@unpublished{16450, abstract = {{In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate all robots within a $2\times 2$-sized area that is not known beforehand. Two robots are connected if they are vertical or horizontal neighbors on the grid. The locality constraint means that no global control, no compass, no global communication and only local vision is available; hence, a robot can only see its grid neighbors up to a constant $L_1$-distance, which also limits its movements. A robot can move to one of its eight neighboring grid cells and if two or more robots move to the same location they are \emph{merged} to be only one robot. The locality constraint is the significant challenging issue here, since robot movements must not harm the (only globally checkable) swarm connectivity. For solving the gathering problem, we provide a synchronous algorithm -- executed by every robot -- which ensures that robots merge without breaking the swarm connectivity. In our model, robots can obtain a special state, which marks such a robot to be performing specific connectivity preserving movements in order to allow later merge operations of the swarm. Compared to the grid, for gathering in the Euclidean plane for the same robot and time model the best known upper bound is $\mathcal{O}(n^2)$.}}, author = {{Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, booktitle = {{arXiv:1602.03303}}, title = {{{Asymptotically Optimal Gathering on a Grid}}}, year = {{2016}}, } @inproceedings{157, abstract = {{Consider a scheduling problem in which a set of jobs with interjob communication, canonically represented by a weighted tree, needs to be scheduled on m parallel processors interconnected by a shared communication channel. In each time step, we may allow any processed job to use a certain capacity of the channel in order to satisfy (parts of) its communication demands to adjacent jobs processed in parallel. The goal is to find a schedule that minimizes the makespan and in which communication demands of all jobs are satisfied.We show that this problem is NP-hard in the strong sense even if the number of processors and the maximum degree of the underlying tree is constant.Consequently, we design and analyze simple approximation algorithms with asymptotic approximation ratio 2-2/m in case of paths and a ratio of 5/2 in case of arbitrary trees.}}, author = {{König, Jürgen and Mäcker, Alexander and Meyer auf der Heide, Friedhelm and Riechers, Sören}}, booktitle = {{Proceedings of the 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA)}}, pages = {{563----577}}, title = {{{Scheduling with Interjob Communication on Parallel Processors}}}, doi = {{10.1007/978-3-319-48749-6_41}}, year = {{2016}}, } @proceedings{163, editor = {{Dressler, Falko and Meyer auf der Heide, Friedhelm}}, location = {{Paderborn, Germany}}, publisher = {{ACM}}, title = {{{Proceedings of the 17th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc)}}}, doi = {{10.1145/2942358}}, year = {{2016}}, } @inproceedings{16351, abstract = {{Defining, measuring, and comparing the quality and efficiency of rendering algorithms in computer graphics is a demanding challenge: quality measures are often application specific and efficiency is strongly influenced by properties of the rendered scene and the used hardware. We survey the currently employed evaluation methods for AQ1 the development process of rendering algorithms. Then, we present our PADrend framework, which supports systematic and flexible development, evaluation, adaptation, and comparison of rendering algorithms, and provides a comfortable and easy-to-use platform for developers of rendering algorithms. The system includes a new evaluation method to improve the objectivity of experimental evaluations of rendering algorithms. }}, author = {{Fischer, Matthias and Jähn, Claudius and Meyer auf der Heide, Friedhelm and Petring, Ralf}}, booktitle = {{Algorithm Engineering}}, editor = {{Kliemann, Lasse and Sanders, Peter}}, pages = {{226--244}}, publisher = {{Springer}}, title = {{{Algorithm Engineering Aspects of Real-Time Rendering Algorithms}}}, doi = {{10.1007/978-3-319-49487-6_7 }}, volume = {{9220}}, year = {{2016}}, } @inproceedings{16358, author = {{Li, Shouwei and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}}, booktitle = {{Algorithms for Sensor Systems, Proceedings of the 12th International Symposium on Algorithms and Experiments for Wireless Sensor Networks (ALGOSENSORS)}}, publisher = {{Springer}}, title = {{{The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots}}}, doi = {{10.1007/978-3-319-53058-1_5 }}, year = {{2016}}, } @inproceedings{16359, abstract = {{In this paper, we solve the local gathering problem of a swarm of n indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time O(n) in the fully synchronous FSYNC time model. Given an arbitrarily distributed (yet connected) swarm of robots, the gathering problem on the grid is to locate all robots within a 2x2- sized area that is not known beforehand. Two robots are connected if they are vertical or horizontal neighbors on the grid. The locality constraint means that no global control, no compass, no global communication and only local vision is available; hence, a robot can only see its grid neighbors up to a constant L1-distance, which also limits its movements. A robot can move to one of its eight neighboring grid cells and if two or more robots move to the same location they are merged to be only one robot. The locality constraint is the significant challenging issue here, since robot move- ments must not harm the (only globally checkable) swarm connectivity. For solving the gathering problem, we provide a synchronous algorithm { executed by every robot { which ensures that robots merge without breaking the swarm con- nectivity. In our model, robots can obtain a special state, which marks such a robot to be performing specific connec- tivity preserving movements in order to allow later merge operations of the swarm. Compared to the grid, for gath- ering in the Euclidean plane for the same robot and time model the best known upper bound is O(n^2).