25,544 research outputs found
Scalable Kernelization for Maximum Independent Sets
The most efficient algorithms for finding maximum independent sets in both
theory and practice use reduction rules to obtain a much smaller problem
instance called a kernel. The kernel can then be solved quickly using exact or
heuristic algorithms---or by repeatedly kernelizing recursively in the
branch-and-reduce paradigm. It is of critical importance for these algorithms
that kernelization is fast and returns a small kernel. Current algorithms are
either slow but produce a small kernel, or fast and give a large kernel. We
attempt to accomplish both of these goals simultaneously, by giving an
efficient parallel kernelization algorithm based on graph partitioning and
parallel bipartite maximum matching. We combine our parallelization techniques
with two techniques to accelerate kernelization further: dependency checking
that prunes reductions that cannot be applied, and reduction tracking that
allows us to stop kernelization when reductions become less fruitful. Our
algorithm produces kernels that are orders of magnitude smaller than the
fastest kernelization methods, while having a similar execution time.
Furthermore, our algorithm is able to compute kernels with size comparable to
the smallest known kernels, but up to two orders of magnitude faster than
previously possible. Finally, we show that our kernelization algorithm can be
used to accelerate existing state-of-the-art heuristic algorithms, allowing us
to find larger independent sets faster on large real-world networks and
synthetic instances.Comment: Extended versio
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Efficient Constellation-Based Map-Merging for Semantic SLAM
Data association in SLAM is fundamentally challenging, and handling ambiguity
well is crucial to achieve robust operation in real-world environments. When
ambiguous measurements arise, conservatism often mandates that the measurement
is discarded or a new landmark is initialized rather than risking an incorrect
association. To address the inevitable `duplicate' landmarks that arise, we
present an efficient map-merging framework to detect duplicate constellations
of landmarks, providing a high-confidence loop-closure mechanism well-suited
for object-level SLAM. This approach uses an incrementally-computable
approximation of landmark uncertainty that only depends on local information in
the SLAM graph, avoiding expensive recovery of the full system covariance
matrix. This enables a search based on geometric consistency (GC) (rather than
full joint compatibility (JC)) that inexpensively reduces the search space to a
handful of `best' hypotheses. Furthermore, we reformulate the commonly-used
interpretation tree to allow for more efficient integration of clique-based
pairwise compatibility, accelerating the branch-and-bound max-cardinality
search. Our method is demonstrated to match the performance of full JC methods
at significantly-reduced computational cost, facilitating robust object-based
loop-closure over large SLAM problems.Comment: Accepted to IEEE International Conference on Robotics and Automation
(ICRA) 201
GOGMA: Globally-Optimal Gaussian Mixture Alignment
Gaussian mixture alignment is a family of approaches that are frequently used
for robustly solving the point-set registration problem. However, since they
use local optimisation, they are susceptible to local minima and can only
guarantee local optimality. Consequently, their accuracy is strongly dependent
on the quality of the initialisation. This paper presents the first
globally-optimal solution to the 3D rigid Gaussian mixture alignment problem
under the L2 distance between mixtures. The algorithm, named GOGMA, employs a
branch-and-bound approach to search the space of 3D rigid motions SE(3),
guaranteeing global optimality regardless of the initialisation. The geometry
of SE(3) was used to find novel upper and lower bounds for the objective
function and local optimisation was integrated into the scheme to accelerate
convergence without voiding the optimality guarantee. The evaluation
empirically supported the optimality proof and showed that the method performed
much more robustly on two challenging datasets than an existing
globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and
Pattern Recognitio
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