01.04. 11:00  virtual  Janosch Ruff  Lovász local lemma meets Kolmogorov Complexity
The talk is about a constructive proof of the Lovász local lemma. A beautiful result on its own, Robin A. Moser presented a remarkable simple algorithm to construct a combinatorial object with properties known to exist thanks to the probabilistic method.
The main focus of the talk is an elegant proof technique that tries to compress the incompressible by a Kolmogorov Complexity argument giving an efficient algorithm as a byproduct. This one is definitely from "The Book". You don't have to believe in God, but you should believe in "The Book".

08.04. 11:00  virtual  BachelorProject TomTom 22/21  Routing Speedup Techniques and Electric Vehicle Overhead Visualisations
In this talk we will present theoretical and practical results of our Bachelor Project in the field of (electric vehicle) routing. Therefore we split our talk in two parts:
In the first part we will talk about the routing speedup technique ArcFlags. In particular we will present our approaches and ideas on explaining this algorithms efficiency using the graph parameter Skeleton Dimension.
In the second part we will then visually compare electric vehicle routing to conventional routing and highlight the differences regarding travel time, costs and detours based on real world data.

22.04. 11:00  virtual  BachelorProject Valyria 22/21  Next Generation RealEstate Valuation
In our bachelors project, we come up with machine learning models to predict the price of real estate objects. In particular, we are aiming to employ transfer learning to improve the prediction quality on domains where only little training data is available. In our presentation, we will explore four concepts that we have been working with over the past semester. We will cover some simple transfer learning ideas for Deep Neural Networks and, in contrast, two techniques to improve DNN performance in a nontransfer context. Following that, we will present two other machine learning algorithms, knearestneighbour and clustering, and how we adapt them to a transfer learning setting.

16.05. 15:00  Belvedere (hybrid)  Aneta Neumann Frank Neumann  Advanced Mine Optimisation under Uncertainty
In many realworld scenarios, it is necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be avoided. A lot of evolutionary multiobjective algorithms have recently been analyzed and applied to submodular problems with different types of constraints. This talk will provide you insights on the impact of uncertainty in advanced mine optimisation on the realword stochastic optimisation problem which allow one to mitigate the uncertainty in the deposit while maintaining high profitability. We will also show the behavior of evolutionary multiobjective algorithms on different submodular chance constrained network problems.
Joint work with Benjamin Doerr, Carola Doerr, Frank Neumann, Simon Ratcliffe, Will Reid, Michael Stimson, Andrew M. Sutton.
Evolutionary Diversity Optimization for Combinatorial Optimization
Diversity plays a crucial role in the area of evolutionary computation. Traditionally, diversity has been used to enable successful crossover operations and prevent premature convergence. In recent years, computing sets of solutions that have structural or behavioural diversity has gained significant attention under the terms evolutionary diversity optimization and quality diversity. This talk will give an overview on this area of research and point out some recent results. We will cover results in the area of evolutionary diversity optimization for the classical traveling salesperson problem and show how quality diversity approaches can be used to achieve better solutions for the traveling thief problem.
Joint work with Viet Anh Do, Mingyu Guo, Aneta Neumann, Adel Nikfarjam

20.05. 11:00  virtual  Elazar Goldberg  Measuring distances between strings, embedding and drunk walks
In many applications one wants to measure distances between a given pair of strings.
The simplest way, called Hamming distance, is scanning the strings and comparing the number of characters by which they differ.
However, in many cases this is not very useful.
Instead, a very common measurement is called edit distance, which counts the minimal number of edit operations needed for converting the first string into the second. Where the set of edit operations consists of character substitution, insertion and deletion.
While the edit distance is more applicable, computationally, it seems to be more challenging.
A possible method to bridge between the measurements is called embedding: This is a mapping that preserves distances.
In this talk I'll show an embedding protocol. The correctness analysis follows by an argument concerning a drunk walk.
No prior knowledge is needed.
The talk is based on a joint work with Michal Koucky and Diptarka Chakraborty.

27.05. 11:00  virtual  Stefan Neubert  Best of: Communication Complexity WS 21/22
When we talk about complexity in TCS, we usually refer to the time complexity of algorithms and problems in a rather simple model. We assume a single processing unit that has access to a lot of fast memory. In practice, this is mostly not the case: huge amounts of data are spread out over distributed systems (or at least separated components of a single system) and must be combined to compute some function on that data. For such systems – but also to analyze streaming algorithms, data structures, VLSI circuits and more – it is interesting to analyze the amount of communication that has to take place to compute that function.
In winter semester 2021 I gave a lecture on the basics of Communication Complexity. This talk gives an overview on the model and some interesting results from the field.

