TY - CONF
AB - Dominating set based virtual backbones are used for rou-ting in wireless ad-hoc networks. Such backbones receive and transmit messages from/to every node in the network. Existing distributed algorithms only consider undirected graphs, which model symmetric networks with uniform transmission ranges. We are particularly interested in the well-established disk graphs, which model asymmetric networks with non-uniform transmission ranges. 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. We introduce the first distributed algorithm for this problem in disk graphs. The algorithm gives an O(k^4) -approximation ratio and has a runtime bound of O(Diam) where Diam is the diameter of the graph and k denotes the transmission ratio r_{max}/r_{min} with r_{max} and r_{min} being the maximum and minimum transmission range, respectively. Moreover, we apply our algorithm on the subgraph of disk graphs consisting of only bidirectional edges. Our algorithm gives an O(ln k) -approximation and a runtime bound of O(k^8 log^∗ n) , which, for bounded k , is an optimal approximation for the problem, following Lenzen and Wattenhofer’s Ω(log^∗ n) runtime lower bound for distributed constant approximation in disk graphs.
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Schubert, Michael
ID - 563
T2 - Proceedings of the 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics (ALGOSENSORS)
TI - A Distributed Approximation Algorithm for Strongly Connected Dominating-Absorbent Sets in Asymmetric Wireless Ad-Hoc Networks
ER -
TY - CONF
AB - We study two-party communication in the context of directed dynamic networks that are controlled by an adaptive adversary. This adversary is able to change all edges as long as the networks stay strongly-connected in each round. In this work, we establish a relation between counting the total number of nodes in the network and the problem of exchanging tokens between two communication partners which communicate through a dynamic network. We show that the communication problem for a constant fraction of n tokens in a dynamic network with n nodes is at most as hard as counting the number of nodes in a dynamic network with at most 4n+3 nodes. For the proof, we construct a family of directed dynamic networks and apply a lower bound from two-party communication complexity.
AU - Abshoff, Sebastian
AU - Benter, Markus
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 507
T2 - Proceedings of the 17th International Conference on Principles of Distributed Systems (OPODIS)
TI - On Two-Party Communication Through Dynamic Networks
ER -
TY - THES
AB - Diese Arbeit besch{\"a}ftigt sich mit dem Facility Location Problem. Dies ist ein Optimierungsproblem, bei dem festgelegt werden muss an welchen Positionen Ressourcen zur Verf{\"u}gung gestellt werden, so dass diese von Nutzern gut erreicht werden k{\"o}nnen. Es sollen dabei Kosten minimiert werden, die zum einen durch Bereitstellung von Ressourcen und zum anderen durch Verbindungskosten zwischen Nutzern und Ressourcen entstehen. Die Schwierigkeit des Problems liegt darin, dass man einerseits m{\"o}glichst wenige Ressourcen zur Verf{\"u}gung stellen m{\"o}chte, andererseits daf{\"u}r sorgen muss, dass sich Nutzer nicht all zu weit weg von Ressourcen befinden. Dies w{\"u}rde n{\"a}mlich hohe Verbindungskosten nach sich ziehen. Das Facility Location Problem wurde bereits sehr intensiv in vielen unterschiedlichen Varianten untersucht. In dieser Arbeit werden drei Varianten des Problems modelliert und neue Algorithmen f{\"u}r sie entwickelt und bez{\"u}glich ihres Approximationsfaktors und ihrer Laufzeit analysiert. Jede dieser drei untersuchten Varianten hat einen besonderen Schwerpunkt. Bei der ersten Varianten handelt es sich um ein Online Problem, da hier die Eingabe nicht von Anfang an bekannt ist, sondern Schritt f{\"u}r Schritt enth{\"u}llt wird. Die Schwierigkeit hierbei besteht darin unwiderrufliche Entscheidungen treffen zu m{\"u}ssen ohne dabei die Zukunft zu kennen und trotzdem eine zu jeder Zeit gute L{\"o}sung angeben zu k{\"o}nnen. Der Schwerpunkt der zweiten Variante liegt auf Lokalit{\"a}t, die z.B. in Sensornetzwerken von großer Bedeutung ist. Hier soll eine L{\"o}sung verteilt und nur mit Hilfe von lokalen Information berechnet werden. Schließlich besch{\"a}ftigt sich die dritte Variante mit einer verteilten Berechnung, bei welcher nur eine stark beschr{\"a}nkte Datenmenge verschickt werden darf und dabei trotzdem ein sehr guter Approximationsfaktor erreicht werden muss. Die bei der Analyse der Approximationsfaktoren bzw. der Kompetitivit{\"a}t verwendeten Techniken basieren zum großen Teil auf Absch{\"a}tzung der primalen L{\"o}sung mit Hilfe einer L{\"o}sung des zugeh{\"o}rigen dualen Problems. F{\"u}r die Modellierung von Lokalit{\"a}t wird das weitverbreitete LOCAL Modell verwendet. In diesem Modell werden f{\"u}r die Algorithmen subpolynomielle obere Laufzeitschranken gezeigt.
