MPI fur Informatik

Saarbrücken, Germany

MPI fur Informatik

Saarbrücken, Germany
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Bei X.,Nanyang Technological University | Garg J.,University of Illinois at Urbana - Champaign | Hoefer M.,Saarland University | Mehlhorn K.,MPI fur Informatik
Leibniz International Proceedings in Informatics, LIPIcs | Year: 2016

We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement this positive result with a number of hardness results for related computational questions. We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good. © Xiaohui Bei, Jugal Garg, Martin Hoefer, and Kurt Mehlhorn.

Sviridenko M.,University of Warwick | Wiese A.,MPI fur Informatik
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

Configuration-LPs have proved to be successful in the design and analysis of approximation algorithms for a variety of discrete optimization problems. In addition, lower bounds based on configuration-LPs are a tool of choice for many practitioners especially those solving transportation and bin packing problems. In this work we initiate a study of linear programming relaxations with exponential number of variables for unrelated parallel machine scheduling problems with total weighted sum of completion times objective. We design a polynomial time approximation scheme to solve such a relaxation for R|r ij | Σ wj Cj and a fully polynomial time approximation scheme to solve a relaxation of R∥ Σ wj Cj . As a byproduct of our techniques we derive a polynomial time approximation scheme for the one machine scheduling problem with rejection penalties, release dates and the total weighted sum of completion times objective. © 2013 Springer-Verlag.

Klasing R.,French National Center for Scientific Research | Kosowski A.,French Institute for Research in Computer Science and Automation | Pajak D.,French Institute for Research in Computer Science and Automation | Sauerwald T.,MPI fur Informatik
Proceedings of the Annual ACM Symposium on Principles of Distributed Computing | Year: 2013

The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks. We show that on the ring the rotor-router with k agents admits a cover time of between θ(n2/k 2) in the best case and θ(n2/log k) in the worst case, depending on the initial locations of the agents, and that both these bounds are tight. The corresponding expected value of cover time for k random walks, depending on the initial locations of the walkers, is proven to belong to a similar range, namely between θ(n2/(k2/log 2 k)) and θ(n2/log k). Finally, we study the limit behavior of the rotor-router system. We show that, once the rotor-router system has stabilized, all the nodes of the ring are always visited by some agent every θ(n/k) steps, regardless of how the system was initialized. This asymptotic bound corresponds to the expected time between successive visits to a node in the case of k random walks. All our results hold up to a polynomially large number of agents (1 ≤ k < n1/11). Copyright 2013 ACM.

Heggernes P.,University of Bergen | Van 'T Hof P.,University of Bergen | Van Leeuwen E.J.,MPI fur Informatik | Saei R.,University of Bergen
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

The well-known Disjoint Paths problem takes as input a graph G and a set of k pairs of terminals in G, and the task is to decide whether there exists a collection of k pairwise vertex-disjoint paths in G such that the vertices in each terminal pair are connected to each other by one of the paths. This problem is known to NP-complete, even when restricted to planar graphs or interval graphs. Moreover, although the problem is fixed-parameter tractable when parameterized by k due to a celebrated result by Robertson and Seymour, it is known not to admit a polynomial kernel unless NP † coNP/poly. We prove that Disjoint Paths remains NP-complete on split graphs, and show that the problem admits a kernel with O(k 2) vertices when restricted to this graph class. We furthermore prove that, on split graphs, the edge-disjoint variant of the problem is also NP-complete and admits a kernel with O(k 3) vertices. To the best of our knowledge, our kernelization results are the first non-trivial kernelization results for these problems on graph classes. © 2014 Springer International Publishing Switzerland.

Hashemi V.,MPI fur Informatik | Hashemi V.,Saarland University | Hatefi H.,Saarland University | Krcal J.,Saarland University
Electronic Proceedings in Theoretical Computer Science, EPTCS | Year: 2014

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models which are studied in the literature and that result in two different definitions of bisimulations. We give algorithms to compute the quotients of these bisimulations in time polynomial in the size of the model and exponential in the uncertain branching. Finally, we show by a case study that large models in practice can have small branching and that a substantial state space reduction can be achieved by our approach. © 2014 V. Hashemi, H. Hatefi & J. Krčál.

