Upper bounds on the bisection width of 3- and 4-regular graphs

AbstractWe derive new upper bounds on the bisection width of graphs which have a regular vertex degree. We show that the bisection width of sufficiently large 3-regular graphs with |V| vertices is at most (16+ε)|V|, ε>0. For the bisection width of sufficiently large 4-regular graphs we show an upper bound of (25+ε)|V|, ε>0

The Price of Anarchy for Polynomial Social Cost

In this work, we consider an interesting variant of the well-studied KP model [KP99] for selfish routing that reflects some influence from the much older Wardrop [War52]. In the new model, user traffics are still unsplittable, while social cost is now the expectation of the sum, over all links, of a certain polynomial evaluated at the total latency incurred by all users choosing the link; we call it polynomial social cost. The polynomials that we consider have non-negative coefficients. We are interested in evaluating Nash equilibria in this model, and we use the Price of Anarchy as our evaluation measure. We prove the Fully Mixed Nash Equilibrium Conjecture for identical users and two links, and establish an approximate version of the conjecture for arbitrary many links. Moreover, we give upper bounds on the Price of Anarchy

A new model for selfish routing

AbstractIn this work, we introduce and study a new, potentially rich model for selfish routing over non-cooperative networks, as an interesting hybridization of the two prevailing such models, namely the KPmodel [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404–413] and the Wmodel [J.G. Wardrop, Some theoretical aspects of road traffic research, Proceedings of the of the Institute of Civil Engineers 1 (Pt. II) (1952) 325–378].In the hybrid model, each of n users is using a mixed strategy to ship its unsplittable traffic over a network consisting of m parallel links. In a Nash equilibrium, no user can unilaterally improve its Expected Individual Cost. To evaluate Nash equilibria, we introduce Quadratic Social Cost as the sum of the expectations of the latencies, incurred by the squares of the accumulated traffic. This modeling is unlike the KP model, where Social Cost [E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404–413] is the expectation of the maximum latency incurred by the accumulated traffic; but it is like the W model since the Quadratic Social Cost can be expressed as a weighted sum of Expected Individual Costs. We use the Quadratic Social Cost to define Quadratic Coordination Ratio. Here are our main findings: •Quadratic Social Cost can be computed in polynomial time. This is unlike the #P-completeness [D. Fotakis, S. Kontogiannis, E. Koutsoupias, M. Mavronicolas, P. Spirakis, The structure and complexity of Nash equilibria for a selfish routing game, in: P. Widmayer, F. Triguero, R. Morales, M. Hennessy, S. Eidenbenz, R. Conejo (Eds.), Proceedings of the 29th International Colloquium on Automata, Languages and Programming, in: Lecture Notes in Computer Science, vol. 2380, Springer-Verlag, 2002, pp. 123–134] of computing Social Cost for the KP model.•For the case of identical users and identical links, the fully mixed Nash equilibrium [M. Mavronicolas, P. Spirakis, The price of selfish routing, Algorithmica 48 (1) (2007) 91–126], where each user assigns positive probability to every link, maximizes Quadratic Social Cost.•As our main result, we present a comprehensive collection of tight, constant (that is, independent of m and n), strictly less than 2, lower and upper bounds on the Quadratic Coordination Ratio for several, interesting special cases. Some of the bounds stand in contrast to corresponding super-constant bounds on the Coordination Ratio previously shown in [A. Czumaj, B. Vöcking, Tight bounds for worst-case equilibria, ACM Transactions on Algorithms 3 (1) (2007); E. Koutsoupias, M. Mavronicolas, P. Spirakis, Approximate equilibria and ball fusion, Theory of Computing Systems 36 (6) (2003) 683–693; E. Koutsoupias, C.H. Papadimitriou, Worst-case equilibria, in: G. Meinel, S. Tison (Eds.), Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science, in: Lecture Notes in Computer Science, vol. 1563, Springer-Verlag, 1999, pp. 404–413; M. Mavronicolas, P. Spirakis, The price of selfish routing, Algorithmica 48 (1) (2007) 91–126] for the KP model

Accelerating shape optimizing load balancing for parallel FEM simulations by algebraic multigrid

We propose a load balancing heuristic for parallel adaptive finite element method (FEM) simulations. In contrast to most existing approaches, the heuristic fo-cuses on good partition shapes rather than on mini-mizing the classical edge-cut metric. By applying Alge-braic Multigrid (AMG), we are able to speed up the two most time consuming calculations of the approach while maintaining its large amount of natural parallelism

Verbundprojekt PARALOR: Parallele Algorithmen für Routingprobleme im Flug- und Straßenverkehr

Im Verbundprojekt PARALOR wird untersucht, wie parallele Algorithmen der kombinatorischen Optimierung zur Lösung großer Optimierungsprobleme aus der industriellen Praxis eingesetzt werden können. Dabei werden insbesondere konkrete Aufgabenstellungen aus dem Bereich der Flugplanoptimierung und der integrierten Steuerung von Fertigungslagern bearbeitet. Der Beitrag gibt einen Überblick über die jeweiligen Problemstellungen, die verwendeten Algorithmen und die bisher erzielten Resultate. Insbesondere werden mit dem Parallelen Simulated Trading und dem Parallelen Branch-and-Bound parallele Methoden betrachtet, mit denen eine breite Klasse kombinatorischer Optimierungsprobleme behandelt werden kann

Verbundprojekt PARALOR: Parallele Verfahren zur Wegoptimierung in Flugplanung und Logistik

Die Lösung kombinatorischer Optimierungsprobleme ist in vielen Bereichen von Wirtschaft und Technik der Schlüssel zur Steigerung der Effizienz technischer Abläufen, zur Verbesserung der Produktqualität und zur Veringerung von Produktions-, Material- und Transportkosten. Der Einsatz herkömmlicher sequentieller Verfahren ist für praxisrelevante Probleme aufgrund der enormen Rechenzeiterfordernisse nur sehr eingeschränkt möglich. Parallele Systeme bieten eine Möglichkeit, derartige Probleme in vertretbarer Zeit zu lösen. Im Rahmen des Verbundprojektes PARALOR wird untersucht, wie parallele Algorithmen der kombinatorischen Optimierung in konkreten, industriellen Anwendungen aus der Flugplanung sowie der Speditionslogistik effizient eingesetzt werden können. In diesem Artikel werden wesentliche Ergebnisse des Projekts exemplarisch vorgestellt

Biolabile ferrous iron bearing nanoparticles in glacial sediments

Glaciers and ice sheets are a significant source of nanoparticulate Fe, which is potentially important in sustaining the high productivity observed in the near-coastal regions proximal to terrestrial ice cover. However, the bioavailability of particulate iron is poorly understood, despite its importance in the ocean Fe inventory. We combined high-resolution imaging and spectroscopy to investigate the abundance, morphology and valence state of particulate iron in glacial sediments. Our results document the widespread occurrence of amorphous and Fe(II)-rich and Fe(II)-bearing nanoparticles in Arctic glacial meltwaters and iceberg debris, compared to Fe(III)-rich dominated particulates in an aeolian dust sample. Fe(II) is thought to be highly biolabile in marine environments. Our work shows that glacially derived Fe is more labile than previously assumed, and consequently that glaciers and ice sheets are therefore able to export potentially bioavailable Fe(II)-containing nanoparticulate material to downstream ecosystems, including those in a marine setting. Our findings provide further evidence that Greenland Ice Sheet meltwaters may provide biolabile particulate Fe that may fuel the large summer phytoplankton bloom in the Labrador Sea, and that Fe(II)-rich particulates from a region of very high productivity downstream of a polar ice sheet may be glacial in origin