Continuous Protocols for Swarm Robotics - Kling, Peter; Meyer auf der Heide, Friedhelm (Distributed Computing by Mobile Entities, Current Research in Moving and Computing)

Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location - Markarian, Christine; Meyer auf der Heide, Friedhelm (Proceedings of the 8th International Conference on Operations Research and Enterprise Systems)

Efficient parallel algorithms for parameterized problems - Abu-Khzam, Faisal N.; Li, Shouwei; Markarian, Christine; Meyer auf der Heide, Friedhelm; Podlipyan, Pavel (Theoretical Computer Science)

A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks - Castenow, Jannik; Kolb, Christina; Scheideler, Christian (Proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO))

From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation - Feldotto, Matthias; Lenzner, Pascal; Molitor, Louise; Skopalik, Alexander (Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems)
Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.

Scheduling Algorithms for Multi-Operation Jobs with Setups on a Single Machine - Pukrop, Simon

Fully-Dynamic Bin Packing with Little Repacking - Feldkord, Björn; Feldotto, Matthias; Gupta, Anupam; Guruganesh, Guru; Kumar, Amit; Riechers, Sören; Wajc, David (45th International Colloquium on Automata, Languages, and Programming (ICALP 2018))
We study the classic bin packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio while repacking items sparingly between updates. Formally, each item i has a movement cost c_i >= 0, and we want to use alpha * OPT bins and incur a movement cost gamma * c_i, either in the worst case, or in an amortized sense, for alpha, gamma as small as possible. We call gamma the recourse of the algorithm. This is motivated by cloud storage applications, where fully-dynamic bin packing models the problem of data backup to minimize the number of disks used, as well as communication incurred in moving file backups between disks. Since the set of files changes over time, we could recompute a solution periodically from scratch, but this would give a high number of disk rewrites, incurring a high energy cost and possible wear and tear of the disks. In this work, we present optimal tradeoffs between number of bins used and number of items repacked, as well as natural extensions of the latter measure.

Online Facility Location with Mobile Facilities - Feldkord, Björn; Meyer auf der Heide, Friedhelm (Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA))

Influence of Stationary Robots on Continuous Robot Formation Problems - Liedtke, David Jan
We consider a group of $n$ autonomous mobile robots of which $m$ are stationary thus cannot move. Robots are represented by points in the Euclidean plane. They have no memory, do not communicate or share a common coordinate system and they move solely based on the positioning of other robots within their limited viewing range of 1. The goal is to gather the robots inside of the convex hull of all stationary robots. A variant of this problem, the general gathering problem, has been studied in various different time models. In this work, we consider a continuous time model, where robots continuously observe their neighbors, compute the next target of movement and move with a speed limit of 1 at any time. Regarding the robots' local strategy, we only study contracting algorithms in which every robot that is positioned on the border of the convex hull of all robots moves into this hull. We present a time bound of $\mathcal{O}(nd)$ for any general contracting algorithms in a configuration with only a single stationary robot. For configurations with more stationary robots, we prove that robots converge against the convex hull of all stationary robots and that no upper bound on the runtime exists. For the specific contracting algorithms Go-To-The-Left, Go-On-Bisector and Go-To-The-Middle, we provide linear time bounds.

Online Connected Dominating Set Leasing - Markarian, Christine (arXiv:1805.02994)
We introduce the Online Connected Dominating Set Leasing problem (OCDSL) in which we are given an undirected connected graph $G = (V, E)$, a set $\mathcal{L}$ of lease types each characterized by a duration and cost, and a sequence of subsets of $V$ arriving over time. A node can be leased using lease type $l$ for cost $c_l$ and remains active for time $d_l$. The adversary gives in each step $t$ a subset of nodes that need to be dominated by a connected subgraph consisting of nodes active at time $t$. The goal is to minimize the total leasing costs. OCDSL contains the Parking Permit Problem~\cite{PPP} as a special subcase and generalizes the classical offline Connected Dominating Set problem~\cite{Guha1998}. It has an $Ω(\log ^2 n + \log |\mathcal{L}|)$ randomized lower bound resulting from lower bounds for the Parking Permit Problem and the Online Set Cover problem~\cite{Alon:2003:OSC:780542.780558,Korman}, where $|\mathcal{L}|$ is the number of available lease types and $n$ is the number of nodes in the input graph. We give a randomized $\mathcal{O}(\log ^2 n + \log |\mathcal{L}| \log n)$-competitive algorithm for OCDSL. We also give a deterministic algorithm for a variant of OCDSL in which the dominating subgraph need not be connected, the Online Dominating Set Leasing problem. The latter is based on a simple primal-dual approach and has an $\mathcal{O}(|\mathcal{L}| · Δ)$-competitive ratio, where $Δ$ is the maximum degree of the input graph.

