Fakultät II - Mathematik und Naturwissenschaften

Institut für Mathematik, Secr. MA 5-2

Technische Universität Berlin

Straße des 17. Juni 136

10623 Berlin

Office: MA 510

Telephone: +49 30 314 23598

Email: (lastname)@math.tu-berlin.de

- Teaching assistant for the lecture
**Computerorientierte Mathematik I**

Winter 23/24 - Teaching assistant for the lecture
**Discrete Optimization (ADM II)**

Summer 2022 - Teaching assistant for the lecture
**Introduction to Linear and Discrete Optimization (ADM I)**

Winter 21/22

**Information Design for Bayesian Networks**

Math+ project AA3-9. Project head: Max Klimm

- Deterministic Impartial Selection with Weights ( )

WINE 2023 – Proc. 19th Conference on Web and Internet Economics.

@inproceedings{CembranoGriesbachStahlberg2023,

author = {Javier Cembrano and Svenja M. Griesbach and Maximilian J. Stahlberg},

title = {Deterministic Impartial Selection with Weights},

booktitle = {WINE 2023 – Proc. 19th Conference on Web and Internet Economics},

year = {to appear},

accepted = {08.09.2023},

}In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is $\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by the subset of size $k$ with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly $1/\lceil 2n/k\rceil$. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of $1/k$ for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to $k$ agents are to be selected, with a loss in the approximation ratio of $1/2$.

- Book Embeddings of $k$-Framed Graphs and $k$-Map Graphs ( )

Discrete Mathematics, 347:113690, 2024.

@article{BekosLozzoGriesbach+2024,

author = {Michael A. Bekos and Giordano Da Lozzo and Svenja M. Griesbach and Martin Gronemann and Fabrizio Montecchiani and Chrysanthi Raftopoulou},

title = {Book Embeddings of $k$-Framed Graphs and $k$-Map Graphs},

journal = {Discrete Mathematics},

volume = {347},

issue = {1},

pages = {113690},

year = {2024},

accepted = {18.08.2023},

}An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. For planar graphs, a fundamental result is due to Yannakakis, who proposed an algorithm to compute embeddings of planar graphs in books with four pages. Our main contribution is a technique that generalizes this result to a much wider family of nonplanar graphs, namely to $k$-map graphs. In fact, our technique can deal with any nonplanar graph having a biconnected skeleton of crossing-free edges whose faces have bounded degree. We prove that this family of graphs has book thickness bounded in $k$, and as a corollary, we obtain the first constant upper bound for the book thickness of optimal $2$-planar graphs.

- Improved Approximation Algorithms for the Expanding Search Problem ( )

ESA 2023 – Proc. 31st European Symposium on Algorithms, pp. 54:1–54:15.

@inproceedings{GriesbachHommelsheimKlimm+2023,

author = {Svenja M. Griesbach and Felix Hommelsheim and Max Klimm and Kevin Schewior},

title = {Improved Approximation Algorithms for the Expanding Search Problem},

booktitle = {ESA 2023 – Proc. 31st European Symposium on Algorithms},

year = {2023},

accepted = {23.06.2023},

pages = {54:1--54:15},

doi = {10.4230/LIPIcs.ESA.2023.54},

}A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a $(2e+\varepsilon)$-approximation for any $\varepsilon > 0$. For the case that all vertices have unit weight, we provide a $2e$-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an $8$-approximation was known.

- Public Signals in Network Congestion Games ( )

EC 2022 – Proc. 23rd ACM Conference on Economics and Computation, pp. 736.

