15.10. 11:00  virtual  Jatin Batra  Improved Approximations for Min Sum Vertex Cover and Generalized Min Sum Set Cover
We study the generalized min sum set cover (GMSSC) problem, wherein given a collection of hyperedges E with arbitrary covering requirements k_e, the goal is to find an ordering of the vertices to minimize the total cover time of the hyperedges; a hyperedge e is considered covered by the first time when k_e many of its vertices appear in the ordering. We give a 4.642 approximation algorithm for GMSSC, coming close to the best possible bound of 4, already for the classical special case (with all k_e=1) of min sum set cover (MSSC) studied by Feige, Lovász and Tetali, and improving upon the previous best known bound of 12.4 due to Im, Sviridenko and van der Zwaan. Our algorithm is based on transforming the LP solution by a suitable kernel and applying randomized rounding. This also gives an LPbased 4 approximation for MSSC. As part of the analysis of our algorithm, we also derive an inequality on the lower tail of a sum of independent Bernoulli random variables, which might be of independent interest and broader utility.
Another wellknown special case is the min sum vertex cover (MSVC) problem, in which the input hypergraph is a graph and k_e=1, for every edge. We give a 16/9 approximation for MSVC, and show a matching integrality gap for the natural LP relaxation. This improves upon the previous best 1.999946 approximation of Barenholz, Feige and Peleg. Finally, we revisit MSSC and consider the ell_p norm of covertime of the hyperedges. Using a dual fitting argument, we show that the natural greedy algorithm achieves tight, up to NPhardness, approximation guarantees of (p+1)^{1+1/p}, for all p>=1. For p=1, this gives yet another proof of the 4 approximation for MSSC.

29.10. 11:00  virtual  Martin Schirneck  An Optimal Lower Bound for Upper DominationAn upper dominating set in a graph is an inclusionwise minimal dominating set of maximum cardinality.
Berge and Duchet in 1975 showed how to compute the upper domination number \(k^*\) of an \(n\)vertex graph in time \(O(n^{k^*+3})\).
Conversely, Bazgan et al. [TCS 2018] proved that \(k^*\) cannot be computed in time \(f(k^*) n^{o(\sqrt{k^*})}\)
for any computable function \(f\), unless the Exponential Time Hypothesis (ETH) fails.
Very recently and independently of each other, Araújo et al. [ArXiv 2021] as well as Dublois, Lampis, and Paschos [CIAC 2021] closed this gap
in ruling out any algorithm running in time \(f(k^*) n^{o(k^*)}\) under ETH.
In the talk, we walk through the proof of Araújo et al. and discuss some open problems regarding the transversal rank of a hypergraph.

5.11. 11:00  virtual  Nico Klodt  Epidemic thresholds for the SIS contact processon stars and clique stars
Contact processes are used to model various phenomena such as the spread of viruses and information through a network. An interesting aspect of a contact process is whether such an 'infection' becomes epidemic or dies out fast. In the SIS model for contact processes, the underlying network is represented by a graph. Each vertex of that graph can either be healthy or infected. Infected vertices can randomly infect their neighbors and become susceptible to the infection again when they heal. The infection rate λ of the process indicates how frequently vertices infect their neighbors. We analyze the survival time of the contact processes depending on λ on stars and clique stars. Clique stars are stars with additional edges, that connect the leaves to multiple cliques of equal size. We show a smooth transition between fast die out and long survival on stars and clique stars and prove that the additional edges of a clique star only impact the survival time notably if the cliques are sufficiently large.

12.11. 10:00  virtual  George Skretas  Actively Dynamic Networks
Dynamic networks is a research area in the field of theoretical computer science tasked with investigating the algorithmic and structural properties of networked systems whose structure changes over time. The algorithmic theory of dynamic networks has risen in popularity due to the multitude of motivating systems that exist such as wireless systems, reconfigurable robotics and biological systems. Most of the work focuses on passively dynamic networks where the dynamic changes are decided by an external scheduler. In the past few years, there is a growing interest in actively dynamic networks where the changes are controlled by the network itself. This allows the network to reconfigure its own structure in order to more efficiently solve different tasks. In this talk, I will briefly introduce different models in the area of actively dynamic networks and continue by focusing on one such model where given an initial network G_s, the goal is to program the nodes with a distributed algorithm in order to reconfigure themselves, via edge activations/deactivations into a target network G_t with a small diameter.

19.11. 11:00  virtual  Hans Gawendowicz  On a Social Distancing Network Creation Game
During a pandemic, people have to find a tradeoff between meeting others and staying at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a gametheoretic network creation model in which selfish agents can form bilateral connections. They benefit from their neighbors but at the same time they want to keep large distances to all the other agents. We look at two variants of this model. In the first variant, there are no restrictions on the connections being formed. In the second variant, we restrict which connections can be formed by introducing a host network defining the possible connections. We characterize optimal and equilibrium networks and give bounds on the Price of Anarchy and Price of Stability. For that, we also introduce the concept of Maximum RoutingCost Spanning Trees, which are spanning trees maximizing the sum of distances between all pairs of nodes.

