The Online Multi-Commodity Facility Location Problem - Castenow, Jannik; Feldkord, Björn; Knollmann, Till; Malatyali, Manuel; Meyer auf der Heide, Friedhelm (Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures)
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 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 \( Ω ( \sqrt{|S|} + \frac{\log n}{\log \log n} ) \) that already holds for simple line metrics. Here, \( n \) is the number of requests. On the other side, we establish a deterministic \( \mathcal{O}(\sqrt{|S|} · \log n) \)-competitive algorithm and a randomized \( \mathcal{O}(\sqrt{|S|} · \frac{\log n}{\log \log n} ) \)-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.
Keywords: Online Multi-Commodity Facility Location; Competitive Ratio; Online Optimization; Facility Location Problem

Brief Announcement: A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up - Castenow, Jannik; Kling, Peter; Knollmann, Till; Meyer auf der Heide, Friedhelm (Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures)

Local Gathering of Mobile Robots in Three Dimensions - Braun, Michael; Castenow, Jannik; Meyer auf der Heide, Friedhelm (Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO))
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 $Θ(n^2)$ 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 $O(Δ · n^{3/2})$ for any three-dimensional contracting strategy, where $Δ$ denotes the diameter of the initial configuration. This comes up to a factor of $\sqrt{n}$ close to the lower bound of $Ω (Δ · n)$ 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.

Mobile Resource Allocation - Feldkord, Björn

Multi-Oracle Coevolutionary Learning of Requirements Specifications from Examples in On-The-Fly Markets - Wever, Marcel Dominik; van Rooijen, Lorijn; Hamann, Heiko (Evolutionary Computation)
In software engineering, the imprecise requirements of a user are transformed to a formal requirements specification during the requirements elicitation process. This process is usually guided by requirements engineers interviewing the user. We want to partially automate this first step of the software engineering process in order to enable users to specify a desired software system on their own. With our approach, users are only asked to provide exemplary behavioral descriptions. The problem of synthesizing a requirements specification from examples can partially be reduced to the problem of grammatical inference, to which we apply an active coevolutionary learning approach. However, this approach would usually require many feedback queries to be sent to the user. In this work, we extend and generalize our active learning approach to receive knowledge from multiple oracles, also known as proactive learning. The ‘user oracle’ represents input received from the user and the ‘knowledge oracle’ represents available, formalized domain knowledge. We call our two-oracle approach the ‘first apply knowledge then query’ (FAKT/Q) algorithm. We compare FAKT/Q to the active learning approach and provide an extensive benchmark evaluation. As result we find that the number of required user queries is reduced and the inference process is sped up significantly. Finally, with so-called On-The-Fly Markets, we present a motivation and an application of our approach where such knowledge is available.

A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks - Castenow, Jannik; Kolb, Christina; Scheideler, Christian (Proceedings of the 21st International Conference on Distributed Computing and Networking (ICDCN))

Gathering Anonymous, Oblivious Robots on a Grid - Castenow, Jannik; Fischer, Matthias; Harbig, Jonas; Jung, Daniel; Meyer auf der Heide, Friedhelm (Theoretical Computer Science)

Approximating Weighted Completion Time for Order Scheduling with Setup Times - Pukrop, Simon; Mäcker, Alexander; Meyer auf der Heide, Friedhelm (Proceedings of the 46th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM))

A Case for a New IT Ecosystem: On-The-Fly Computing - Karl, Holger; Kundisch, Dennis; Meyer auf der Heide, Friedhelm; Wehrheim, Heike (Business & Information Systems Engineering)

Fault Tolerant and Fully Dynamic DFS in Undirected Graphs: Simple Yet Efficient - Baswana, Surender; Gupta, Shiv; Tulsyan, Ayush (44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019))