}}, author = {{Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 28th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)}}, pages = {{301--312}}, publisher = {{ACM}}, title = {{{Asymptotically Optimal Gathering on a Grid}}}, doi = {{10.1145/2935764.2935789}}, year = {{2016}}, } @inproceedings{16360, abstract = {{We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of n indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid and must keep this connectivity during the whole process of their gathering. Connectivity means, that neighboring robots of the chain need to be positioned at the same or neighboring points of the grid. In our model, gathering means to keep shortening the chain until the robots are located inside a 2*2 subgrid. Our model is completely local (no global control, no global coordinates, no compass, no global communication or vision, ...). Each robot can only see its next constant number of left and right neighbors on the chain. This fixed constant is called the viewing path length. All its operations and detections are restricted to this constant number of robots. Other robots, even if located at neighboring or the same grid point cannot be detected. Only based on the relative positions of its detectable chain neighbors, a robot can decide to obtain a certain state. Based on this state and their local knowledge, the robots do local modifications to the chain by moving to neighboring grid points without breaking the chain. These modifications are performed without the knowledge whether they lead to a global progress or not. We assume the fully synchronous FSYNC model. For this problem, we present a gathering algorithm which needs linear time. This result generalizes a result, where an open chain with specified distinguishable (and fixed) endpoints is considered. }}, author = {{Abshoff, Sebastian and Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 30th International Parallel and Distributed Processing Symposium (IPDPS)}}, pages = {{689--699}}, publisher = {{IEEE}}, title = {{{Gathering a Closed Chain of Robots on a Grid}}}, doi = {{10.1109/IPDPS.2016.51}}, year = {{2016}}, } @inproceedings{16364, author = {{Macker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}}, booktitle = {{2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS)}}, isbn = {{9781509021406}}, title = {{{On Competitive Algorithms for Approximations of Top-k-Position Monitoring of Distributed Streams}}}, doi = {{10.1109/ipdps.2016.91}}, year = {{2016}}, } @unpublished{16396, abstract = {{We consider a scheduling problem where machines need to be rented from the cloud in order to process jobs. There are two types of machines available which can be rented for machine-type dependent prices and for arbitrary durations. However, a machine-type dependent setup time is required before a machine is available for processing. Jobs arrive online over time, have machine-type dependent sizes and have individual deadlines. The objective is to rent machines and schedule jobs so as to meet all deadlines while minimizing the rental cost. Since we observe the slack of jobs to have a fundamental influence on the competitiveness, we study the model when instances are parameterized by their (minimum) slack. An instance is called to have a slack of $\beta$ if, for all jobs, the difference between the job's release time and the latest point in time at which it needs to be started is at least $\beta$. While for $\beta < s$ no finite competitiveness is possible, our main result is an $O(\frac{c}{\varepsilon} + \frac{1}{\varepsilon^3})$-competitive online algorithm for $\beta = (1+\varepsilon)s$ with $\frac{1}{s} \leq \varepsilon \leq 1$, where $s$ and $c$ denotes the largest setup time and the cost ratio of the machine-types, respectively. It is complemented by a lower bound of $\Omega(\frac{c}{\varepsilon})$.}}, author = {{Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören}}, booktitle = {{arXiv:1609.01184}}, title = {{{Cost-efficient Scheduling on Machines from the Cloud}}}, year = {{2016}}, } @article{139, abstract = {{We consider online optimization problems in which certain goods have to be acquired in order to provide a service or infrastructure. Classically, decisions for such problems are considered as final: one buys the goods. However, in many real world applications, there is a shift away from the idea of buying goods. Instead, leasing is often a more flexible and lucrative business model. Research has realized this shift and recently initiated the theoretical study of leasing models (Anthony and Gupta in Proceedings of the integer programming and combinatorial optimization: 12th International IPCO Conference, Ithaca, NY, USA, June 25–27, 2007; Meyerson in Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), 23–25 Oct 2005, Pittsburgh, PA, USA, 2005; Nagarajan and Williamson in Discret