TY - CONF
AB - 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.
AU - Castenow, Jannik
AU - Feldkord, Björn
AU - Knollmann, Till
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 17370
KW - Online Multi-Commodity Facility Location
KW - Competitive Ratio
KW - Online Optimization
KW - Facility Location Problem
SN - 9781450369350
T2 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures
TI - The Online Multi-Commodity Facility Location Problem
ER -
TY - CONF
AU - Castenow, Jannik
AU - Kling, Peter
AU - Knollmann, Till
AU - Meyer auf der Heide, Friedhelm
ID - 17371
SN - 9781450369350
T2 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures
TI - A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up
ER -
TY - CONF
AB - 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.
AU - Braun, Michael
AU - Castenow, Jannik
AU - Meyer auf der Heide, Friedhelm
ID - 16968
T2 - Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)
TI - Local Gathering of Mobile Robots in Three Dimensions
ER -
TY - CONF
AU - Pukrop, Simon
AU - Mäcker, Alexander
AU - Meyer auf der Heide, Friedhelm
ID - 13868
T2 - Proceedings of the 46th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM)
TI - Approximating Weighted Completion Time for Order Scheduling with Setup Times
ER -
TY - JOUR
AU - Castenow, Jannik
AU - Fischer, Matthias
AU - Harbig, Jonas
AU - Jung, Daniel
AU - Meyer auf der Heide, Friedhelm
ID - 16299
JF - Theoretical Computer Science
SN - 0304-3975
TI - Gathering Anonymous, Oblivious Robots on a Grid
VL - 815
ER -
TY - CONF
AU - Feldkord, Björn
AU - Knollmann, Till
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 12870
T2 - Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA)
TI - Managing Multiple Mobile Resources
ER -
TY - JOUR
AU - Feldkord, Björn
AU - Meyer auf der Heide, Friedhelm
ID - 13873
IS - 3
JF - ACM Transactions on Parallel Computing (TOPC)
TI - The Mobile Server Problem
VL - 6
ER -
TY - GEN
AB - 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.
AU - Brandt, Sascha
AU - Jähn, Claudius
AU - Fischer, Matthias
AU - Meyer auf der Heide, Friedhelm
ID - 16341
T2 - arXiv:1904.08225
TI - Rendering of Complex Heterogenous Scenes using Progressive Blue Surfels
ER -
TY - JOUR
AU - Meyer auf der Heide, Friedhelm
ID - 13937
IS - 2
JF - Mathematische Semesterberichte
TI - Paul Curzon, Peter W. McOwan: Computational Thinking; Die Welt des algorithmischen Denkens – in Spielen, Zaubertricks und Rätseln
VL - 66
ER -
TY - CHAP
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
ID - 13939
T2 - Distributed Computing by Mobile Entities, Current Research in Moving and Computing
TI - Continuous Protocols for Swarm Robotics
VL - 11340
ER -
TY - JOUR
AU - Karl, Holger
AU - Kundisch, Dennis
AU - Meyer auf der Heide, Friedhelm
AU - Wehrheim, Heike
ID - 13770
JF - Business & Information Systems Engineering
TI - A Case for a New IT Ecosystem: On-The-Fly Computing
ER -
TY - JOUR
AU - Brandt, Sascha
AU - Jähn, Claudius
AU - Fischer, Matthias
AU - Meyer auf der Heide, Friedhelm
ID - 16337
IS - 7
JF - Computer Graphics Forum
SN - 0167-7055
TI - Visibility‐Aware Progressive Farthest Point Sampling on the GPU
VL - 38
ER -
TY - JOUR
AU - Abu-Khzam, Faisal N.
AU - Li, Shouwei
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 13946
JF - Theoretical Computer Science
TI - Efficient parallel algorithms for parameterized problems
VL - 786
ER -
TY - CONF
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 13942
T2 - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems
TI - Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location
ER -
TY - CONF
AU - Meyer auf der Heide, Friedhelm
AU - Schaefer, Johannes Sebastian
ID - 7570
SN - 9781450357999
T2 - Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures - SPAA '18
TI - Brief Announcement: Communication in Systems of Home Based Mobile Agents
ER -
TY - CHAP
AU - Feldkord, Björn
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 16392
SN - 0302-9743
T2 - Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
TI - A Dynamic Distributed Data Structure for Top-k and k-Select Queries
ER -
TY - JOUR
AU - Li, Shouwei
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 2848
IS - 5
JF - Algorithmica
TI - Towards Flexible Demands in Online Leasing Problems.
VL - 80
ER -
TY - CONF
AU - Hamann, Heiko
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Wahby, Mostafa
ID - 2850
T2 - Ninth International Conference on Fun with Algorithms (FUN)
TI - Pick, Pack, & Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets
ER -
TY - CONF
AB - 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.
AU - Benter, Markus
AU - Knollmann, Till
AU - Meyer auf der Heide, Friedhelm
AU - Setzer, Alexander
AU - Sundermeier, Jannik
ID - 4375
KW - Distributed Storage
KW - Multi-Dimensional Range Queries
KW - Peer-to-Peer
KW - Hilbert Curve
T2 - Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD)
TI - A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension
ER -
TY - JOUR
AU - Abu-Khzam, Faisal N.
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Schubert, Michael
ID - 2849
JF - Theory of Computing Systems
TI - Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks
ER -