@inproceedings{17370,
abstract = { We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set \( S \) of commodities.
Ravi and Sinha (SODA 2004) introduced the model as the \emph{Multi-Commodity Facility Location Problem} (MFLP) and considered it an offline optimization problem.
The model itself is similar to the FLP: i.e., requests are located at points of a finite metric space and the task of an algorithm is to construct facilities and assign requests to facilities while minimizing the construction cost and the sum over all assignment distances.
In addition, requests and facilities are heterogeneous; they request or offer multiple commodities out of $S$.
A request has to be connected to a set of facilities jointly offering the commodities demanded by it.
In comparison to the FLP, an algorithm has to decide not only if and where to place facilities, but also which commodities to offer at each.
To the best of our knowledge we are the first to study the problem in its online variant in which requests, their positions and their commodities are not known beforehand but revealed over time.
We present results regarding the competitive ratio.
On the one hand, we show that heterogeneity influences the competitive ratio by developing a lower bound on the competitive ratio for any randomized online algorithm of \( \Omega ( \sqrt{|S|} + \frac{\log n}{\log \log n} ) \) that already holds for simple line metrics.
Here, \( n \) is the number of requests.
On the other side, we establish a deterministic \( \mathcal{O}(\sqrt{|S|} \cdot \log n) \)-competitive algorithm and a randomized \( \mathcal{O}(\sqrt{|S|} \cdot \frac{\log n}{\log \log n} ) \)-competitive algorithm.
Further, we show that when considering a more special class of cost functions for the construction cost of a facility, the competitive ratio decreases given by our deterministic algorithm depending on the function.},
author = {Castenow, Jannik and Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm},
booktitle = {Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures},
isbn = {9781450369350},
keyword = {Online Multi-Commodity Facility Location, Competitive Ratio, Online Optimization, Facility Location Problem},
title = {{The Online Multi-Commodity Facility Location Problem}},
doi = {10.1145/3350755.3400281},
year = {2020},
}
@inproceedings{17371,
author = {Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm},
booktitle = {Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures},
isbn = {9781450369350},
title = {{A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up}},
doi = {10.1145/3350755.3400263},
year = {2020},
}
@inproceedings{16968,
abstract = {In this work, we initiate the research about the Gathering problem for robots
with limited viewing range in the three-dimensional Euclidean space. In the
Gathering problem, a set of initially scattered robots is required to gather at
the same position. The robots' capabilities are very restricted -- they do not
agree on any coordinate system or compass, have a limited viewing range, have
no memory of the past and cannot communicate. We study the problem in two
different time models, in FSYNC (fully synchronized discrete rounds) and the
continuous time model. For FSYNC, we introduce the 3D-Go-To-The-Center-strategy
and prove a runtime of $\Theta(n^2)$ that matches the currently best runtime
bound for the same model in the Euclidean plane [SPAA'11]. Our main result is
the generalization of contracting strategies (continuous time) from
[Algosensors'17] to three dimensions. In contracting strategies, every robot
that is located on the global convex hull of all robots' positions moves with
full speed towards the inside of the convex hull. We prove a runtime bound of
$O(\Delta \cdot n^{3/2})$ for any three-dimensional contracting strategy, where
$\Delta$ denotes the diameter of the initial configuration. This comes up to a
factor of $\sqrt{n}$ close to the lower bound of $\Omega (\Delta \cdot n)$
which is already true in two dimensions. In general, it might be hard for
robots with limited viewing range to decide whether they are located on the
global convex hull and which movement maintains the connectivity of the swarm,
rendering the design of concrete contracting strategies a challenging task. We
prove that the continuous variant of 3D-Go-To-The-Center is contracting and
keeps the swarm connected. Moreover, we give a simple design criterion for
three-dimensional contracting strategies that maintains the connectivity of the
swarm and introduce an exemplary strategy based on this criterion.},
author = {Braun, Michael and Castenow, Jannik and Meyer auf der Heide, Friedhelm},
booktitle = {Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)},
location = {Paderborn},
publisher = {Springer},
title = {{Local Gathering of Mobile Robots in Three Dimensions}},
doi = {10.1007/978-3-030-54921-3_4},
year = {2020},
}
@inproceedings{13868,
author = {Pukrop, Simon and Mäcker, Alexander and Meyer auf der Heide, Friedhelm},
booktitle = {Proceedings of the 46th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM)},
title = {{Approximating Weighted Completion Time for Order Scheduling with Setup Times}},
year = {2020},
}
@phdthesis{15631,
author = {Feldkord, Björn},
title = {{Mobile Resource Allocation}},
doi = {10.17619/UNIPB/1-869},
year = {2020},
}
@inproceedings{15169,
author = {Castenow, Jannik and Kolb, Christina and Scheideler, Christian},
booktitle = {Proceedings of the 21st International Conference on Distributed Computing and Networking (ICDCN)},
location = {Kolkata, Indien},
publisher = {ACM},
title = {{A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks}},
year = {2020},
}
@article{16299,
author = {Castenow, Jannik and Fischer, Matthias and Harbig, Jonas and Jung, Daniel and Meyer auf der Heide, Friedhelm},
issn = {0304-3975},
journal = {Theoretical Computer Science},
pages = {289--309},
title = {{Gathering Anonymous, Oblivious Robots on a Grid}},
doi = {10.1016/j.tcs.2020.02.018},
volume = {815},
year = {2020},
}
@inproceedings{12870,
author = {Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm},
booktitle = {Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA)},
pages = {120 -- 137},
publisher = {Springer},
title = {{Managing Multiple Mobile Resources}},
doi = {10.1007/978-3-030-39479-0_9},
year = {2019},
}
@article{13873,
author = {Feldkord, Björn and Meyer auf der Heide, Friedhelm},
journal = {ACM Transactions on Parallel Computing (TOPC)},
number = {3},
title = {{The Mobile Server Problem}},
doi = {10.1145/3364204},
volume = {6},
year = {2019},
}
@unpublished{16341,
abstract = {We present a technique for rendering highly complex 3D scenes in real-time by
generating uniformly distributed points on the scene's visible surfaces. The
technique is applicable to a wide range of scene types, like scenes directly
based on complex and detailed CAD data consisting of billions of polygons (in
contrast to scenes handcrafted solely for visualization). This allows to
visualize such scenes smoothly even in VR on a HMD with good image quality,
while maintaining the necessary frame-rates. In contrast to other point based
rendering methods, we place points in an approximated blue noise distribution
only on visible surfaces and store them in a highly GPU efficient data
structure, allowing to progressively refine the number of rendered points to
maximize the image quality for a given target frame rate. Our evaluation shows
that scenes consisting of a high amount of polygons can be rendered with
interactive frame rates with good visual quality on standard hardware.},
author = {Brandt, Sascha and Jähn, Claudius and Fischer, Matthias and Meyer auf der Heide, Friedhelm},
booktitle = {arXiv:1904.08225},
title = {{Rendering of Complex Heterogenous Scenes using Progressive Blue Surfels}},
year = {2019},
}