Optim 10(4):361–370, 2013) We extend this line of work and suggest a more systematic study of leasing aspects for a class of online optimization problems. We provide two major technical results. We introduce the leasing variant of online set multicover and give an O(log(mK)logn)-competitive algorithm (with n, m, and K being the number of elements, sets, and leases, respectively). Our results also imply improvements for the non-leasing variant of online set cover. Moreover, we extend results for the leasing variant of online facility location. Nagarajan and Williamson (Discret Optim 10(4):361–370, 2013) gave an O(Klogn)-competitive algorithm for this problem (with n and K being the number of clients and leases, respectively). We remove the dependency on n (and, thereby, on time). In general, this leads to a bound of O(lmaxloglmax) (with the maximal lease length lmax). For many natural problem instances, the bound improves to O(K2).}}, author = {{Abshoff, Sebastian and Kling, Peter and Markarian, Christine and Meyer auf der Heide, Friedhelm and Pietrzyk, Peter }}, journal = {{Journal of Combinatorial Optimization}}, number = {{4}}, pages = {{ 1197----1216}}, publisher = {{Springer}}, title = {{{Towards the price of leasing online}}}, doi = {{10.1007/s10878-015-9915-5}}, year = {{2016}}, } @inproceedings{143, abstract = {{We present an efficient parallel algorithm for the general Monotone Circuit Value Problem (MCVP) with n gates and an underlying graph of bounded genus k. Our algorithm generalizes a recent result by Limaye et al. who showed that MCVP with toroidal embedding (genus 1) is in NC when the input contains a toroidal embedding of the circuit. In addition to extending this result from genus 1 to any bounded genus k, and unlike the work reported by Limaye et al., we do not require a precomputed embedding to be given. Most importantly, our results imply that given a P-complete problem, it is possible to find an algorithm that makes the problem fall into NC by fixing one or more parameters. Hence, we deduce the interesting analogy: Fixed Parameter Parallelizable (FPP) is with respect to P-complete what Fixed Parameter Tractable (FPT) is with respect to NP-complete. Similar work that uses treewidth as parameter was also presented by Elberfeld et al. in [6].}}, author = {{Abu-Khzam, Faisal N. and Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}}, booktitle = {{Proceedings of the 22nd International Conference on Computing and Combinatorics (COCOON)}}, pages = {{92--102}}, title = {{{The Monotone Circuit Value Problem with Bounded Genus Is in NC}}}, doi = {{10.1007/978-3-319-42634-1_8}}, year = {{2016}}, } @book{28325, editor = {{Gausemeier, Jürgen and Grafe, Michael and Meyer auf der Heide, Friedhelm}}, publisher = {{Verlagsschriftenreihe des Heinz Nixdorf Instituts; , 12. Paderborner Workshop Augmented & Virtual Reality in der Produktentstehung}}, title = {{{Augmented & Virtual Reality in der Produktentstehung: Grundlagen, Methoden und Werkzeuge; Interaktions- und Visualisierungstechniken, Virtual Prototyping intelligenter technischer Systeme mit AR/VR}}}, volume = {{Band 342 }}, year = {{2015}}, } @book{26229, author = {{Gausemeier, Jürgen and Grafe, Michael and Meyer auf der Heide, Friedhelm}}, publisher = {{Verlagsschriftenreihe des Heinz Nixdorf Instituts, Paderborn}}, title = {{{Augmented & Virtual Reality in der Produktentstehung: Grundlagen, Methoden und Werkzeuge; Interaktions- und Visualisierungstechniken, Virtual Prototyping intelligenter technischer Systeme mit AR/VR }}}, volume = {{342}}, year = {{2015}}, } @inproceedings{266, abstract = {{Many markets have seen a shift from the idea of buying and moved to leasing instead. Arguably, the latter has been the major catalyst for their success. Ten years ago, research realized this shift and initiated the study of "online leasing problems" by introducing leasing to online optimization problems. Resources required to provide a service in an "online leasing problem" are no more bought but leased for different durations. In this paper, we provide an overview of results that contribute to the understanding of "online resource leasing problems". }}, author = {{Markarian, Christine and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC)}}, pages = {{343--344}}, title = {{{Online Resource Leasing}}}, doi = {{10.1145/2767386.2767454}}, year = {{2015}}, } @inproceedings{274, abstract = {{Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n,m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3/2.}}, author = {{Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören}}, booktitle = {{Algorithms and Data Structures: 14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015. Proceedings}}, editor = {{Dehne, Frank and Sack, Jörg Rüdiger and Stege, Ulrike}}, pages = {{542----553}}, title = {{{Non-preemptive Scheduling on Machines with Setup Times}}}, doi = {{10.1007/978-3-319-21840-3_45}}, year = {{2015}}, } @book{17431, editor = {{Gausemeier, Jürgen and Grafe, Michael and Meyer auf der Heide, Friedhelm}}, publisher = {{Verlagsschriftenreihe des Heinz Nixdorf Instituts}}, title = {{{Augmented & Virtual Reality in der Produktentstehung: Grundlagen, Methoden und Werkzeuge; Interaktions- und Visualisierungstechniken, Virtual Prototyping intelligenter technischer Systeme mit AR/VR}}}, volume = {{342}}, year = {{2015}}, } @inproceedings{240, abstract = {{We consider online leasing problems in which demands arrive over time and need to be served by leasing resources. We introduce a new model for these problems such that a resource can be leased for K different durations each incurring a different cost (longer leases cost less per time unit). Each demand i can be served anytime between its arrival ai and its deadline ai+di by a leased resource. The objective is to meet all deadlines while minimizing the total leasing costs. This model is a natural generalization of Meyerson’s ParkingPermitProblem (FOCS 2005) in which di=0 for all i. We propose an online algorithm that is Θ(K+dmaxlmin)-competitive where dmax and lmin denote the largest di and the shortest available lease length, respectively. We also extend the SetCoverLeasing problem by deadlines and give a competitive online algorithm which also improves on existing solutions for the original SetCoverLeasing problem.