139,934 research outputs found
Linear-Space Data Structures for Range Mode Query in Arrays
A mode of a multiset is an element of maximum multiplicity;
that is, occurs at least as frequently as any other element in . Given a
list of items, we consider the problem of constructing a data
structure that efficiently answers range mode queries on . Each query
consists of an input pair of indices for which a mode of must
be returned. We present an -space static data structure
that supports range mode queries in time in the worst case, for
any fixed . When , this corresponds to
the first linear-space data structure to guarantee query time. We
then describe three additional linear-space data structures that provide
, , and query time, respectively, where denotes the
number of distinct elements in and denotes the frequency of the mode of
. Finally, we examine generalizing our data structures to higher dimensions.Comment: 13 pages, 2 figure
Efficient Exploration of the Space of Reconciled Gene Trees
Gene trees record the combination of gene level events, such as duplication,
transfer and loss, and species level events, such as speciation and extinction.
Gene tree-species tree reconciliation methods model these processes by drawing
gene trees into the species tree using a series of gene and species level
events. The reconstruction of gene trees based on sequence alone almost always
involves choosing between statistically equivalent or weakly distinguishable
relationships that could be much better resolved based on a putative species
tree. To exploit this potential for accurate reconstruction of gene trees the
space of reconciled gene trees must be explored according to a joint model of
sequence evolution and gene tree-species tree reconciliation.
Here we present amalgamated likelihood estimation (ALE), a probabilistic
approach to exhaustively explore all reconciled gene trees that can be
amalgamated as a combination of clades observed in a sample of trees. We
implement ALE in the context of a reconciliation model, which allows for the
duplication, transfer and loss of genes. We use ALE to efficiently approximate
the sum of the joint likelihood over amalgamations and to find the reconciled
gene tree that maximizes the joint likelihood.
We demonstrate using simulations that gene trees reconstructed using the
joint likelihood are substantially more accurate than those reconstructed using
sequence alone. Using realistic topologies, branch lengths and alignment sizes,
we demonstrate that ALE produces more accurate gene trees even if the model of
sequence evolution is greatly simplified. Finally, examining 1099 gene families
from 36 cyanobacterial genomes we find that joint likelihood-based inference
results in a striking reduction in apparent phylogenetic discord, with 24%, 59%
and 46% percent reductions in the mean numbers of duplications, transfers and
losses.Comment: Manuscript accepted pending revision in Systematic Biolog
QuickCSG: Fast Arbitrary Boolean Combinations of N Solids
QuickCSG computes the result for general N-polyhedron boolean expressions
without an intermediate tree of solids. We propose a vertex-centric view of the
problem, which simplifies the identification of final geometric contributions,
and facilitates its spatial decomposition. The problem is then cast in a single
KD-tree exploration, geared toward the result by early pruning of any region of
space not contributing to the final surface. We assume strong regularity
properties on the input meshes and that they are in general position. This
simplifying assumption, in combination with our vertex-centric approach,
improves the speed of the approach. Complemented with a task-stealing
parallelization, the algorithm achieves breakthrough performance, one to two
orders of magnitude speedups with respect to state-of-the-art CPU algorithms,
on boolean operations over two to dozens of polyhedra. The algorithm also
outperforms GPU implementations with approximate discretizations, while
producing an output without redundant facets. Despite the restrictive
assumptions on the input, we show the usefulness of QuickCSG for applications
with large CSG problems and strong temporal constraints, e.g. modeling for 3D
printers, reconstruction from visual hulls and collision detection
GraphMatch: Efficient Large-Scale Graph Construction for Structure from Motion
We present GraphMatch, an approximate yet efficient method for building the
matching graph for large-scale structure-from-motion (SfM) pipelines. Unlike
modern SfM pipelines that use vocabulary (Voc.) trees to quickly build the
matching graph and avoid a costly brute-force search of matching image pairs,
GraphMatch does not require an expensive offline pre-processing phase to
construct a Voc. tree. Instead, GraphMatch leverages two priors that can
predict which image pairs are likely to match, thereby making the matching
process for SfM much more efficient. The first is a score computed from the
distance between the Fisher vectors of any two images. The second prior is
based on the graph distance between vertices in the underlying matching graph.
GraphMatch combines these two priors into an iterative "sample-and-propagate"
scheme similar to the PatchMatch algorithm. Its sampling stage uses Fisher
similarity priors to guide the search for matching image pairs, while its
propagation stage explores neighbors of matched pairs to find new ones with a
high image similarity score. Our experiments show that GraphMatch finds the
most image pairs as compared to competing, approximate methods while at the
same time being the most efficient.Comment: Published at IEEE 3DV 201
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