@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{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{14539,
author = {Castenow, Jannik and Kolb, Christina and Scheideler, Christian},
booktitle = {Proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO)},
location = {L'Aquila, Italy},
pages = {345--348},
title = {{A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks}},
doi = {10.1007/978-3-030-24922-9\_26},
year = {2019},
}
@inproceedings{4375,
abstract = {We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\
The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07).
We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range.
Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds.
Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.},
author = {Benter, Markus and Knollmann, Till and Meyer auf der Heide, Friedhelm and Setzer, Alexander and Sundermeier, Jannik},
booktitle = {Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD)},
keyword = {Distributed Storage, Multi-Dimensional Range Queries, Peer-to-Peer, Hilbert Curve},
location = {Helsinki},
title = {{A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension}},
doi = {10.1007/978-3-030-19759-9_4},
year = {2018},
}
@inproceedings{4565,
author = {Jung, Daniel and Kolb, Christina and Scheideler, Christian and Sundermeier, Jannik},
booktitle = {Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA)},
isbn = {9781450357999},
location = {Wien},
publisher = {ACM Press},
title = {{Brief Announcement: Competitive Routing in Hybrid Communication Networks}},
doi = {10.1145/3210377.3210663},
year = {2018},
}
@inproceedings{4563,
abstract = {Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion.
In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work.
},
author = {Jung, Daniel and Kolb, Christina and Scheideler, Christian and Sundermeier, Jannik},
booktitle = {Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS) },
keyword = {greedy routing, ad hoc networks, convex hulls, c-competitiveness},
location = {Helsinki},
publisher = {Springer},
title = {{Competitive Routing in Hybrid Communication Networks}},
year = {2018},
}
@inbook{16461,
author = {Bemmann, Pascal and Biermeier, Felix and Bürmann, Jan and Kemper, Arne and Knollmann, Till and Knorr, Steffen and Kothe, Nils and Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören and Schaefer, Johannes and Sundermeier, Jannik},
booktitle = {Structural Information and Communication Complexity},
isbn = {9783319720494},
issn = {0302-9743},
title = {{Monitoring of Domain-Related Problems in Distributed Data Streams}},
doi = {10.1007/978-3-319-72050-0_13},
year = {2017},
}
@misc{699,
author = {Sundermeier, Jannik},
publisher = {Universität Paderborn},
title = {{Routing in Hybrid Communication Networks with Holes - Considering Bounding Boxes as Hole Abstractions}},
year = {2017},
}
@misc{18006,
author = {Sundermeier, Jannik},
title = {{Implementierung eines selbststabilisierenden verteilten Stacks}},
year = {2015},
}