@inproceedings{GriesbachHoeferKlimm+2022,

arxiv = {2205.09823},

author = {Svenja M. Griesbach and Martin Hoefer and Max Klimm and Tim Koglin},

booktitle = {EC 2022 – Proc. 23rd ACM Conference on Economics and Computation},

doi = {10.1145/3490486.3538349},

pages = {736},

title = {Public Signals in Network Congestion Games},

year = {2022},

}We consider a largely untapped potential for the improvement of traffic networks that is rooted in the inherent uncertainty of travel times. Travel times are subject to stochastic uncertainty resulting from various parameters such as weather condition, occurrences of road works, or traffic accidents. Large mobility services have an informational advantage over single network users as they are able to learn traffic conditions from data. A benevolent mobility service may use this informational advantage in order to steer the traffic equilibrium into a favorable direction. The resulting optimization problem is a task commonly referred to as signaling or Bayesian persuasion. Previous work has shown that the underlying signaling problem can be NP-hard to approximate within any non-trivial bounds, even for affine cost functions with stochastic offsets. In contrast, we show that in this case, the signaling problem is easy for many networks. We tightly characterize the class of single-commodity networks, in which full information revelation is always an optimal signaling strategy. Moreover, we construct a reduction from optimal signaling to computing an optimal collection of support vectors for the Wardrop equilibrium. For two states, this insight can be used to compute an optimal signaling scheme. The algorithm runs in polynomial time whenever the number of different supports resulting from any signal distribution is bounded to a polynomial in the input size. Using a cell decomposition technique, we extend the approach to a polynomial-time algorithm for multi-commodity parallel link networks with a constant number of commodities, even when we have a constant number of different states of nature. - Improved Approximation Algorithms for the Expanding Search Problem ( )

Preprint, 2022.

@techreport{GriesbachHommelsheimKlimm+2022,

author = {Svenja M. Griesbach and Felix Hommelsheim and Max Klimm and Kevin Schewior},

title = {Improved Approximation Algorithms for the Expanding Search Problem},

year = {2022},

}A searcher faces a graph with edge costs and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge cost. The goal is to minimize the vertex-weighted sum of the exploration times of all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the case that all vertices have unit weight, we provide a $2e$-approximation. For the general case, we give a $(5e/2+\epsilon)$-approximation for any $\epsilon > 0$. Previously, for both cases only an $8$-approximation was known. Finally, we provide a PTAS for the case of a Euclidean graph.

- Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages ( )

SoCG 2020 – Proc. 36th International Symposium on Computational Geometry, pp. 16:1–16:17.

@inproceedings{BekosDaLozzoGriesbach+2020,

address = {Dagstuhl, Germany},

annote = {Keywords: Book embeddings, Book thickness, Nonplanar graphs, Planar skeleton},

author = {Michael A. Bekos and Giordano Da Lozzo and Svenja M. Griesbach and Martin Gronemann and Fabrizio Montecchiani and Chrysanthi Raftopoulou},

booktitle = {SoCG 2020 – Proc. 36th International Symposium on Computational Geometry},

doi = {10.4230/LIPIcs.SoCG.2020.16},

editor = {Sergio Cabello and Danny Z. Chen},

pages = {16:1--16:17},

title = {Book Embeddings of Nonplanar Graphs with Small Faces in Few Pages},

urn = {urn:nbn:de:0030-drops-121749},

volume = {164},

year = {2020},

}An embedding of a graph in a book, called book embedding, consists of a linear ordering of its vertices along the spine of the book and an assignment of its edges to the pages of the book, so that no two edges on the same page cross. The book thickness of a graph is the minimum number of pages over all its book embeddings. For planar graphs, a fundamental result is due to Yannakakis, who proposed an algorithm to compute embeddings of planar graphs in books with four pages. Our main contribution is a technique that generalizes this result to a much wider family of nonplanar graphs, which is characterized by a biconnected skeleton of crossing-free edges whose faces have bounded degree. Notably, this family includes all 1-planar and all optimal 2-planar graphs as subgraphs. We prove that this family of graphs has bounded book thickness, and as a corollary, we obtain the first constant upper bound for the book thickness of optimal 2-planar graphs.

**Improved Approximation Algorithms for the Expanding Search Problem**, ESA 2023, 05. Sep 23**Improved Approximation Algorithms for the Expanding Search Problem**, International Conference on Operations Research, 30. Aug 23**Information Design for Congestion Games with Unknown Demand**, ICALP Workshop on Congestion Games, 10. Jul 23**Information Design for Bayesian Networks**, Math+ Spotlight Talk Series, 14. Jun 23**Improved Approximation Algorithms for the Expanding Search Problem**, University of Bremen, 27. Apr 23**Public Signals in Network Congestion Games**, 3rd GOR Meeting on Game Theory and Behavioral Management Science, 31. Jan 23**Public Signals in Network Congestion Games**, DMV Annual Meeting 2022, 16. Sep 22**Public Signals in Network Congestion Games**, EC 2022, 13. Jul 22