AU - Pietrzyk, Peter
ID - 514
TI - Local and Online Algorithms for Facility Location
ER -
TY - CONF
AB - We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors.Moreover, we provide a tight analysis of the algorithm's competitiveness.Our results generalize and improve upon work by \citet{Chan:2010}, which considers a single speed-scalable processor.Using significantly different techniques, we can not only extend their model to multiprocessors but also prove an enhanced and tight competitive ratio for our algorithm.In our scheduling problem, jobs arrive over time and are preemptable.They have different workloads, values, and deadlines.The scheduler may decide not to finish a job but instead to suffer a loss equaling the job's value.However, to process a job's workload until its deadline the scheduler must invest a certain amount of energy.The cost of a schedule is the sum of lost values and invested energy.In order to finish a job the scheduler has to determine which processors to use and set their speeds accordingly.A processor's energy consumption is power $\Power{s}$ integrated over time, where $\Power{s}=s^{\alpha}$ is the power consumption when running at speed $s$.Since we consider the online variant of the problem, the scheduler has no knowledge about future jobs.This problem was introduced by~\citet{Chan:2010} for the case of a single processor.They presented an online algorithm which is $\alpha^{\alpha}+2e\alpha$-competitive.We provide an online algorithm for the case of multiple processors with an improved competitive ratio of $\alpha^{\alpha}$.
AU - Kling, Peter
AU - Pietrzyk, Peter
ID - 499
T2 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Profitable Scheduling on Multiple Speed-Scalable Processors
ER -
TY - GEN
ED - Flocchini, Paola
ED - Gao, Jie
ED - Kranakis, Evangelos
ED - Meyer auf der Heide, Friedhelm
ID - 558
TI - Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics
VL - 8243
ER -
TY - CONF
AB - We consider an online facility location problem where clients arrive over time and their demands have to be served by opening facilities and assigning the clients to opened facilities. When opening a facility we must choose one of K different lease types to use. A lease type k has a certain lease length lk. Opening a facility i using lease type k causes a cost of f k i and ensures that i is open for the next lk time steps. In addition to costs for opening facilities, we have to take connection costs ci j into account when assigning a client j to facility i. We develop and analyze the first online algorithm for this problem that has a time-independent competitive factor.This variant of the online facility location problem was introduced by Nagarajan and Williamson [7] and is strongly related to both the online facility problem by Meyerson [5] and the parking permit problem by Meyerson [6]. Nagarajan and Williamson gave a 3-approximation algorithm for the offline problem and an O(Klogn)-competitive algorithm for the online variant. Here, n denotes the total number of clients arriving over time. We extend their result by removing the dependency on n (and thereby on the time). In general, our algorithm is O(lmax log(lmax))-competitive. Here lmax denotes the maximum lease length. Moreover, we prove that it is O(log2(lmax))-competitive for many “natural” cases. Such cases include, for example, situations where the number of clients arriving in each time step does not vary too much, or is non-increasing, or is polynomially bounded in lmax.
