TY - GEN
AU - Pahl, David
ID - 373
TI - Reputationssysteme für zusammengesetzte Dienstleistungen
ER -
TY - CONF
AB - Network creation games model the creation and usage costs of networks formed by n selfish nodes. Each node v can buy a set of edges, each for a fixed price α > 0. Its goal is to minimize its private costs, i.e., the sum (SUM-game, Fabrikant et al., PODC 2003) or maximum (MAX-game, Demaine et al., PODC 2007) of distances from v to all other nodes plus the prices of the bought edges. The above papers show the existence of Nash equilibria as well as upper and lower bounds for the prices of anarchy and stability. In several subsequent papers, these bounds were improved for a wide range of prices α. In this paper, we extend these models by incorporating quality-of-service aspects: Each edge cannot only be bought at a fixed quality (edge length one) for a fixed price α. Instead, we assume that quality levels (i.e., edge lengths) are varying in a fixed interval [βˇ,β^] , 0 series = {LNCS}
AU - Cord-Landwehr, Andreas
AU - Mäcker, Alexander
AU - Meyer auf der Heide, Friedhelm
ID - 380
T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE)
TI - Quality of Service in Network Creation Games
ER -
TY - CONF
AB - In this paper we present and analyze HSkip+, a self-stabilizing overlay network for nodes with arbitrary heterogeneous bandwidths. HSkip+ has the same topology as the Skip+ graph proposed by Jacob et al. [PODC 2009] but its self-stabilization mechanism significantly outperforms the self-stabilization mechanism proposed for Skip+. Also, the nodes are now ordered according to their bandwidths and not according to their identifiers. Various other solutions have already been proposed for overlay networks with heterogeneous bandwidths, but they are not self-stabilizing. In addition to HSkip+ being self-stabilizing, its performance is on par with the best previous bounds on the time and work for joining or leaving a network of peers of logarithmic diameter and degree and arbitrary bandwidths. Also, the dilation and congestion for routing messages is on par with the best previous bounds for such networks, so that HSkip+ combines the advantages of both worlds. Our theoretical investigations are backed by simulations demonstrating that HSkip+ is indeed performing much better than Skip+ and working correctly under high churn rates.
AU - Feldotto, Matthias
AU - Scheideler, Christian
AU - Graffi, Kalman
ID - 412
T2 - Proceedings of the 14th IEEE International Conference on Peer-to-Peer Computing (P2P)
TI - HSkip+: A Self-Stabilizing Overlay Network for Nodes with Heterogeneous Bandwidths
ER -
TY - THES
AB - In meiner Dissertation besch{\"a}ftige ich mich mit dem Entwurf und der Analyse energieeffizienter Schedulingalgorithmen, insbesondere f{\"u}r sogenannte Speed-Scaling Modelle. Diese stellen das theoretische Pendant von Techniken wie AMDs PowerNOW! und Intels SpeedStep dar, welche es erlauben die Geschwindigkeit von Prozessoren zur Laufzeit an die derzeitigen Bedingungen anzupassen. Theoretische Untersuchungen solcher Modelle sind auf eine Arbeit von Yao, Demers und Shenker (FOCS'95) zur{\"u}ckzuf{\"u}hren. Hier kombinieren die Autoren klassisches Deadline-Scheduling mit einem Prozessor der Speed-Scaling beherrscht. Es gilt Jobs verschiedener Gr{\"o}ße fristgerecht abzuarbeiten und die dabei verwendete Energie zu minimieren. Der Energieverbrauch des Prozessors wird durch eine konvexe Funktion $\POW\colon\R_{\geq0}\to\R_{\geq0}$ modelliert, welche die Geschwindigkeit auf den Energieverbrauch abbildet.Meine Dissertation betrachtet verschiedene Varianten des urspr{\"u}nglichen Speed-Scaling Modells. Forschungsrelevante Ergebnisse sind in den Kapiteln 3 bis 6 zu finden und erstrecken sich {\"u}ber die im Folgenden beschriebenen Aspekte:- Kapitel 3 und 4 betrachten verschiedene \emph{Price-Collecting} Varianten des Originalproblems. Hier d{\"u}rfen einzelne Deadlines verfehlt werden, sofern eine jobabh{\"a}ngige Strafe gezahlt wird. Ich entwerfe insbesondere Online-Algorithmen mit einer beweisbar guten Competitiveness. Dabei liefern meine Ergebnisse substantielle Verbesserungen bestehender Arbeiten und erweitern diese unter Anderem auf Szenarien mit mehreren Prozessoren.