@article{20683,
author = {Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm},
journal = {Theory of Computing Systems},
title = {{Managing Multiple Mobile Resources}},
doi = {10.1007/s00224-020-10023-8},
year = {2021},
}
@inproceedings{20817,
author = {Bienkowski, Marcin and Feldkord, Björn and Schmidt, Pawel},
booktitle = {Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS)},
pages = {14:1 -- 14:17},
title = {{A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location}},
doi = {10.4230/LIPIcs.STACS.2021.14},
year = {2021},
}
@article{21096,
abstract = {While many research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. However, when peers in peer-to-peer networks crash, a distributed data structure may not remain intact. We present a self-stabilizing protocol for a distributed data structure called the Hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has many applications while offering low overhead and efficient operations when embedded on top of a Distributed Hash Table. Especially, longest prefix matching for x can be done in O(log |x|) hash table read accesses. We show how to maintain the structure in a self-stabilizing way, while assuring a low overhead in a legal state and an asymptotically optimal memory demand of O(d) bits, where d is the number of bits needed for storing all keys.},
author = {Knollmann, Till and Scheideler, Christian},
issn = {0890-5401},
journal = {Information and Computation},
title = {{A self-stabilizing Hashed Patricia Trie}},
doi = {10.1016/j.ic.2021.104697},
year = {2021},
}
@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 = {{Brief Announcement: A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up}},
doi = {10.1145/3350755.3400263},
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{20159,
abstract = {Let G = (V,E) be an undirected graph on n vertices with non-negative capacities on its edges. The mincut sensitivity problem for the insertion of an edge is defined as follows. Build a compact data structure for G and a given set S ⊆ V of vertices that, on receiving any edge (x,y) ∈ S×S of positive capacity as query input, can efficiently report the set of all pairs from S× S whose mincut value increases upon insertion of the edge (x,y) to G. The only result that exists for this problem is for a single pair of vertices (Picard and Queyranne, Mathematical Programming Study, 13 (1980), 8-16). We present the following results for the single source and the all-pairs versions of this problem.
1) Single source: Given any designated source vertex s, there exists a data structure of size 𝒪(|S|) that can output all those vertices from S whose mincut value to s increases upon insertion of any given edge. The time taken by the data structure to answer any query is 𝒪(|S|).
2) All-pairs: There exists an 𝒪(|S|²) size data structure that can output all those pairs of vertices from S× S whose mincut value gets increased upon insertion of any given edge. The time taken by the data structure to answer any query is 𝒪(k), where k is the number of pairs of vertices whose mincut increases.
For both these versions, we also address the problem of reporting the values of the mincuts upon insertion of any given edge. To derive our results, we use interesting insights into the nearest and the farthest mincuts for a pair of vertices. In addition, a crucial result, that we establish and use in our data structures, is that there exists a directed acyclic graph of 𝒪(n) size that compactly stores the farthest mincuts from all vertices of V to a designated vertex s in the graph. We believe that this result is of independent interest, especially, because it also complements a previously existing result by Hariharan et al. (STOC 2007) that the nearest mincuts from all vertices of V to s is a laminar family, and hence, can be stored compactly in a tree of 𝒪(n) size.},
author = {Baswana, Surender and Gupta, Shiv and Knollmann, Till},
booktitle = {28th Annual European Symposium on Algorithms (ESA 2020)},
editor = {Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
isbn = {978-3-95977-162-7},
issn = {1868-8969},
keyword = {Mincut, Sensitivity, Data Structure},
pages = {12:1--12:14},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
title = {{Mincut Sensitivity Data Structures for the Insertion of an Edge}},
doi = {10.4230/LIPIcs.ESA.2020.12},
volume = {173},
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{20185,
author = {Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm},
booktitle = {Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings },
editor = {Devismes, Stéphane and Mittal, Neeraj},
isbn = {978-3-030-64347-8},
pages = {60--64},
publisher = {Springer},
title = {{Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility }},
doi = {10.1007/978-3-030-64348-5_5},
volume = {12514},
year = {2020},
}
@article{13770,
author = {Karl, Holger and Kundisch, Dennis and Meyer auf der Heide, Friedhelm and Wehrheim, Heike},
journal = {Business & Information Systems Engineering},
number = {6},
pages = {467--481},
publisher = {Springer},
title = {{A Case for a New IT Ecosystem: On-The-Fly Computing}},
doi = {10.1007/s12599-019-00627-x},
volume = {62},
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{19899,
abstract = {Most existing robot formation problems seek a target formation of a certain
minimal and, thus, efficient structure. Examples include the Gathering
and the Chain-Formation problem. In this work, we study formation problems that
try to reach a maximal structure, supporting for example an efficient
coverage in exploration scenarios. A recent example is the NASA Shapeshifter
project, which describes how the robots form a relay chain along which gathered
data from extraterrestrial cave explorations may be sent to a home base.