AU - Meyer auf der Heide, Friedhelm
AU - Pietrzyk, Peter
AU - Kling, Peter
ID - 636
T2 - Proceedings of the 19th International Colloquium on Structural Information & Communication Complexity (SIROCCO)
TI - An Algorithm for Facility Leasing
ER -
TY - CONF
AB - We present and study a new model for energy-aware and profit-oriented scheduling on a single processor.The processor features dynamic speed scaling as well as suspension to a sleep mode.Jobs arrive over time, are preemptable, and have different sizes, values, and deadlines.On the arrival of a new job, the scheduler may either accept or reject the job.Accepted jobs need a certain energy investment to be finished in time, while rejected jobs cause costs equal to their values.Here, power consumption at speed $s$ is given by $P(s)=s^{\alpha}+\beta$ and the energy investment is power integrated over time.Additionally, the scheduler may decide to suspend the processor to a sleep mode in which no energy is consumed, though awaking entails fixed transition costs $\gamma$.The objective is to minimize the total value of rejected jobs plus the total energy.Our model combines aspects from advanced energy conservation techniques (namely speed scaling and sleep states) and profit-oriented scheduling models.We show that \emph{rejection-oblivious} schedulers (whose rejection decisions are not based on former decisions) have – in contrast to the model without sleep states – an unbounded competitive ratio.It turns out that the jobs' value densities (the ratio between a job's value and its work) are crucial for the performance of such schedulers.We give an algorithm whose competitiveness nearly matches the lower bound w.r.t\text{.} the maximum value density.If the maximum value density is not too large, the competitiveness becomes $\alpha^{\alpha}+2e\alpha$.Also, we show that it suffices to restrict the value density of low-value jobs only.Using a technique from \cite{Chan:2010} we transfer our results to processors with a fixed maximum speed.
AU - Cord-Landwehr, Andreas
AU - Kling, Peter
AU - Mallmann Trenn, Fredrik
ED - Even, Guy
ED - Rawitz, Dror
ID - 580
T2 - Proceedings of the 1st Mediterranean Conference on Algorithms (MedAlg)
TI - Slow Down & Sleep for Profit in Online Deadline Scheduling
ER -
TY - JOUR
AB - A left-to-right maximum in a sequence of n numbers s_1, …, s_n is a number that is strictly larger than all preceding numbers. In this article we present a smoothed analysis of the number of left-to-right maxima in the presence of additive random noise. We show that for every sequence of n numbers s_i ∈ [0,1] that are perturbed by uniform noise from the interval [-ε,ε], the expected number of left-to-right maxima is Θ(&sqrt;n/ε + log n) for ε>1/n. For Gaussian noise with standard deviation σ we obtain a bound of O((log3/2 n)/σ + log n).We apply our results to the analysis of the smoothed height of binary search trees and the smoothed number of comparisons in the quicksort algorithm and prove bounds of Θ(&sqrt;n/ε + log n) and Θ(n/ε+1&sqrt;n/ε + n log n), respectively, for uniform random noise from the interval [-ε,ε]. Our results can also be applied to bound the smoothed number of points on a convex hull of points in the two-dimensional plane and to smoothed motion complexity, a concept we describe in this article. We bound how often one needs to update a data structure storing the smallest axis-aligned box enclosing a set of points moving in d-dimensional space.
AU - Damerow, Valentina
AU - Manthey, Bodo
AU - Meyer auf der Heide, Friedhelm
AU - Räcke, Harald
AU - Scheideler, Christian
AU - Sohler, Christian
AU - Tantau, Till
ID - 579
IS - 3
JF - Transactions on Algorithms
TI - Smoothed analysis of left-to-right maxima with applications
ER -
TY - THES
AB - Wir betrachten eine Gruppe von mobilen, autonomen Robotern in einem ebenen Gel{\"a}nde. Es gibt keine zentrale Steuerung und die Roboter m{\"u}ssen sich selbst koordinieren. Zentrale Herausforderung dabei ist, dass jeder Roboter nur seine unmittelbare Nachbarschaft sieht und auch nur mit Robotern in seiner unmittelbaren Nachbarschaft kommunizieren kann. Daraus ergeben sich viele algorithmische Fragestellungen. In dieser Arbeit wird untersucht, unter welchen Voraussetzungen die Roboter sich auf einem Punkt versammeln bzw. eine Linie zwischen zwei festen Stationen bilden k{\"o}nnen. Daf{\"u}r werden mehrere Roboter-Strategien in verschiedenen Bewegungsmodellen vorgestellt. Diese Strategien werden auf ihre Effizienz hin untersucht. Es werden obere und untere Schranken f{\"u}r die ben{\"o}tigte Anzahl Runden und die Bewegungsdistanz gezeigt. In einigen F{\"a}llen wird außerdem die ben{\"o}tigte Bewegungsdistanz mit derjenigen Bewegungsdistanz verglichen, die eine optimale globale Strategie auf der gleichen Instanz ben{\"o}tigen w{\"u}rde. So werden kompetititve Faktoren hergeleitet.