- In Kapitel 5 wird statt des klassischen Deadline-Schedulings eine Linearkombination der durchschnittlichen Antwortzeit und des Energieverbrauchs betrachtet. Die Frage, ob dieses Problem NP-schwer ist, stellt eine der zentralen Forschungsfragen in diesem Gebiet dar. F{\"u}r eine relaxierte Form dieser Frage entwerfe ich einen effizienter Algorithmus und beweise seine Optimalit{\"a}t.- Das letzte Kapitel betrachtet ein Modell, welches – auf den ersten Blick – nicht direkt zur Speed-Scaling Literatur z{\"a}hlt. Hier geht es stattdessen um ein allgemeines Resource-Constrained Scheduling, in dem sich die Prozessoren zusammen eine gemeinsame, beliebig aufteilbare Ressource teilen. Ich untersuche die Komplexit{\"a}t des Problems und entwerfe verschiedene Approximationsalgorithmen.
AU - Kling, Peter
ID - 431
TI - Energy-efficient Scheduling Algorithms
ER -
TY - CONF
AB - We discuss a technique to analyze complex infinitely repeated games using techniques from the fields of game theory and simulations. Our research is motivated by the analysis of electronic markets with thousands of participants and possibly complex strategic behavior. We consider an example of a global market of composed IT services to demonstrate the use of our simulation technique. We present our current work in this area and we want to discuss further approaches for the future.
AU - Feldotto, Matthias
AU - Skopalik, Alexander
ID - 462
T2 - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2014)
TI - A Simulation Framework for Analyzing Complex Infinitely Repeated Games
ER -
TY - CONF
AB - We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.
AU - Hansknecht, Christoph
AU - Klimm, Max
AU - Skopalik, Alexander
ID - 455
T2 - Proceedings of the 17th. International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX)
TI - Approximate pure Nash equilibria in weighted congestion games
ER -
TY - CONF
AB - In the leasing variant of Set Cover presented by Anthony et al.[1], elements U arrive over time and must be covered by sets from a familyF of subsets of U. Each set can be leased for K different periods of time.Let |U| = n and |F| = m. Leasing a set S for a period k incurs a cost ckS and allows S to cover its elements for the next lk time steps. The objectiveis to minimize the total cost of the sets leased, such that elements arrivingat any time t are covered by sets which contain them and are leased duringtime t. Anthony et al. [1] gave an optimal O(log n)-approximation forthe problem in the offline setting, unless P = NP [22]. In this paper, wegive randomized algorithms for variants of Set Cover Leasing in the onlinesetting, including a generalization of Online Set Cover with Repetitionspresented by Alon et al. [2], where elements appear multiple times andmust be covered by a different set at each arrival. Our results improve theO(log2(mn)) competitive factor of Online Set Cover with Repetitions [2]to O(log d log(dn)) = O(logmlog(mn)), where d is the maximum numberof sets an element belongs to.
AU - Abshoff, Sebastian
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 379
T2 - Proceedings of the 8th Annual International Conference on Combinatorial Optimization and Applications (COCOA)
TI - Randomized Online Algorithms for Set Cover Leasing Problems
ER -
TY - CONF
AB - We introduce the concept of budget games. Players choose a set of tasks and each task has a certain demand on every resource in the game. Each resource has a budget. If the budget is not enough to satisfy the sum of all demands, it has to be shared between the tasks. We study strategic budget games, where the budget is shared proportionally. We also consider a variant in which the order of the strategic decisions influences the distribution of the budgets. The complexity of the optimal solution as well as existence, complexity and quality of equilibria are analysed. Finally, we show that the time an ordered budget game needs to convergence towards an equilibrium may be exponential.
