@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 Symposium on Theoretical Aspects of Computer Science (STACS)},
title = {{A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location}},
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},
}