AU - Kempkes, Barbara
ID - 601
TI - Local strategies for robot formation problems
ER -
TY - CONF
AB - Dynamics in networks is caused by a variety of reasons, like nodes moving in 2D (or 3D) in multihop cellphone networks, joins and leaves in peer-to-peer networks, evolution in social networks, and many others. In order to understand such kinds of dynamics, and to design distributed algorithms that behave well under dynamics, many ways to model dynamics are introduced and analyzed w.r.t. correctness and eciency of distributed algorithms. In [16], Kuhn, Lynch, and Oshman have introduced a very general, worst case type model of dynamics: The edge set of the network may change arbitrarily from step to step, the only restriction is that it is connected at all times and the set of nodes does not change. An extended model demands that a xed connected subnetwork is maintained over each time interval of length T (T-interval dynamics). They have presented, among others, algorithms for counting the number of nodes under such general models of dynamics.In this paper, we generalize their models and algorithms by adding random edge faults, i.e., we consider fault-prone dynamic networks: We assume that an edge currently existing may fail to transmit data with some probability p. We rst observe that strong counting, i.e., each node knows the correct count and stops, is not possible in a model with random edge faults. Our main two positive results are feasibility and runtime bounds for weak counting, i.e., stopping is no longer required (but still a correct count in each node), and for strong counting with an upper bound, i.e., an upper bound N on n is known to all nodes.
AU - Brandes, Philipp
AU - Meyer auf der Heide, Friedhelm
ID - 619
T2 - Proceedings of the 4th Workshop on Theoretical Aspects of Dynamic Distributed Systems (TADDS)
TI - Distributed Computing in Fault-Prone Dynamic Networks
ER -
TY - GEN
AU - Eidens, Fabian
ID - 638
TI - Adaptive Verbindungsstrategien in dynamischen Suchnetzwerken
ER -
TY - CONF
AB - Network creation games model the creation and usage costs of networks formed by a set of selfish peers.Each peer has the ability to change the network in a limited way, e.g., by creating or deleting incident links.In doing so, a peer can reduce its individual communication cost.Typically, these costs are modeled by the maximum or average distance in the network.We introduce a generalized version of the basic network creation game (BNCG).In the BNCG (by Alon et al., SPAA 2010), each peer may replace one of its incident links by a link to an arbitrary peer.This is done in a selfish way in order to minimize either the maximum or average distance to all other peers.That is, each peer works towards a network structure that allows himself to communicate efficiently with all other peers.However, participants of large networks are seldom interested in all peers.Rather, they want to communicate efficiently with a small subset only.Our model incorporates these (communication) interests explicitly.Given peers with interests and a communication network forming a tree, we prove several results on the structure and quality of equilibria in our model.We focus on the MAX-version, i.e., each node tries to minimize the maximum distance to nodes it is interested in, and give an upper bound of O(\sqrt(n)) for the private costs in an equilibrium of n peers.Moreover, we give an equilibrium for a circular interest graph where a node has private cost Omega(\sqrt(n)), showing that our bound is tight.This example can be extended such that we get a tight bound of Theta(\sqrt(n)) for the price of anarchy.For the case of general networks we show the price of anarchy to be Theta(n).Additionally, we prove an interesting connection between a maximum independent set in the interest graph and the private costs of the peers.