AU - Drees, Maximilian
AU - Riechers, Sören
AU - Skopalik, Alexander
ED - Lavi, Ron
ID - 451
T2 - Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT)
TI - Budget-restricted utility games with ordered strategic decisions
ER -
TY - CONF
AB - We study the existence of approximate pure Nash equilibriain social context congestion games. For any given set of allowed costfunctions F, we provide a threshold value μ(F), and show that for theclass of social context congestion games with cost functions from F, α-Nash dynamics are guaranteed to converge to α-approximate pure Nashequilibrium if and only if α > μ(F).Interestingly, μ(F) is related and always upper bounded by Roughgarden’sanarchy value [19].
AU - Gairing, Martin
AU - Kotsialou, Grammateia
AU - Skopalik, Alexander
ID - 456
T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE)
TI - Approximate pure Nash equilibria in Social Context Congestion Games
ER -
TY - CONF
AB - We consider the problem of scheduling a number of jobs on $m$ identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement r_j \in {0,1}. The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of r_j, it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their \emph{processing speeds}, have been studied under the term discrete-continuous scheduling. Known results are either very pessimistic or heuristic in nature.In this paper, we suggest and analyze a slightly simplified model. It focuses on the assignment of shared continuous resources to the processors. The job assignment to processors and the ordering of the jobs have already been fixed. It is shown that, even for unit size jobs, finding an optimal solution is NP-hard if the number of processors is part of the input. Positive results for unit size jobs include an efficient optimal algorithm for 2 processors. Moreover, we prove that balanced schedules yield a 2-1/m-approximation for a fixed number of processors. Such schedules are computed by our GreedyBalance algorithm, for which the bound is tight.
AU - Brinkmann, Andre
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
AU - Nagel, Lars
AU - Riechers, Sören
AU - Süss, Tim
ID - 368
T2 - Proceedings of the 26th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Scheduling Shared Continuous Resources on Many-Cores
ER -
TY - CONF
AB - Today's networks, like the Internet, do not consist of one but a mixture of several interconnected networks. Each has individual qualities and hence the performance of a network node results from the networks' interplay.We introduce a new game theoretic model capturing the interplay between a high-speed backbone network and a low-speed general purpose network. In our model, n nodes are connected by a static network and each node can decide individually to become a gateway node. A gateway node pays a fixed price for its connection to the high-speed network, but can utilize the high-speed network to gain communication distance 0 to all other gateways. Communication distances in the low-speed network are given by the hop distances. The effective communication distance between any two nodes then is given by the shortest path, which is possibly improved by using gateways as shortcuts.Every node v has the objective to minimize its communication costs, given by the sum (SUM-game) or maximum (MAX-game) of the effective communication distances from v to all other nodes plus a fixed price \alpha > 0, if it decides to be a gateway. For both games and different ranges of \alpha, we study the existence of equilibria, the price of anarchy, and convergence properties of best-response dynamics.
AU - Abshoff, Sebastian
AU - Cord-Landwehr, Andreas
AU - Jung, Daniel
AU - Skopalik, Alexander
ED - Lavi, Ron
ID - 452
T2 - Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT)
TI - Brief Announcement: A Model for Multilevel Network Games
ER -
TY - CONF
AB - Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs).We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.
AU - Harks, Tobias
AU - Höfer, Martin
AU - Schewior, Kevin
AU - Skopalik, Alexander
ID - 370
T2 - Proceedings of the 33rd Annual IEEE International Conference on Computer Communications (INFOCOM'14)
TI - Routing Games with Progressive Filling
ER -
TY - CONF
AB - We consider the k-token dissemination problem, where k initially arbitrarily distributed tokens have to be disseminated to all nodes in a dynamic network (as introduced by Kuhn et al., STOC 2010). In contrast to general dynamic networks, our dynamic networks are unit disk graphs, i.e., nodes are embedded into the Euclidean plane and two nodes are connected if and only if their distance is at most R. Our worst-case adversary is allowed to move the nodes on the plane, but the maximum velocity v_max of each node is limited and the graph must be connected in each round. For this model, we provide almost tight lower and upper bounds for k-token dissemination if nodes are restricted to send only one token per round. It turns out that the maximum velocity v_max is a meaningful parameter to characterize dynamics in our model.