Disaggregating User Evaluations Using the Shapley Value - Feldotto, Matthias; Haake, Claus-Jochen; Skopalik, Alexander; Stroh-Maraun, Nadja (Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018))
We consider a market where final products or services are compositions of a number of basic services. Users are asked to evaluate the quality of the composed product after purchase. The quality of the basic service influences the performance of the composed services but cannot be observed directly. The question we pose is whether it is possible to use user evaluations on composed services to assess the quality of basic services. We discuss how to combine aggregation of evaluations across users and disaggregation of information on composed services to derive valuations for the single components. As a solution we propose to use the (weighted) average as aggregation device in connection with the Shapley value as disaggregation method, since this combination fulfills natural requirements in our context. In addition, we address some occurring computational issues: We give an approximate solution concept using only a limited number of evaluations which guarantees nearly optimal results with reduced running time. Lastly, we show that a slightly modified Shapley value and the weighted average are still applicable if the evaluation profiles are incomplete.

Towards Flexible Demands in Online Leasing Problems. - Li, Shouwei; Markarian, Christine; Meyer auf der Heide, Friedhelm (Algorithmica)

Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks - Abu-Khzam, Faisal N.; Markarian, Christine; Meyer auf der Heide, Friedhelm; Schubert, Michael (Theory of Computing Systems)

Pick, Pack, & Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets - Hamann, Heiko; Markarian, Christine; Meyer auf der Heide, Friedhelm; Wahby, Mostafa (Ninth International Conference on Fun with Algorithms (FUN))

An Optimal Algorithm for Online Prize-Collecting Node-Weighted Steiner Forest - Markarian, Christine (International Workshop on Combinatorial Algorithms (IWOCA))
We study the Online Prize-collecting Node-weighted Steiner Forest problem (OPC-NWSF) in which we are given an undirected graph \(G=(V, E)\) with \(|V| = n\) and node-weight function \(w: V → \mathcal {R}^+\). A sequence of k pairs of nodes of G, each associated with a penalty, arrives online. OPC-NWSF asks to construct a subgraph H such that each pair \(\{s, t\}\) is either connected (there is a path between s and t in H) or its associated penalty is paid. The goal is to minimize the weight of H and the total penalties paid. The current best result for OPC-NWSF is a randomized \(\mathcal {O}(\log ^4 n)\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014). We improve this by proposing a randomized \(\mathcal {O}(\log n \log k)\)-competitive algorithm for OPC-NWSF, which is optimal up to constant factor since OPC-NWSF has a randomized lower bound of \(\varOmega (\log ^2 n)\) due to Korman [11]. Moreover, our result also implies an improvement for two special cases of OPC-NWSF, the Online Prize-collecting Node-weighted Steiner Tree problem (OPC-NWST) and the Online Node-weighted Steiner Forest problem (ONWSF). In OPC-NWST, there is a distinguished node which is one of the nodes in each pair. In ONWSF, all penalties are set to infinity. The currently best known results for OPC-NWST and ONWSF are a randomized \(\mathcal {O}(\log ^3 n)\)-competitive algorithm due to Hajiaghayi et al. (ICALP 2014) and a randomized \(\mathcal {O}(\log n \log ^2 k)\)-competitive algorithm due to Hajiaghayi et al. (FOCS 2013), respectively.