}}, author = {{Li, Shouwei and Mäcker, Alexander and Markarian, Christine and Meyer auf der Heide, Friedhelm and Riechers, Sören}}, booktitle = {{Proceedings of the 21st Annual International Computing and Combinatorics Conference (COCOON)}}, pages = {{277----288}}, title = {{{Towards Flexible Demands in Online Leasing Problems}}}, doi = {{10.1007/978-3-319-21398-9_22}}, year = {{2015}}, } @unpublished{16449, abstract = {{We consider the following variant of the two dimensional gathering problem for swarms of robots: Given a swarm of $n$ indistinguishable, point shaped robots on a two dimensional grid. Initially, the robots form a closed chain on the grid and must keep this connectivity during the whole process of their gathering. Connectivity means, that neighboring robots of the chain need to be positioned at the same or neighboring points of the grid. In our model, gathering means to keep shortening the chain until the robots are located inside a $2\times 2$ subgrid. Our model is completely local (no global control, no global coordinates, no compass, no global communication or vision, \ldots). Each robot can only see its next constant number of left and right neighbors on the chain. This fixed constant is called the \emph{viewing path length}. All its operations and detections are restricted to this constant number of robots. Other robots, even if located at neighboring or the same grid point cannot be detected. Only based on the relative positions of its detectable chain neighbors, a robot can decide to obtain a certain state. Based on this state and their local knowledge, the robots do local modifications to the chain by moving to neighboring grid points without breaking the chain. These modifications are performed without the knowledge whether they lead to a global progress or not. We assume the fully synchronous $\mathcal{FSYNC}$ model. For this problem, we present a gathering algorithm which needs linear time. This result generalizes the result from \cite{hopper}, where an open chain with specified distinguishable (and fixed) endpoints is considered.}}, author = {{Abshoff, Sebastian and Cord-Landwehr, Andreas and Fischer, Matthias and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, booktitle = {{arXiv:1510.05454}}, title = {{{Gathering a Closed Chain of Robots on a Grid}}}, year = {{2015}}, } @unpublished{16452, abstract = {{We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The corresponding graph theoretic problem seeks a strongly connected dominating-absorbent set of minimum cardinality in a digraph. A subset of nodes in a digraph is a strongly connected dominating-absorbent set if the subgraph induced by these nodes is strongly connected and each node in the graph is either in the set or has both an in-neighbor and an out-neighbor in it. Distributed algorithms for this problem are of practical significance due to the dynamic nature of ad-hoc networks. We present a first distributed approximation algorithm, with a constant approximation factor and O(Diam) running time, where Diam is the diameter of the graph. Moreover we present a simple heuristic algorithm and conduct an extensive simulation study showing that our heuristic outperforms previously known approaches for the problem.}}, author = {{Abu-Khzam, Faisal N. and Markarian, Christine and Meyer auf der Heide, Friedhelm and Schubert, Michael}}, booktitle = {{arXiv:1510.01866}}, title = {{{Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-Hoc Networks}}}, year = {{2015}}, } @inproceedings{16460, abstract = {{Consider n nodes connected to a single coordinator. Each node receives an individual online data stream of numbers and, at any point in time, the coordinator has to know the k nodes currently observing the largest values, for a given k between 1 and n. We design and analyze an algorithm that solves this problem while bounding the amount of messages exchanged between the nodes and the coordinator. Our algorithm employs the idea of using filters which, intuitively speaking, leads to few messages to be sent, if the new input is "similar" to the previous ones. The algorithm uses a number of messages that is on expectation by a factor of O((log {\Delta} + k) log n) larger than that of an offline algorithm that sets filters in an optimal way, where {\Delta} is upper bounded by the largest value observed by any node.}}, author = {{Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 29th International Parallel and Distributed Processing Symposium (IPDPS)}}, pages = {{357--364}}, publisher = {{IEEE}}, title = {{{Online Top-k-Position Monitoring of Distributed Data Streams}}}, doi = {{10.1109/IPDPS.2015.40}}, year = {{2015}}, }