AU - Abshoff, Sebastian
AU - Benter, Markus
AU - Cord-Landwehr, Andreas
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
ID - 477
T2 - Algorithms for Sensor Systems - 9th International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, {ALGOSENSORS} 2013, Sophia Antipolis, France, September 5-6, 2013, Revised Selected Papers
TI - Token Dissemination in Geometric Dynamic Networks
ER -
TY - CONF
AB - In this paper we introduce “On-The-Fly Computing”, our vision of future IT services that will be provided by assembling modular software components available on world-wide markets. After suitable components have been found, they are automatically integrated, configured and brought to execution in an On-The-Fly Compute Center. We envision that these future compute centers will continue to leverage three current trends in large scale computing which are an increasing amount of parallel processing, a trend to use heterogeneous computing resources, and—in the light of rising energy cost—energy-efficiency as a primary goal in the design and operation of computing systems. In this paper, we point out three research challenges and our current work in these areas.
AU - Happe, Markus
AU - Kling, Peter
AU - Plessl, Christian
AU - Platzner, Marco
AU - Meyer auf der Heide, Friedhelm
ID - 505
T2 - Proceedings of the 9th IEEE Workshop on Software Technology for Future embedded and Ubiquitous Systems (SEUS)
TI - On-The-Fly Computing: A Novel Paradigm for Individualized IT Services
ER -
TY - GEN
AB - We study the complexity theory for the local distributed setting introduced by Korman, Peleg and Fraigniaud. They have defined three complexity classes LD (Local Decision), NLD (Nondeterministic Local Decision) and NLD^#n. The class LD consists of all languages which can be decided with a constant number of communication rounds. The class NLD consists of all languages which can be verified by a nondeterministic algorithm with a constant number of communication rounds. In order to define the nondeterministic classes, they have transferred the notation of nondeterminism into the distributed setting by the use of certificates and verifiers. The class NLD^#n consists of all languages which can be verified by a nondeterministic algorithm where each node has access to an oracle for the number of nodes. They have shown the hierarchy LD subset NLD subset NLD^#n. Our main contributions are strict hierarchies within the classes defined by Korman, Peleg and Fraigniaud. We define additional complexity classes: the class LD(t) consists of all languages which can be decided with at most t communication rounds. The class NLD-O(f) consists of all languages which can be verified by a local verifier such that the size of the certificates that are needed to verify the language are bounded by a function from O(f). Our main results are refined strict hierarchies within these nondeterministic classes.
AU - Meyer auf der Heide, Friedhelm
AU - Swirkot, Kamil
ID - 524
TI - Hierarchies in Local Distributed Decision
ER -
TY - CONF
AB - In Distributed Cloud Computing, applications are deployed across many data centres at topologically diverse locations to improved network-related quality of service (QoS). As we focus on interactive applications, we minimize the latency between users and an application by allocating Cloud resources nearby the customers. Allocating resources at all locations will result in the best latency but also in the highest expenses. So we need to find an optimal subset of locations which reduces the latency but also the expenses – the facility location problem (FLP). In addition, we consider resource capacity restrictions, as a resource can only serve a limited amount of users. An FLP can be globally solved. Additionally, we propose a local, distributed heuristic. This heuristic is running within the network and does not depend on a global component. No distributed, local approximations for the capacitated FLP have been proposed so far due to the complexity of the problem. We compared the heuristic with an optimal solution obtained from a mixed integer program for different network topologies. We investigated the influence of different parameters like overall resource utilization or different latency weights.
AU - Keller, Matthias
AU - Pawlik, Stefan
AU - Pietrzyk, Peter
AU - Karl, Holger
ID - 562
T2 - Proceedings of the 6th International Conference on Utility and Cloud Computing (UCC) workshop on Distributed cloud computing
TI - A Local Heuristic for Latency-Optimized Distributed Cloud Deployment
ER -
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 -