AU - Cord-Landwehr, Andreas
AU - Huellmann (married name: Eikel), Martina
AU - Kling, Peter
AU - Setzer, Alexander
ID - 628
T2 - Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT)
TI - Basic Network Creation Games with Communication Interests
ER -
TY - GEN
ED - Meyer auf der Heide, Friedhelm
ED - Rajaraman, Rajmohan
ID - 667
TI - 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures
ER -
TY - GEN
AU - Swierkot, Kamil
ID - 663
TI - Complexity Classes for Local Computation
ER -
TY - CONF
AB - Web Computing is a variant of parallel computing where the idle times of PCs donated by worldwide distributed users are employed to execute parallel programs. The PUB-Web library developed by us supports this kind of usage of computing resources. A major problem for the efficient execution of such parallel programs is load balancing. In the Web Computing context, this problem becomes more difficult because of the dynamic behavior of the underlying "parallel computer": the set of available processors (donated PCs) as well as their availability (idle times) change over time in an unpredictable fashion.In this paper, we experimentally evaluate and compare load balancing algorithms in this scenario, namely a variant of the well-established Work Stealing algorithm and strategies based on a heterogeneous version of distributed hash-tables (DHHTs) introduced recently. In order to run a meaningful experimental evaluation, we employ, in addition to our Web Computing library PUB-Web, realistic data sets for the job input streams and for the dynamics of the availability of the resources.Our experimental evaluations suggest that Work Stealing is the better strategy if the number of processes ready to run matches the number of available processors. But a suitable variant of DHHTs outperforms Work Stealing if there are significantly more processes ready to run than available processors.
AU - Gehweiler, Joachim
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
ID - 664
T2 - Proceedings of the 9th International Conference on Parallel Processing and Applied Mathematics (PPAM)
TI - An Experimental Comparison of Load Balancing Strategies in a Web Computing Environment
ER -
TY - CONF
AB - We present two distributed, constant factor approximation algorithms for the metric facility location problem. Both algorithms have been designed with a strong emphasis on applicability in the area of wireless sensor networks: in order to execute them, each sensor node only requires limited local knowledge and simple computations. Also, the algorithms can cope with measurement errors and take into account that communication costs between sensor nodes do not necessarily increase linearly with the distance, but can be represented by a polynomial. Since it cannot always be expected that sensor nodes execute algorithms in a synchronized way, our algorithms are executed in an asynchronous model (but they are still able to break symmetry that might occur when two neighboring nodes act at exactly the same time). Furthermore, they can deal with dynamic scenarios: if a node moves, the solution is updated and the update affects only nodes in the local neighborhood. Finally, the algorithms are robust in the sense that incorrect behavior of some nodes during some round will, in the end, still result in a good approximation. The first algorithm runs in expected O(log_{1+\epsilon} n) communication rounds and yields a \my^4(1+4\my^2(1+\epsilon)^{1/p})^p approximation, while the second has a running time of expected O(log^2_{1+\epsilon} n) communication rounds and an approximation factor of \my^4(1 + 2(1 + \epsilon)^{1/p})^p. Here, \epsilon > 0 is an arbitrarily small constant, p the exponent of the polynomial representing the communication costs, and \my the relative measurement error.
AU - Abshoff, Sebastan
AU - Cord-Landwehr, Andreas
AU - Degener, Bastian
AU - Kempkes, Barbara
AU - Pietrzyk, Peter
ID - 657
T2 - Proceedings of the 7th International Symposium on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities (ALGOSENSORS)
TI - Local Approximation Algorithms for the Uncapacitated Metric Facility Location Problem in Power-Aware Sensor Networks
ER -
TY - CHAP
AU - Degener, Bastian
AU - Kempkes, Barbara
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
ID - 16365
SN - 0302-9743
T2 - Structural Information and Communication Complexity
TI - A Continuous, Local Strategy for Constructing a Short Chain of Mobile Robots
ER -
TY - JOUR
AU - Ziegler, Martin
ID - 15058
JF - Theoretical Computer Science
SN - 0304-3975
TI - Stability versus speed in a computable algebraic model
ER -