Approaches for Collaborative Security Defences in Multi Network Environments - Koning, Ralph; Polevoy, Gleb; Meijer, Lydia; de Laat, Cees; Grosso, Paola (2019 6th IEEE International Conference on Cyber Security and Cloud Computing (CSCloud)/ 2019 5th IEEE International Conference on Edge Computing and Scalable Cloud (EdgeCom))
Resolving distributed attacks benefits from collaboration between networks. We present three approaches for the same multi-domain defensive action that can be applied in such an alliance: 1) Counteract Everywhere, 2) Minimize Countermeasures, and 3) Minimize Propagation. First, we provide a formula to compute efficiency of a defense; then we use this formula to compute the efficiency of the approaches under various circumstances. Finally, we discuss how task execution order and timing influence defense efficiency. Our results show that the Minimize Propagation approach is the most efficient method when defending against the chosen attack.
Keywords: computer network security; multinetwork environments; multidomain defensive action; task execution order; timing influence defense efficiency; distributed attacks; collaborative security defence approach; minimize propagation approach; minimize countermeasure approach; counteract everywhere approach; Conferences; Cloud computing; Computer crime; Edge computing; Security; Defense Approaches; Multi-Domain Defense; Collaborative Defense; Defense Algorithms; Computer Networks

Big Data: Sublinear Algorithms for Distributed Data Streams - Malatyali, Manuel

Approximate Pure Nash Equilibria in Congestion, Opinion Formation and Facility Location Games - Feldotto, Matthias
This thesis investigates approximate pure Nash equilibria in different game-theoretic models. In such an outcome, no player can improve her objective by more than a given factor through a deviation to another strategy. In the first part, we investigate two variants of Congestion Games in which the existence of pure Nash equilibria is guaranteed through a potential function argument. However, the computation of such equilibria might be hard. We construct and analyze approximation algorithms that enable the computation of states with low approximation factors in polynomial time. To show their guarantees we use sub games among players, bound the potential function values of arbitrary states and exploit a connection between Shapley and proportional cost shares. Furthermore, we apply and analyze sampling techniques for the computation of approximate Shapley values in different settings. In the second part, we concentrate on the existence of approximate pure Nash equilibria in games in which no pure Nash equilibria exist in general. In the model of Coevolving Opinion Formation Games, we bound the approximation guarantees for natural states nearly independent of the specific definition of the players' neighborhoods by applying a concept of virtual costs. For the special case of only one influential neighbor, we even show lower approximation factors for a natural strategy. Then, we investigate a two-sided Facility Location Game among facilities and clients on a line with an objective function consisting of distance and load. We show tight bounds on the approximation factor for settings with three facilities and infinitely many clients. For the general scenario with an arbitrary number of facilities, we bound the approximation factor for two promising candidates, namely facilities that are uniformly distributed and which are paired.

Scheduling on (Un-)Related Machines with Setup Times - Jansen, Klaus; Maack, Marten; Mäcker, Alexander (Proceedings of the 33rd IEEE International Parallel and Distributed Processing Symposium (IPDPS))

Multi-unit Bilateral Trade - Lazos, Philip; Goldberg, Paul; Skopalik, Alexander; Gerstgrasser, Matthias; de Keijzer, Bart (Proceedings of the Thirty-Third AAAI Conference on Artificial Intelligence (AAAI))
We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1-e) approximation mechanism, matching the best known bounds for the single-item setting.

Managing Multiple Mobile Resources - Feldkord, Björn; Knollmann, Till; Malatyali, Manuel; Meyer auf der Heide, Friedhelm (Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA))

On Scheduling with Setup Times - Mäcker, Alexander

Rendering of Complex Heterogenous Scenes using Progressive Blue Surfels - Brandt, Sascha; Jähn, Claudius; Fischer, Matthias; Meyer auf der Heide, Friedhelm (arXiv:1904.08225)
We present a technique for rendering highly complex 3D scenes in real-time by generating uniformly distributed points on the scene's visible surfaces. The technique is applicable to a wide range of scene types, like scenes directly based on complex and detailed CAD data consisting of billions of polygons (in contrast to scenes handcrafted solely for visualization). This allows to visualize such scenes smoothly even in VR on a HMD with good image quality, while maintaining the necessary frame-rates. In contrast to other point based rendering methods, we place points in an approximated blue noise distribution only on visible surfaces and store them in a highly GPU efficient data structure, allowing to progressively refine the number of rendered points to maximize the image quality for a given target frame rate. Our evaluation shows that scenes consisting of a high amount of polygons can be rendered with interactive frame rates with good visual quality on standard hardware.

The Mobile Server Problem - Feldkord, Björn; Meyer auf der Heide, Friedhelm (ACM Transactions on Parallel Computing (TOPC))

Paul Curzon, Peter W. McOwan: Computational Thinking; Die Welt des algorithmischen Denkens – in Spielen, Zaubertricks und Rätseln - Meyer auf der Heide, Friedhelm (Mathematische Semesterberichte)