227,553 research outputs found
Optimal web-scale tiering as a flow problem
We present a fast online solver for large scale parametric max-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics. Our algorithm solves an integer linear program in an online fashion. It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game. The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows. We apply the algorithm to optimize tier arrangement of over 84 million web pages on a layered set of caches to serve an incoming query stream optimally
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
DeepFlow: Large displacement optical flow with deep matching
International audienceOptical flow computation is a key component in many computer vision systems designed for tasks such as action detection or activity recognition. However, despite several major advances over the last decade, handling large displacement in optical flow remains an open problem. Inspired by the large displacement optical flow of Brox and Malik, our approach, termed DeepFlow, blends a matching algorithm with a variational approach for optical flow. We propose a descriptor matching algorithm, tailored to the optical flow problem, that allows to boost performance on fast motions. The matching algorithm builds upon a multi-stage architecture with 6 layers, interleaving convolutions and max-pooling, a construction akin to deep convolutional nets. Using dense sampling, it allows to efficiently retrieve quasi-dense correspondences, and enjoys a built-in smoothing effect on descriptors matches, a valuable asset for integration into an energy minimization framework for optical flow estimation. DeepFlow efficiently handles large displacements occurring in realistic videos, and shows competitive performance on optical flow benchmarks. Furthermore, it sets a new state-of-the-art on the MPI-Sintel dataset
Max-flow vitality in undirected unweighted planar graphs
We show a fast algorithm for determining the set of relevant edges in a
planar undirected unweighted graph with respect to the maximum flow. This is a
special case of the \emph{max flow vitality} problem, that has been efficiently
solved for general undirected graphs and -planar graphs. The
\emph{vitality} of an edge of a graph with respect to the maximum flow between
two fixed vertices and is defined as the reduction of the maximum flow
caused by the removal of that edge. In this paper we show that the set of edges
having vitality greater than zero in a planar undirected unweighted graph with
vertices, can be found in worst-case time and space.Comment: 9 pages, 4 figure
Maximum Flow on Highly Dynamic Graphs
Recent advances in dynamic graph processing have enabled the analysis of
highly dynamic graphs with change at rates as high as millions of edge changes
per second. Solutions in this domain, however, have been demonstrated only for
relatively simple algorithms like PageRank, breadth-first search, and connected
components. Expanding beyond this, we explore the maximum flow problem, a
fundamental, yet more complex problem, in graph analytics. We propose a novel,
distributed algorithm for max-flow on dynamic graphs, and implement it on top
of an asynchronous vertex-centric abstraction. We show that our algorithm can
process both additions and deletions of vertices and edges efficiently at scale
on fast-evolving graphs, and provide a comprehensive analysis by evaluating, in
addition to throughput, two criteria that are important when applied to
real-world problems: result latency and solution stability
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