03.06. 11:00  virtual  Ben Bals  Towards Explainable Real Estate Valuation via Evolutionary Algorithms
Human lives are increasingly influenced by algorithms, which therefore need to meet higher standards not only in accuracy but also with respect to explainability. This is especially true for highstakes areas such as real estate valuation. Unfortunately, the
methods applied there often exhibit a tradeoff between accuracy and explainability. One explainable approach is casebased reasoning (CBR), where each decision is supported by specific previous cases. However, such methods can be wanting in accuracy. The unexplainable machine learning approaches are often observed to provide higher accuracy but are not scrutable in their decisionmaking.
In this paper, we apply evolutionary algorithms (EAs) to CBR
predictors in order to improve their performance. In particular, we
deploy EAs to the similarity functions (used in CBR to find
comparable cases), which are fitted to the data set at hand. As a
consequence, we achieve higher accuracy than stateoftheart deep
neural networks (DNNs), while keeping interpretability and
explainability.
These results stem from our empirical evaluation on a large data set
of real estate offers where we compare known similarity functions,
their EAimproved counterparts, and DNNs. Surprisingly, DNNs are
only on par with standard CBR techniques. However, using EAlearned
similarity functions does yield an improved performance.

10.06. 11:00  virtual  Leon Schiller, Simon Wietheger  Embeddings for Geometric Inhomogeneous Random Graphs
Graph embeddings are a popular tool in Network Science and Machine Learning that helps understand the structure of complex networks. For this reason, embeddings have various practical applications such as link prediction, community detection, or visualization. We want to focus on embedding techniques that are in accordance with established generative network models as these models reliably explain the most important properties of realworld networks. One such model, that is likewise used for embeddings, are Hyperbolic Random Graphs (HRGs). However, many existing embedders for HRGs compute embeddings only in twodimensional hyperbolic space which is in contrast to many alternative embedding techniques from Machine Learning where very high dimensional spaces are used in practice. A recent generalization of HRGs are Geometric Inhomogeneous Random Graphs (GIRGs) which allow for adjusting the dimensionality of the ground space while being technically simpler than HRGs but similarly realistic. We investigate the suitability of this model for embedding networks by generalizing embedding techniques of HRGs to this model, whereby we pay special attention to the influence of the dimensionality. Our goal is to answer the question if highdimensional spaces are actually necessary or if a similar performance can be achieved in a lowdimensional space. Besides conducting such practical experiments, we analyze the geometric properties of the GIRG ground space and study the properties of GIRGs as a function of their dimensionality which is often assumed to be constant in the literature. Our preliminary results show that the GIRG model has geometric properties very similar to that of hyperbolic space. This suggests that it is capable of embedding hierarchical structures already in lowdimensional spaces. The goal of the thesis is to find out what GIRGdimensionality can be considered realistic for realworld networks and to make theoretical contributions regarding the properties of GIRGs based on their dimensionality.
Fair Correlation Clustering (on Trees)
Unweighted Correlation Clustering is a clustering problem defined on complete graphs, where every edge is labeled either positively or negatively. The goal is to partition the vertices such that the number of negative edges inside each cluster plus the number of positive edges between different clusters is minimized. While Correlation Clustering is well established, we focus on the rather young area of Fair Correlation Clustering. There, each vertex of the graph is labeled with some color. A partition is called fair if in each of its sets the color ratio is the same as in the whole graph. Fair Correlation Clustering asks for a fair partition that minimizes the correlation clustering cost. With Correlation Clustering itself being NPhard and the fairness constraints putting additional challenges, we start our examinations on instances where the positively labeled edges form a tree, which turns out to be already very challenging.

24.06. 11:00  virtual  Vanja Doskoč, Julian Berger  Maps of Restrictions for Behaviourally Correct Learning
We study classes of formal languages learned by computable learners imposed with certain restrictions. In particular, we compare, for each considered restriction, the set of learnable classes with each other. When requiring the learners to eventually provide a single, correct explanation of the target language (explanatory learning), the literature already provides plenty completed comparisons, depicted in lucid maps.
However, when expecting the learners to provide a semantically correct, but possibly syntactically changing description of the target language (behaviourally correct learning), only partial results are known. We complete these results and provide full behaviourally correct maps for different types of data presentation.
This is joint work with Timo Kötzing.
Greedy Routing Network Creation Games
Network Creation Games are a popular tool to study the emergence of networks created by selfish agents, such as the Internet. As navigation is an important function of many networks and information about the global network structure is not always available locally, we study Network Creation Games that enforce greedy routing. We examine different variants of that model and analyze the existence of equilibria, computational hardness, as well as other game theoretic properties.