Tompkin J.,University College London | Kim K.I.,MPI fur Informatik | Kautz J.,University College London | Theobalt C.,MPI fur Informatik
ACM Transactions on Graphics | Year: 2012

The abundance of mobile devices and digital cameras with video capture makes it easy to obtain large collections of video clips that contain the same location, environment, or event. However, such an unstructured collection is difficult to comprehend and explore. We propose a system that analyzes collections of unstructured but related video data to create a Videoscape: a data structure that enables interactive exploration of video collections by visually navigating - spatially and/or temporally - between different clips. We automatically identify transition opportunities, or portals. From these portals, we construct the Videoscape, a graph whose edges are video clips and whose nodes are portals between clips. Now structured, the videos can be interactively explored by walking the graph or by geographic map. Given this system, we gauge preference for different video transition styles in a user study, and generate heuristics that automatically choose an appropriate transition style. We evaluate our system using three further user studies, which allows us to conclude that Videoscapes provides significant benefits over related methods. Our system leads to previously unseen ways of interactive spatio-temporal exploration of casually captured videos, and we demonstrate this on several video collections. © 2012 ACM 0730-0301/2012/08-ART68.

Schmidt J.M.,MPI fur Informatik
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

One of the most noted construction methods of 3-vertex-connected graphs is due to Tutte and based on the following fact: Every 3-vertex-connected graph G on more than 4 vertices contains a contractible edge, i. e., an edge whose contraction generates a 3-connected graph. This implies the existence of a sequence of edge contractions from G to K 4 such that every intermediate graph is 3-vertex-connected. A theorem of Barnette and Grünbaum yields a similar sequence using removals of edges instead of contractions. We show how to compute both sequences in optimal time, improving the previously best known running times of O(|V|2) to O(|E|). Based on this result, we give a linear-time test of 3-connectivity that is certifying; finding such an algorithm has been a major open problem in the design of certifying algorithms in the last years. The 3-connectivity test is conceptually different from well-known linear-time tests of 3-connectivity; it uses a certificate that is easy to verify in time O(|E|). We also provide an optimal certifying test of 3-edge-connectivity. © 2012 Springer-Verlag.

Baumgartner P.,Australian National University | Waldmann U.,MPI fur Informatik
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2013

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide a new completeness result for the fragment where all background-sorted terms are ground. © 2013 Springer-Verlag.

Baumgartner P.,Australian National University | Waldmann U.,MPI fur Informatik
Journal of Automated Reasoning | Year: 2011

We present a new calculus for first-order theorem proving with equality, Mσ+Sup, which generalizes both the Superposition calculus and the Model Evolution calculus (with equality) by integrating their inference rules and redundancy criteria in a non-trivial way. The main motivation is to combine the advantageous features of these two rather complementary calculi in a single framework. In particular, Model Evolution, as a lifted version of the propositional DPLL procedure, contributes a non-ground splitting rule that effectively permits to split a clause into non variable disjoint subclauses. In the paper we present the calculus in detail. Our main result is its completeness under semantically justified redundancy criteria and simplification rules. We also show how under certain assumptions the model representation computed by a (finite and fair) derivation can be queried in an effective way. © 2010 Springer Science+Business Media B.V.

Granados M.,MPI Fur Informatik | Kim K.I.,MPI Fur Informatik | Tompkin J.,MPI Fur Informatik | Theobalt C.,MPI Fur Informatik
ACM Transactions on Graphics | Year: 2013

High dynamic range reconstruction of dynamic scenes requires careful handling of dynamic objects to prevent ghosting. However, in a recent review, Srikantha et al. [2012] conclude that "there is no single best method and the selection of an approach depends on the user's goal". We attempt to solve this problem with a novel approach that models the noise distribution of color values. We estimate the likelihood that a pair of colors in different images are observations of the same irradiance, and we use a Markov random field prior to reconstruct irradiance from pixels that are likely to correspond to the same static scene object. Dynamic content is handled by selecting a single low dynamic range source image and hand-held capture is supported through homography-based image alignment. Our noise-based reconstruction method achieves better ghost detection and removal than state-of-the-art methods for cluttered scenes with large object displacements. As such, our method is broadly applicable and helps move the field towards a single method for dynamic scene HDR reconstruction.

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