and present new optimizations that yield strong improvements
in both running time and memory consumption. The resulting algorithms are
tested using the freely available software package Regina.Comment: 27 pages, 12 figures; v2: Removed the 3^n bound from Section 3.3,
fixed the projective equation in Lemma 4.4, clarified "most triangulations"
in the introduction to section 5; v3: replace -ise with -ize for Mathematics
of Computation (note that this changes the title of the paper
Drawing Planar Graphs with Few Geometric Primitives
We define the \emph{visual complexity} of a plane graph drawing to be the
number of basic geometric objects needed to represent all its edges. In
particular, one object may represent multiple edges (e.g., one needs only one
line segment to draw a path with an arbitrary number of edges). Let denote
the number of vertices of a graph. We show that trees can be drawn with
straight-line segments on a polynomial grid, and with straight-line
segments on a quasi-polynomial grid. Further, we present an algorithm for
drawing planar 3-trees with segments on an
grid. This algorithm can also be used with a small modification to draw maximal
outerplanar graphs with edges on an grid. We also
study the problem of drawing maximal planar graphs with circular arcs and
provide an algorithm to draw such graphs using only arcs. This is
significantly smaller than the lower bound of for line segments for a
nontrivial graph class.Comment: Appeared at Proc. 43rd International Workshop on Graph-Theoretic
Concepts in Computer Science (WG 2017
\v{C}ech-Delaunay gradient flow and homology inference for self-maps
We call a continuous self-map that reveals itself through a discrete set of
point-value pairs a sampled dynamical system. Capturing the available
information with chain maps on Delaunay complexes, we use persistent homology
to quantify the evidence of recurrent behavior. We establish a sampling theorem
to recover the eigenspace of the endomorphism on homology induced by the
self-map. Using a combinatorial gradient flow arising from the discrete Morse
theory for \v{C}ech and Delaunay complexes, we construct a chain map to
transform the problem from the natural but expensive \v{C}ech complexes to the
computationally efficient Delaunay triangulations. The fast chain map algorithm
has applications beyond dynamical systems.Comment: 22 pages, 8 figure
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On a linear program for minimum-weight triangulation
Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial-time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-studied, but previously no connection was known between any LP and any approximation algorithm or heuristic for MWT. Here we show the first such connections: For an LP formulation due to Dantzig, Hoffman, and Hu [Math. Programming, 31 (1985), pp. 1-14], (i) the integrality gap is constant, and (ii) given any instance, if the aforementioned heuristics find the MWT, then so does the LP. © 2014 Society for Industrial and Applied Mathematics
Combining information seeking services into a meta supply chain of facts
The World Wide Web has become a vital supplier of information that allows organizations to carry on such tasks as business intelligence, security monitoring, and risk assessments. Having a quick and reliable supply of correct facts from perspective is often mission critical. By following design science guidelines, we have explored ways to recombine facts from multiple sources, each with possibly different levels of responsiveness and accuracy, into one robust supply chain. Inspired by prior research on keyword-based meta-search engines (e.g., metacrawler.com), we have adapted the existing question answering algorithms for the task of analysis and triangulation of facts. We present a first prototype for a meta approach to fact seeking. Our meta engine sends a user's question to several fact seeking services that are publicly available on the Web (e.g., ask.com, brainboost.com, answerbus.com, NSIR, etc.) and analyzes the returned results jointly to identify and present to the user those that are most likely to be factually correct. The results of our evaluation on the standard test sets widely used in prior research support the evidence for the following: 1) the value-added of the meta approach: its performance surpasses the performance of each supplier, 2) the importance of using fact seeking services as suppliers to the meta engine rather than keyword driven search portals, and 3) the resilience of the meta approach: eliminating a single service does not noticeably impact the overall performance. We show that these properties make the meta-approach a more reliable supplier of facts than any of the currently available stand-alone services
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