29.06. 16:00  virtual  Hans Gawendowicz, Martin Schirneck  Social Distancing Network Creation
During a pandemic people have to find a tradeoff between meeting others and staying safely 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 network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the wellstudied Network Creation Game by Fabrikant et al.~[PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is inline with studies that compare minimization problems with their maximization versions.
We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model's generalization that allows restrictions on the connections that can be formed. As our main result, we prove that SwapMaximal RoutingCost Spanning Trees, an efficiently computable weaker variant of Maximum RoutingCost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that, compared the wellstudied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.
(Joint work with Tobias Friedrich, Pascal Lenzner, and Anna Melnichenko)
Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances
An edge faulttolerant diameter oracle (FDO) is a data structure that preprocesses a graph \(G\) and, when queried with an edge \(e\), returns the (approximate) diameter of the graph \(Ge\) in which that edge failed. The problem of designing FDOs was originally raised by Henzinger et al. [ITCS 2017] and recently received some renewed interest by Bilò et al. [MFCS 2021]. We continue this study with a special focus on space efficienty.
Bilò et al. showed that for every positive integer \(m\) there is a graph \(G\) with \(m\) edges such that every FDO for \(G\) with a stretch better than \(3/2\) requires \(\Omega(m)\) bits of space. The original bound was proven with a lowdiameter graph and we show that this assumption is essential. For graphs with a large diameter of \(\omega(n^{5/6})\), we give a \((1+o(1))\)approximate FDO taking \(\widetilde{O}(n)\) space, braking the \(\Omega(m)\) barrier. This raises the question of the smallest diameter that allows for \(o(m)\)space oracles. We narrow the gap by first extending the \(\Omega(m)\)bound up to diameter \(D = O(n/\sqrt{m})\) and stretch better than \(3/2  1/D\). Conversely, we show that for diameter \(\omega(n^{4/3} \log n/(\varepsilon \sqrt{m}))\), \((1+\varepsilon)\)approximate FDOs with \(o(m)\) space are possible.
Initially, our oracle construction are randomized relying on a sampling technique that is frequently used in fault tolerance. We develop a new framework for efficient derandomization. We show its versatility by not only applying it to our own data structures but also to results from the literature. In particular, we derandomize the distance sensitivity oracle (DSO) by Ren [JCSS 2022] to obtain the first deterministic DSO with subcubic preprocessing time. We also derandomize the SingleSource Shortest Paths algorithm by Chechik and Magen [ICALP 2020].
This is joint work with Davide Bilò, Keerti Choudhary, Sarel Cohen, and Tobias Friedrich.

29.08. 11:00  virtual  Arthur Zahn  Price of Anarchy in Bilateral Network Creation Games
Many realworld networks, like the Internet, are not the result of central design but instead the outcome of the interaction of local agents who are selfishly optimizing for their individual utility. The famous Network Creation Game [Fabrikant et al,, PODC'03] enables us to understand such processes, their dynamics, and their outcomes in the form of equilibrium states. In this model, agents buy incident edges towards other agents for a price of \(\alpha\) and simultaneously try to minimize their buying cost and their total hop distance. Since in many realworld networks, e.g., social networks, consent from both sides is required to maintain a connection, Corbo and Parkes [PODC'05] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that the bilateral version has a significantly higher Price of Anarchy, compared to the unilateral version. This is counterintuitive, since cooperation should help to avoid socially bad states.
We investigate this phenomenon by analyzing the Price of Anarchy of the bilateral version with respect to different solution concepts that allow for various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. We present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation on the quality of tree networks and we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge price.

14.09. 11:00  virtual  Lars Seifert  SinglePeaked Jump Schelling Games
A common phenomenon in urban areas is residential segregation. A wellknown model for its occurrence, even in the absence of discriminatory rules and regulations, are Schelling Games, which are driven purely through the decisions of selfish agents.
In such games, strategic agents of two different types occupy the nodes of a graph. The utility of an agent on a node depends on the fraction of sametype agents in her neighborhood. Then, agents try to maximize their utility either by jumping to empty nodes or swapping locations with other agents, depending on the game's type. In previous work, it is often assumed that the utility is monotonically increasing with the ratio of sametype agents.
Yet, according to surveys, realworld residents prefer diverse neighborhoods.
This motivated the study of Schelling Games in which the utility of an agent is not monotonically increasing but instead singlepeaked at some value \(\Lambda \in (0,1)\). In particular, Bilò et al. (2022) introduced and analysed singlepeaked Swap Schelling Games.
This thesis expands on their work by considering singlepeaked Jump Schelling Games. More specifically, we consider two variants that differ in whether an agent's neighborhood includes the agent herself. Furthermore, we consider the effect of restricting agents to local jumps.
We study the existence of and convergence to equilibria. In particular, we show that even on regular graphs and trees, convergence to equilibria is not guaranteed. For the selfinclusive variant, there are games without equilibria, even on rings. Yet, we still derive a number of conditions under which the existence of equilibria is guaranteed.
Furthermore, we examine the inefficiency of equilibria by bounding the Price of Anarchy and Stability. We give tight bounds for the selfinclusive variant and show that the Price of Anarchy is unbounded for the selfexclusive variant.
Moreover, we prove that deciding if an equilibrium can be reached through improving response dynamics starting from a given initial strategy profile is NPhard.
In addition, we perform experiments on torus grids which indicate that games with integrationoriented agents (\(\Lambda \leq \frac{1}{2}\) ) converge to integrated equilibria.

