Fakultät II - Mathematik und Naturwissenschaften

Institut für Mathematik

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
**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

- 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.