Scheduling with interjob communication on parallel processors - König, Jürgen; Mäcker, Alexander; Meyer auf der Heide, Friedhelm; Riechers, Sören (Journal of Combinatorial Optimization)

Congestion Games mit gewichteten Strategien - Koop, Samuel

Removing Undesirable Flows by Edge Deletion - Polevoy, Gleb; Trajanovski, Stojan; Grosso, Paola; de Laat, Cees (Combinatorial Optimization and Applications)
Consider mitigating the effects of denial of service or of malicious traffic in networks by deleting edges. Edge deletion reduces the DoS or the number of the malicious flows, but it also inadvertently removes some of the desired flows. To model this important problem, we formulate two problems: (1) remove all the undesirable flows while minimizing the damage to the desirable ones and (2) balance removing the undesirable flows and not removing too many of the desirable flows. We prove these problems are equivalent to important theoretical problems, thereby being important not only practically but also theoretically, and very hard to approximate in a general network. We employ reductions to nonetheless approximate the problem and also provide a greedy approximation. When the network is a tree, the problems are still MAX SNP-hard, but we provide a greedy-based 2l-approximation algorithm, where l is the longest desirable flow. We also provide an algorithm, approximating the first and the second problem within {\$}{\$}2 {\backslash}sqrt{\{} 2{\backslash}left| E {\backslash}right| {\}}{\$}{\$}and {\$}{\$}2 {\backslash}sqrt{\{}2 ({\backslash}left| E {\backslash}right| + {\backslash}left| {\backslash}text {\{}undesirable flows{\}} {\backslash}right| ){\}}{\$}{\$}, respectively, where E is the set of the edges of the network. We also provide a fixed-parameter tractable (FPT) algorithm. Finally, if the tree has a root such that every flow in the tree flows on the path from the root to a leaf, we solve the problem exactly using dynamic programming.
Keywords: flow; Red-Blue Set Cover; Positive-Negative Partial Set Cover; approximation; tree; MAX SNP-hard; root; leaf; dynamic programming; FPT

Measuring the efficiency of SDN mitigations against attacks on computer infrastructures - Koning, R.; de Graaff, B.; Polevoy, Gleb; Meijer, R.; de Laat, C.; Grosso, P. (Future Generation Computer Systems)
Software Defined Networks (SDN) and Network Function Virtualisation (NFV) provide the basis for autonomous response and mitigation against attacks on networked computer infrastructures. We propose a new framework that uses SDNs and NFV to achieve this goal: Secure Autonomous Response Network (SARNET). In a SARNET, an agent running a control loop constantly assesses the security state of the network by means of observables. The agent reacts to and resolves security problems, while learning from its previous decisions. Two main metrics govern the decision process in a SARNET: impact and efficiency; these metrics can be used to compare and evaluate countermeasures and are the building blocks for self-learning SARNETs that exhibit autonomous response. In this paper we present the software implementation of the SARNET framework, evaluate it in a real-life network and discuss the tradeoffs between parameters used by the SARNET agent and the efficiency of its actions.
Keywords: Software defined networks; Network function virtualization; Cyber attacks; Cyber security; Defense efficiency; Overlay networks

Scheduling Shared Continuous Resources on Many-Cores - Althaus, Ernst; Brinkmann, Andre; Kling, Peter; Meyer auf der Heide, Friedhelm; Nagel, Lars; Riechers, Sören; Sgall, Jiri; Suess, Tim (Journal of Scheduling)

A Self-Stabilizing Hashed Patricia Trie - Knollmann, Till; Scheideler, Christian (Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS))
While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, we present a self-stabilizing protocol for a distributed data structure called the hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has a wide area of applications including string matching problems while offering low overhead and efficient operations when embedded on top of a distributed hash table. Especially, longest prefix matching for $x$ can be done in $\mathcal{O}(\log |x|)$ hash table read accesses. We show how to maintain the structure in a self-stabilizing way. Our protocol assures low overhead in a legal state and a total (asymptotically optimal) memory demand of $Θ(d)$ bits, where $d$ is the number of bits needed for storing all keys.
Keywords: Self-Stabilizing; Prefix Search; Distributed Data Structure

