TY - JOUR
AU - Degener, Bastian
AU - Kempkes, Barbara
AU - Kling, Peter
AU - Meyer auf der Heide, Friedhelm
ID - 16391
JF - ACM Transactions on Parallel Computing
SN - 2329-4949
TI - Linear and Competitive Strategies for Continuous Robot Formation Problems
ER -
TY - GEN
AU - Pfannschmidt, Karlson
ID - 251
TI - Solving the aggregated bandits problem
ER -
TY - CONF
AB - We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC'03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bilò et al., SPAA'14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the Price of Anarchy.
AU - Cord-Landwehr, Andreas
AU - Lenzner, Pascal
ID - 275
T2 - Proceedings of the 40th Conference on Mathematical Foundations of Computer Science (MFCS)
TI - Network Creation Games: Think Global - Act Local
ER -
TY - THES
AU - Abshoff, Sebastian
ID - 270
TI - On the Complexity of Fundamental Problems in Dynamic Ad-hoc Networks
ER -
TY - GEN
AB - In the gathering problem, n autonomous robots have to meet on a single point.
We consider the gathering of a closed chain of point-shaped, anonymous robots
on a grid. The robots only have local knowledge about a constant number of
neighboring robots along the chain in both directions. Actions are performed in
the fully synchronous time model FSYNC. Every robot has a limited memory that
may contain one timestamp of the global clock, also visible to its direct
neighbors. In this synchronous time model, there is no limited view gathering
algorithm known to perform better than in quadratic runtime. The configurations
that show the quadratic lower bound are closed chains. In this paper, we
present the first sub-quadratic---in fact linear time---gathering algorithm for
closed chains on a grid.
AU - Abshoff, Sebastian
AU - Andreas Cord-Landwehr, Andreas
AU - Jung, Daniel
AU - Meyer auf der Heide, Friedhelm
ID - 16397
T2 - ArXiv: 1501.04877
TI - Towards Gathering Robots with Limited View in Linear Time: The Closed Chain Case
ER -
TY - CONF
AB - 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.
AU - Li, Shouwei
AU - Mäcker, Alexander
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Riechers, Sören
ID - 240
T2 - Proceedings of the 21st Annual International Computing and Combinatorics Conference (COCOON)
TI - Towards Flexible Demands in Online Leasing Problems
ER -
TY - CONF
AB - In \emph{bandwidth allocation games} (BAGs), the strategy of a player consists of various demands on different resources. The player's utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can improve her utility by more than some fixed factor $\alpha$ through unilateral strategy changes. There is a threshold $\alpha_\delta$ (where $\delta$ is a parameter that limits the demand of each player on a specific resource) such that $\alpha$-approximate pure Nash equilibria always exist for $\alpha \geq \alpha_\delta$, but not for $\alpha < \alpha_\delta$. We give both upper and lower bounds on this threshold $\alpha_\delta$ and show that the corresponding decision problem is ${\sf NP}$-hard. We also show that the $\alpha$-approximate price of anarchy for BAGs is $\alpha+1$. For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum.
AU - Drees, Maximilian
AU - Feldotto, Matthias
AU - Riechers, Sören
AU - Skopalik, Alexander
ID - 271
T2 - Proceedings of the 8th International Symposium on Algorithmic Game Theory (SAGT)
TI - On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
ER -
TY - CONF
AU - Jähn, Claudius
AU - Fischer, Matthias
AU - Gerges, Maria
AU - Berssenbrügge, Jan
ID - 17427
T2 - 12. Paderborner Workshop Augmented & Virtual Reality in der Produktentstehung
TI - Automatische Ableitung geometrischer Eigenschaften von Bauteilen aus dem 3-D-Polygonmodell
VL - 342
ER -
TY - GEN
AB - 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.
AU - Abshoff, Sebastian
AU - Cord-Landwehr, Andreas
AU - Fischer, Matthias
AU - Jung, Daniel
AU - Meyer auf der Heide, Friedhelm
ID - 16449
T2 - arXiv:1510.05454
TI - Gathering a Closed Chain of Robots on a Grid
ER -
TY - GEN
AU - Pautz, Jannis
ID - 316
TI - Budget Games with priced strategies
ER -
TY - GEN
AU - Kothe, Nils
ID - 277
TI - Multilevel Netzwerk Spiele mit konstanten Entfernungen im Highspeed-Netzwerk
ER -
TY - GEN
AB - 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.
AU - Abu-Khzam, Faisal N.
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
AU - Schubert, Michael
ID - 16452
T2 - arXiv:1510.01866
TI - Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-Hoc Networks
ER -
TY - THES
AU - Jähn, Claudius
ID - 317
TI - Bewertung von Renderingalgorithmen für komplexe 3-D-Szenen
ER -
TY - CONF
AB - 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".
