1,261 research outputs found
FollowMe: Efficient Online Min-Cost Flow Tracking with Bounded Memory and Computation
One of the most popular approaches to multi-target tracking is
tracking-by-detection. Current min-cost flow algorithms which solve the data
association problem optimally have three main drawbacks: they are
computationally expensive, they assume that the whole video is given as a
batch, and they scale badly in memory and computation with the length of the
video sequence. In this paper, we address each of these issues, resulting in a
computationally and memory-bounded solution. First, we introduce a dynamic
version of the successive shortest-path algorithm which solves the data
association problem optimally while reusing computation, resulting in
significantly faster inference than standard solvers. Second, we address the
optimal solution to the data association problem when dealing with an incoming
stream of data (i.e., online setting). Finally, we present our main
contribution which is an approximate online solution with bounded memory and
computation which is capable of handling videos of arbitrarily length while
performing tracking in real time. We demonstrate the effectiveness of our
algorithms on the KITTI and PETS2009 benchmarks and show state-of-the-art
performance, while being significantly faster than existing solvers
Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees
In a directed graph with non-correlated edge lengths and costs, the
\emph{network design problem with bounded distances} asks for a cost-minimal
spanning subgraph subject to a length bound for all node pairs. We give a
bi-criteria -approximation for this
problem. This improves on the currently best known linear approximation bound,
at the cost of violating the distance bound by a factor of at
most~.
In the course of proving this result, the related problem of \emph{directed
shallow-light Steiner trees} arises as a subproblem. In the context of directed
graphs, approximations to this problem have been elusive. We present the first
non-trivial result by proposing a
-ap\-proxi\-ma\-tion, where are the
terminals.
Finally, we show how to apply our results to obtain an
-approximation for
\emph{light-weight directed -spanners}. For this, no non-trivial
approximation algorithm has been known before. All running times depends on
and and are polynomial in for any fixed
A practical fpt algorithm for Flow Decomposition and transcript assembly
The Flow Decomposition problem, which asks for the smallest set of weighted
paths that "covers" a flow on a DAG, has recently been used as an important
computational step in transcript assembly. We prove the problem is in FPT when
parameterized by the number of paths by giving a practical linear fpt
algorithm. Further, we implement and engineer a Flow Decomposition solver based
on this algorithm, and evaluate its performance on RNA-sequence data.
Crucially, our solver finds exact solutions while achieving runtimes
competitive with a state-of-the-art heuristic. Finally, we contextualize our
design choices with two hardness results related to preprocessing and weight
recovery. Specifically, -Flow Decomposition does not admit polynomial
kernels under standard complexity assumptions, and the related problem of
assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0.
http://dx.doi.org/10.5281/zenodo.82163
Stochastic on-time arrival problem in transit networks
This article considers the stochastic on-time arrival problem in transit
networks where both the travel time and the waiting time for transit services
are stochastic. A specific challenge of this problem is the combinatorial
solution space due to the unknown ordering of transit line arrivals. We propose
a network structure appropriate to the online decision-making of a passenger,
including boarding, waiting and transferring. In this framework, we design a
dynamic programming algorithm that is pseudo-polynomial in the number of
transit stations and travel time budget, and exponential in the number of
transit lines at a station, which is a small number in practice. To reduce the
search space, we propose a definition of transit line dominance, and techniques
to identify dominance, which decrease the computation time by up to 90% in
numerical experiments. Extensive numerical experiments are conducted on both a
synthetic network and the Chicago transit network.Comment: 29 pages; 12 figures. This manuscript version is made available under
the CC-BY-NC-ND 4.0 license
https://creativecommons.org/licenses/by-nc-nd/4.0
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