Competitive Routing in Hybrid Communication Networks - Jung, Daniel; Kolb, Christina; Scheideler, Christian; Sundermeier, Jannik (Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS))
Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion. In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work.
Keywords: greedy routing; ad hoc networks; convex hulls; c-competitiveness

Brief Announcement: Competitive Routing in Hybrid Communication Networks - Jung, Daniel; Kolb, Christina; Scheideler, Christian; Sundermeier, Jannik (Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA))

Brief Announcement: Communication in Systems of Home Based Mobile Agents - Meyer auf der Heide, Friedhelm; Schaefer, Johannes Sebastian (Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures - SPAA '18)

A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension - Benter, Markus; Knollmann, Till; Meyer auf der Heide, Friedhelm; Setzer, Alexander; Sundermeier, Jannik (Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD))
We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\ The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07). We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range. Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds. Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.
Keywords: Distributed Storage; Multi-Dimensional Range Queries; Peer-to-Peer; Hilbert Curve

Mobile Facility Leasing - Geromel, Marcel

Online Algorithmen für das k-Page Migration Problem - Kolpaczki, Patrick Irenäus

Congestion games with mixed objectives - Feldotto, Matthias; Leder, Lennart; Skopalik, Alexander (Journal of Combinatorial Optimization)
We study a new class of games which generalizes congestion games andits bottleneck variant. We introduce congestion games with mixed objectives to modelnetwork scenarios in which players seek to optimize for latency and bandwidths alike.We characterize the (non-)existence of pure Nash equilibria (PNE), the convergenceof improvement dynamics, the quality of equilibria and show the complexity of thedecision problem. For games that do not possess PNE we give bounds on the approx-imation ratio of approximate pure Nash equilibria.

Pure Nash Equilibria in Robust Congestion Games via Potential Functions - Kemper, Arne

Scenario-driven Strategy Analysis in a n-player Composition Game Model - Nachtigall, Marcel

Learning deterministic bandit behaviour form compositions - Kempf, Jérôme

Local Strategies for Swarm Formations on a Grid - Jung, Daniel
My dissertation deals with the Gathering problem for swarms of n point-shaped robots on a grid, in which all robots of the swarm are supposed to gather at a previously undefined point. Special attention is paid to the strong limitation of robot capabilities. These include in particular the lack of global control, a global compass, global visibility and (global) communication skills. Furthermore, all robots are identical. The robots are given only local abilities. This includes a constant range of vision. The robots all work completely synchronously. In this work we present and analyze three different Gathering strategies in different robot models. We formally prove correctness and total running time: Chapter 4 focuses on minimizing the available robot capabilities. The underlying strategy completes the gathering in O(n^2) time. For the following Chapters 5 and 6, the aim is to optimize the total running time under using only local robot capabilities: We additionally allow a constant-sized memory and a constant number of locally visible statuses (lights, flags). For the strategies of both chapters we show an asymptotically optimal running time of O(n). Unlike in Chapters 4 and 5, we additionally restrict connectivity and vision to an initially given chain connectivity in Chapter 6, where two chain neighbors must have a distance of 1 from each other. A robot can only see and interact with a constant number of its direct chain neighbors.

A Dynamic Distributed Data Structure for Top-k and k-Select Queries - Feldkord, Björn; Malatyali, Manuel; Meyer auf der Heide, Friedhelm (Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications)

Pure Nash equilibria in restricted budget games - Drees, Maximilian; Feldotto, Matthias; Riechers, Sören; Skopalik, Alexander (Journal of Combinatorial Optimization)
In budget games, players compete over resources with finite budgets. For every resource, a player has a specific demand and as a strategy, he chooses a subset of resources. If the total demand on a resource does not exceed its budget, the utility of each player who chose that resource equals his demand. Otherwise, the budget is shared proportionally. In the general case, pure Nash equilibria (NE) do not exist for such games. In this paper, we consider the natural classes of singleton and matroid budget games with additional constraints and show that for each, pure NE can be guaranteed. In addition, we introduce a lexicographical potential function to prove that every matroid budget game has an approximate pure NE which depends on the largest ratio between the different demands of each individual player.