AU - Markarian, Christine
AU - Meyer auf der Heide, Friedhelm
ID - 266
T2 - Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing (PODC)
TI - Online Resource Leasing
ER -
TY - BOOK
ED - Gausemeier, Jürgen
ED - Grafe, Michael
ED - Meyer auf der Heide, Friedhelm
ID - 17431
TI - Augmented & Virtual Reality in der Produktentstehung: Grundlagen, Methoden und Werkzeuge; Interaktions- und Visualisierungstechniken, Virtual Prototyping intelligenter technischer Systeme mit AR/VR
VL - 342
ER -
TY - CONF
AB - 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.
AU - Mäcker, Alexander
AU - Malatyali, Manuel
AU - Meyer auf der Heide, Friedhelm
AU - Riechers, Sören
ED - Dehne, Frank
ED - Sack, Jörg Rüdiger
ED - Stege, Ulrike
ID - 274
T2 - Algorithms and Data Structures: 14th International Symposium, WADS 2015, Victoria, BC, Canada, August 5-7, 2015. Proceedings
TI - Non-preemptive Scheduling on Machines with Setup Times
ER -
TY - THES
AU - Markarian, Christine
ID - 267
TI - Online Resource Leasing
ER -
TY - JOUR
AB - We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of pure Nash equilibria is guaranteed by a potential function argument. Unfortunately, this proof of existence is inefficient and computing pure Nash equilibria in such games is a PLS-hard problem even when all players have unit weights. The situation gets worse when superlinear (e.g., quadratic) latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and pure Nash equilibria may not even exist. Given these obstacles, we consider approximate pure Nash equilibria as alternative solution concepts. A ρ--approximate pure Nash equilibrium is a state of a (weighted congestion) game from which no player has any incentive to deviate in order to improve her cost by a multiplicative factor higher than ρ. Do such equilibria exist for small values of ρ? And if so, can we compute them efficiently?We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an “approximation” of such games by a new class of potential games that we call Ψ-games. This allows us to show that these games have d!-approximate pure Nash equilibria, where d is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate pure Nash equilibria when d is a constant. For games with linear latency functions, the approximation guarantee is 3+√5/2 + Oγ for arbitrarily small γ > 0; for latency functions with maximum degree d≥ 2, it is d2d+o(d). The running time is polynomial in the number of bits in the representation of the game and 1/γ. As a byproduct of our techniques, we also show the following interesting structural statement for weighted congestion games with polynomial latency functions of maximum degree d ≥ 2: polynomially-long sequences of best-response moves from any initial state to a dO(d2)-approximate pure Nash equilibrium exist and can be efficiently identified in such games as long as d is a constant.To the best of our knowledge, these are the first positive algorithmic results for approximate pure Nash equilibria in weighted congestion games. Our techniques significantly extend our recent work on unweighted congestion games through the use of Ψ-games. The concept of approximating nonpotential games by potential ones is interesting in itself and might have further applications.
AU - Caragiannis, Ioannis
AU - Fanelli, Angelo
AU - Gravin, Nick
AU - Skopalik, Alexander
ID - 320
IS - 1
JF - Transactions on Economics and Computation
TI - Approximate Pure Nash Equilibria in Weighted Congestion Games: Existence, Efficient Computation, and Structure
VL - 3
ER -
TY - CONF
AU - Berssenbrügge, Jan
AU - Wiederkehr, Olga
AU - Jähn, Claudius
AU - Fischer, Matthias
ID - 17425
T2 - 12. Paderborner Workshop Augmented & Virtual Reality in der Produktentstehung
TI - Anbindung des Virtuellen Prototypen an die Partialmodelle intelligenter technischer Systeme
VL - 343
ER -
TY - CONF
AB - We consider a multilevel network game, where nodes can improvetheir communication costs by connecting to a high-speed network.The n nodes are connected by a static network and each node can decideindividually to become a gateway to the high-speed network. The goalof a node v is to minimize its private costs, i.e., the sum (SUM-game) ormaximum (MAX-game) of communication distances from v to all othernodes plus a fixed price α > 0 if it decides to be a gateway. Between gatewaysthe communication distance is 0, and gateways also improve othernodes’ distances by behaving as shortcuts. For the SUM-game, we showthat for α ≤ n − 1, the price of anarchy is Θ (n/√α) and in this rangeequilibria always exist. In range α ∈ (n−1, n(n−1)) the price of anarchyis Θ(√α), and for α ≥ n(n − 1) it is constant. For the MAX-game, weshow that the price of anarchy is either Θ (1 + n/√α), for α ≥ 1, orelse 1. Given a graph with girth of at least 4α, equilibria always exist.Concerning the dynamics, both games are not potential games. For theSUM-game, we even show that it is not weakly acyclic.
AU - Abshoff, Sebastian
AU - Cord-Landwehr, Andreas
AU - Jung, Daniel
AU - Skopalik, Alexander
ID - 395
T2 - Proceedings of the 10th International Conference on Web and Internet Economics (WINE)
TI - Multilevel Network Games
ER -