As a first step towards understanding such maximization tasks, we introduce
and study the Max-Chain-Formation problem, where $n$ robots are ordered along a
winding, potentially self-intersecting chain and must form a connected,
straight line of maximal length connecting its two endpoints. We propose and
analyze strategies in a discrete and in a continuous time model. In the
discrete case, we give a complete analysis if all robots are initially
collinear, showing that the worst-case time to reach an
$\varepsilon$-approximation is upper bounded by $\mathcal{O}(n^2 \cdot \log
(n/\varepsilon))$ and lower bounded by $\Omega(n^2 \cdot~\log
(1/\varepsilon))$. If one endpoint of the chain remains stationary, this result
can be extended to the non-collinear case. If both endpoints move, we identify
a family of instances whose runtime is unbounded. For the continuous model, we
give a strategy with an optimal runtime bound of $\Theta(n)$. Avoiding an
unbounded runtime similar to the discrete case relies crucially on a
counter-intuitive aspect of the strategy: slowing down the endpoints while all
other robots move at full speed. Surprisingly, we can show that a similar trick
does not work in the discrete model.},
author = {Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm},
booktitle = {Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings},
editor = {Devismes , Stéphane and Mittal, Neeraj },
isbn = {978-3-030-64347-8},
pages = {65--80},
publisher = {Springer},
title = {{A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up}},
doi = {10.1007/978-3-030-64348-5_6},
volume = {12514},
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},
}
@phdthesis{8080,
abstract = {This thesis investigates approximate pure Nash equilibria in different game-theoretic models. In such an outcome, no player can improve her objective by more than a given factor through a deviation to another strategy. In the first part, we investigate two variants of Congestion Games in which the existence of pure Nash equilibria is guaranteed through a potential function argument. However, the computation of such equilibria might be hard. We construct and analyze approximation algorithms that enable the computation of states with low approximation factors in polynomial time. To show their guarantees we use sub games among players, bound the potential function values of arbitrary states and exploit a connection between Shapley and proportional cost shares. Furthermore, we apply and analyze sampling techniques for the computation of approximate Shapley values in different settings. In the second part, we concentrate on the existence of approximate pure Nash equilibria in games in which no pure Nash equilibria exist in general. In the model of Coevolving Opinion Formation Games, we bound the approximation guarantees for natural states nearly independent of the specific definition of the players' neighborhoods by applying a concept of virtual costs. For the special case of only one influential neighbor, we even show lower approximation factors for a natural strategy. Then, we investigate a two-sided Facility Location Game among facilities and clients on a line with an objective function consisting of distance and load. We show tight bounds on the approximation factor for settings with three facilities and infinitely many clients. For the general scenario with an arbitrary number of facilities, we bound the approximation factor for two promising candidates, namely facilities that are uniformly distributed and which are paired.},
author = {Feldotto, Matthias},
title = {{Approximate Pure Nash Equilibria in Congestion, Opinion Formation and Facility Location Games}},
doi = {10.17619/UNIPB/1-588},
year = {2019},
}
@inproceedings{10281,
abstract = {Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.},
author = {Feldotto, Matthias and Lenzner, Pascal and Molitor, Louise and Skopalik, Alexander},
booktitle = {Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems},
location = {Montreal QC, Canada},
pages = {1949----1951},
publisher = {International Foundation for Autonomous Agents and Multiagent Systems},
title = {{ From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation}},
year = {2019},
}
@article{13937,
author = {Meyer auf der Heide, Friedhelm},
journal = {Mathematische Semesterberichte},
number = {2},
pages = {259--260},
title = {{Paul Curzon, Peter W. McOwan: Computational Thinking; Die Welt des algorithmischen Denkens – in Spielen, Zaubertricks und Rätseln}},
doi = {10.1007/s00591-019-00249-0},
volume = {66},
year = {2019},
}