Parallel fixed parameter tractable problems - Li, Shouwei

Leasing with Uncertainty - Markarian, Christine (International Conference on Operations Research (OR))

Scheduling Access to Shared Space in Multi-robot Systems - Khaluf, Yara; Markarian, Christine; Simoens, Pieter; Reina, Andreagiovanni (International Conference on Practical Applications of Agents and Multi-Agent Systems (PAAMS 2017))
Through this study, we introduce the idea of applying scheduling techniques to allocate spatial resources that are shared among multiple robots moving in a static environment and having temporal constraints on the arrival time to destinations. To illustrate this idea, we present an exemplified algorithm that plans and assigns a motion path to each robot. The considered problem is particularly challenging because: (i) the robots share the same environment and thus the planner must take into account overlapping paths which cannot happen at the same time; (ii) there are time deadlines thus the planner must deal with temporal constraints; (iii) new requests arrive without a priori knowledge thus the planner must be able to add new paths online and adjust old plans; (iv) the robot motion is subject to noise thus the planner must be reactive to adapt to online changes. We showcase the functioning of the proposed algorithm through a set of agent-based simulations.

Congestion Games with Complementarities - Feldotto, Matthias; Leder, Lennart; Skopalik, Alexander (Proceedings of the 10th International Conference on Algorithms and Complexity (CIAC))
We study a model of selfish resource allocation that seeks to incorporate dependencies among resources as they exist in in modern networked environments. Our model is inspired by utility functions with constant elasticity of substitution (CES) which is a well-studied model in economics. We consider congestion games with different aggregation functions. In particular, we study $L_p$ norms and analyze the existence and complexity of (approximate) pure Nash equilibria. Additionally, we give an almost tight characterization based on monotonicity properties to describe the set of aggregation functions that guarantee the existence of pure Nash equilibria.

Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games - Feldotto, Matthias; Gairing, Martin; Kotsialou, Grammateia; Skopalik, Alexander (Proceedings of the 13th International Conference on Web and Internet Economics (WINE))
We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to proportional shares) for distributing the total cost of each resource among its users. We focus on the interesting subclass of such games with polynomial resource cost functions and present an algorithm that computes approximate pure Nash equilibria with a polynomial number of strategy updates. Since computing a single strategy update is hard, we apply sampling techniques which allow us to achieve polynomial running time. The algorithm builds on the algorithmic ideas of [7], however, to the best of our knowledge, this is the first algorithmic result on computation of approximate equilibria using other than proportional shares as player costs in this setting. We present a novel relation that approximates the Shapley value of a player by her proportional share and vice versa. As side results, we upper bound the approximate price of anarchy of such games and significantly improve the best known factor for computing approximate pure Nash equilibria in weighted congestion games of [7].

Filtering Undesirable Flows in Networks - Polevoy, Gleb; Trajanovski, Stojan; Grosso, Paola; de Laat, Cees (Combinatorial Optimization and Applications: 11th International Conference, COCOA 2017, Shanghai, China, December 16-18, 2017, Proceedings, Part I)
Keywords: flow; filter; MMSA; set cover; approximation; local ratio algorithm

Reciprocation Effort Games - Polevoy, Gleb; de Weerdt, M.M. (Proceedings of the 29th Benelux Conference on Artificial Intelligence)
Keywords: interaction; reciprocation; contribute; shared effort; curbing; convergence; threshold; Nash equilibrium; social welfare; efficiency; price of anarchy; price of stability

Competition between Cooperative Projects - Polevoy, Gleb; de Weerdt, M.M. (Proceedings of the 29th Benelux Conference on Artificial Intelligence)
Keywords: agents; projects; contribute; shared effort game; competition; quota; threshold; Nash equilibrium; social welfare; efficiency; price of anarchy; price of stability

Gathering Anonymous, Oblivious Robots on a Grid - Fischer, Matthias; Jung, Daniel; Meyer auf der Heide, Friedhelm (arXiv:1702.03400)
We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2× 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved.