28.09. 11:00  virtual  Rishikesh Gajjala  A graph theoretic problem from quantum physics
Greenberger–Horne–Zeilinger (GHZ) states are quantum states involving at least three entangled particles. They are of fundamental interest in quantum information theory and have several applications in quantum communication and cryptography. Physicists have been designing various experiments to create highdimensional GHZ states using multiple entangled particles. Krenn et al. have discovered a bridge connecting this problem to theoretical computer science. Namely, they found that an experiment to create a new GHZ state is associated with an edgecoloured edgeweighted multigraph having certain properties. A graphtheoretic parameter named matching index can be defined for the corresponding unweighted uncoloured simple graph. The edge weights and the edge colourings are parameters which can be tuned by the experiment designer. The maximum dimension of the GHZ state achievable for an experiment by tuning the edge weights and the edge colourings equals the matching index of the corresponding unweighted uncoloured simple graph.
Krenn conjectured that the matching index of a graph nonisomorphic to $K_4$ is at most $2$, and that of $K_4$ is $3$. This problem is surprisingly hard to prove, even on graphs as small as $K_4$. Though it was shown with extensive use of computers that the matching index of $K_4$ is $3$, an analytical proof is not known for this fact. In this talk I will present a bound on the dimension which a GHZ state can achieve with respect to the number of entangled particles when bicoloured edges are not allowed. For the more general case, we resolve Krenn’s conjecture for some graph classes.
Based on joint works with L. Sunil Chandran
Some results of the results I present are available here.

11.10. 13:30  K2.03  Leila ParsaeiMajd  Correlation Clustering
Clustering is the problem of partitioning data points into clusters based on their similarity. Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance, and the main objective in this type of clustering is to minimize the sum of the number of negative edges inside each cluster and the number of positive edges between each pair of clusters. For the first time, correlation clustering was introduced by Bansal, Blum, and Chawla in 2004, and has many applications in different fields such as social networks, financial networks, and image segmentation.
In this talk, we present three algorithms. The first one is a local search to separate the vertices into two parts, and the second and third one are related to the general case. Also, by considering two conditions on the signed graphs we can obtain a 2approximation. The best results obtained in correlation clustering are a 3approximation for signed kpartite graphs (2015), and a 1.994approximation for signed complete graphs (2022).

14.10. 13:15  K2.03  Leon Schiller  Cliques in HighDimensional Geometric Inhomogeneous Random Graphs
Scalefree network models are of great interest for the development and the analysis of algorithms for realworld applications. One of the most famous such models are Hyperbolic Random Graphs (HRGs), which were recently generalized with the introduction of Geometric Inhomogeneous Random Graphs (GIRGs) where the main novelty is that the dimension D of the underlying metric space is adjustable.
Nevertheless, little is known about how the properties of this model depend on D. We make progress towards better understanding this behavior and our contribution in this regard is threefold. Firstly, we investigate the clustering coefficient of the model, which is one of the main characteristics by which geometric and nongeometric models differ and which describes the tendency of a network to form small, densely connected subgrpahs. We derive upper bounds on this quantity that hold with high probability and show that clustering decays exponentially with D. Secondly, we study the case where D is nonconstant. We show that the model converges its nongeometric counterpart, the ChungLu graph, if D > \infty. Furthermore, we study the clique number (i.e. the size of the largest clique) and the expected number of cliques in the model. Here, we distinguish the lowdimensional case, where D grows slower than log(N), and the highdimensional case where D grows as log^{2+\epsilon}(N) or faster. While the number and size of the contained cliques clearly distinguish GIRGs from ChungLu graphs in the lowdimensional regime, we show that, in the highdimensional case, they behave like that of a ChungLu graph. In this regard, we also study the problem of detecting if a graph has some underlying geometric structure by means of statistical testing. We show that the recently proposed weighted triangle statistic acomplishes this taks in the lowdimensional case but fails in the highdimensional regime. We also propose a simple test statistic to recover the dimension D in the lowdimensional case. Lastly, we propose algorithmic approaches for embedding networks in our model. Here, we give a simple algorithm for embedding trees, generalize the relationship between the GIRG model and hyperbolic geometry, and show how to use this connection for applying existing embedding techniques from the literature 