26.11. 11:00  virtual  Wilhelm Friedemann  Parameterized Complexity of the MaximumWeight Connected Subgraph Problem
While last week was about responsible social distancing, this week will be about the opposite: Hosting the best parties in town. The question is  given a graph representing friendship relationships and a weight function representing each friend's coolness  how to select the group of friends who know each other (are connected) and maximize their summed coolness. Apart from party planning, the problem appears as the 'MaximumWeight Connected Subgraph Problem (MWCS)' in many realworld domains, ranging from biological network analysis, where one wants to find signaling pathways in protein networks, to videoprocessing. In the talk, I present the results of my Master's thesis: a variety of fixedparameter intractability results for the MWCS with respect to the weight and cardinality of the solution. But don't worry, I also provide two FPT algorithms, if you know (due to current pandemic constraints) the maximum number of friends you are allowed to invite.

17.12. 10:00  virtual  Michael Vaichenker, Bashini Mahaarachchi  Hardness and Approximation Results for Fair RatioCut
Fair RatioCut is the problem of finding a partitioning of a colored graph that minimizes the ratio between edges cut and the balance of the partitioning, while containing each color to equal amounts within each resulting partition. The consideration of balance yields often more meaningful partitionings and enables the use of divide and conquer approaches for other problems. Fairness constraints allow to mark sensitive attributes in order to avoid solutions that discriminate with regard to the marked attributes. Despite Fair Clustering being a quite popular topic, graphcut problems were considered only recently under fairness constraints. Fair RatioCut in particular remains mostly a blank slate. My master's thesis contributes first theoretical results for this problem.
In this talk I will give you an overview over my results and showcase a proof that Fair RatioCut with many colors cannot be approximated much better than with a factor of \(n^2\), assuming P ≠ NP.
Applying deep learning methods to create parking space maps using satellite images
Managing vehicle parking infrastructure efficiently is important for cities in order to improve traffic planning and avoid congestions. Having a parking space map helps drivers to know where they can park exactly without needing to roam around until they find a vacant parking spot, which directly helps to reduce the CO2 footprint. One way to create such a parking space map is by analysing the aerial images collected by satellites and applying machine learning methods to extract parking spaces information from them. Thus, we introduce a parking space detection machine learning framework that involves preprocessing of satellite images using image augmentation and fusion techniques, and then using a maskregion based convolutional neural network with a feature pyramid network backbone (Mask RCNN FPN) to detect parking spaces on the processed images. We also propose to use a logistic regression model training process as a component of this pipeline in order to improve the performance of the parking space detection framework. The method we propose can be employed successfully to create parking space maps with precise location information using satellite images.

14.01. 10:00  virtual  Martin Schirneck  FixedParameter Sensitivity Oracles
A distance sensitivity oracle (DSO) with sensitivity \(f\) is a data structure that reports the pairwise distances in a given graph, even when up to \(f\) specified edges fail.
A parameterized decision problem is said to be fixedparameter tractable (FPT) if, on \(n\)vertex graphs with parameter \(k\),
the problem can be solved in time \(O(g(k) \cdot poly(n))\) for some function \(g\).
We combine both ideas and introduce sensitivity oracles for FPT graph problems.
Such data structures preprocess the input in time \(O(g(f,k) \cdot poly(n))\) and
report the answer to the graph problem in the presence of up to \(f\) edge failures
in time significantly faster than merely rerunning the fastest known FPT algorithm on the respective subgraph.
As examples, we present multiple oracles for the \(k\)Path and the Vertex Cover problem, respectively.
Our solutions involve careful tradeoffs between the parameters \(f\) and \(k\),
the space requirement, preprocessing time, as well as the query time.
This is joint work with Davide Bilò, Katrin Casel, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Gregor Lagodzinski, and Simon Wietheger.

21.01. 11:00  virtual  Merlin de la Haye  Wireless Network Creation Games
Wireless networks can be a viable alternative to traditional wireline networks, providing increased flexibility in creating and dynamically modifying the resulting networks.
However, the reliability of communication paths decreases with increasing path lengths. The maximum hop count in a network captures this property nicely, and can be used as an indicator for wireless network stability.
With the tools of Algorithmic Game Theory, we model this setting with selfish agents, and introduce a wireless version of the Network Creation Game by Fabrikant et al., with a focus on bidirectional connections and different limitations on the maximum hop count in the network.
In this setting, we analyze the structure of social optimum and equilibrium networks, focusing on uniformly distributed nodes along a line in 1D.
For these networks, we present construction templates for hop counts limited to 2 and 3 hops, and explain how equilibria for arbitrary hop counts can be constructed.
Regarding the quality of equilibrium networks, we prove a constant Price of Anarchy for the uniform 1D 2hop model, and a sqrt(n) bound for both the Price of Stability and Price of Anarchy in the 3hop case.

28.01. 11:00  virtual  Arthur Zahn  TBA 