Non-Clairvoyant Scheduling to Minimize Max Flow Time on a Machine with Setup Times - Mäcker, Alexander; Malatyali, Manuel; Meyer auf der Heide, Friedhelm; Riechers, Sören (Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA))
Consider a problem in which $n$ jobs that are classified into $k$ types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time.The machine requires a setup taking $s$ time units whenever it switches from processing jobs of one type to jobs of a different type.We consider the problem as an online problem where each job is only known to the scheduler as soon as it arrives and where the processing time of a job only becomes known upon its completion (non-clairvoyance).We are interested in the potential of simple ``greedy-like'' algorithms.We analyze a modification of the FIFO strategy and show its competitiveness to be $Θ(\sqrt{n})$, which is optimal for the considered class of algorithms.For $k=2$ types it achieves a constant competitiveness.Our main insight is obtained by an analysis of the smoothed competitiveness.If processing times $p_j$ are independently perturbed to $\hat p_j = (1+X_j)p_j$, we obtain a competitiveness of $O(σ^{-2} \log^2 n)$ when $X_j$ is drawn from a uniform or a (truncated) normal distribution with standard deviation $σ$.The result proves that bad instances are fragile and ``practically'' one might expect a much better performance than given by the $Ω(\sqrt{n})$-bound.

Modular-Width: An Auxiliary Parameter for Parameterized Parallel Complexity - Abu-Khzam, Faisal N.; Li, Shouwei; Markarian, Christine; Meyer auf der Heide, Friedhelm; Podlipyan, Pavel (Proceedings of the 11th International Workshop on Frontiers in Algorithmics (FAW))
Many graph problems such as maximum cut, chromatic number, hamiltonian cycle, and edge dominating set are known to be fixed-parameter tractable (FPT) when parameterized by the treewidth of the input graphs, but become W-hard with respect to the clique-width parameter. Recently, Gajarský et al. proposed a new parameter called modular-width using the notion of modular decomposition of graphs. They showed that the chromatic number problem and the partitioning into paths problem, and hence hamiltonian path and hamiltonian cycle, are FPT when parameterized by this parameter. In this paper, we study modular-width in parameterized parallel complexity and show that the weighted maximum clique problem and the maximum matching problem are fixed-parameter parallel-tractable (FPPT) when parameterized by this parameter.

Sharing is Caring: Multiprocessor Scheduling with a Sharable Resource - Kling, Peter; Mäcker, Alexander; Riechers, Sören; Skopalik, Alexander (Proceedings of the 29th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA))
We consider a scheduling problem on $m$ identical processors sharing an arbitrarily divisible resource. In addition to assigning jobs to processors, the scheduler must distribute the resource among the processors (e.g., for three processors in shares of 20%, 15%, and 65%) and adjust this distribution over time. Each job $j$ comes with a size $p_j \in \mathbb{R}$ and a resource requirement $r_j > 0$. Jobs do not benefit when receiving a share larger than $r_j$ of the resource. But providing them with a fraction of the resource requirement causes a linear decrease in the processing efficiency. We seek a (non-preemptive) job and resource assignment minimizing the makespan.Our main result is an efficient approximation algorithm which achieves an approximation ratio of $2 + 1/(m-2)$. It can be improved to an (asymptotic) ratio of $1 + 1/(m-1)$ if all jobs have unit size. Our algorithms also imply new results for a well-known bin packing problem with splittable items and a restricted number of allowed item parts per bin.Based upon the above solution, we also derive an approximation algorithm with similar guarantees for a setting in which we introduce so-called tasks each containing several jobs and where we are interested in the average completion time of tasks (a task is completed when all its jobs are completed).

Price Fluctuations in Online Leasing - Feldkord, Björn; Markarian, Christine; Meyer auf der Heide, Friedhelm (Proceedings of the 11th Annual International Conference on Combinatorial Optimization and Applications (COCOA))

Local Algorithms for the Continuous Gathering Problem - Podlipyan, Pavel

Scheduling with Scarce Resources - Riechers, Sören

Cost-efficient Scheduling on Machines from the Cloud - Mäcker, Alexander; Malatyali, Manuel; Meyer auf der Heide, Friedhelm; Riechers, Sören (Journal of Combinatorial Optimization)