Relations between cumulants in noncommutative probability

We express classical, free, Boolean and monotone cumulants in terms of each other, using combinatorics of heaps, pyramids, Tutte polynomials and permutations. We completely determine the coefficients of these formulas with the exception of the formula for classical cumulants in terms of monotone cumulants whose coefficients are only partially computed.Comment: 27 pages, 7 figures, AMS LaTe

A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein's algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n + m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude. Further, the running time is far better predictable due to very small dispersion

Implementation of operations in double-ended heaps

Existuje viacero spôsobov ako vytvoriť dvojkoncovú haldu z dvoch klasických háld. V tejto práci rozšírime dvojkoncovú haldu založenú na prepojení listov a vytvoríme novú schému nazvanú L-korešpondencia. Táto schéma rozšíri triedu možných klasických háld použiteľných pre vytvorenie dvojkoncovej haldy (napr. Fibonacci halda, Rank-pairing halda). Ďalej umožní operácie ``Zníž prioritu'' a ``Zvýš prioritu''. Tento prístup ukážeme na troch konkrétnych haldách a odhadneme časovú zložitosť pre všetky operácie. Ďalším výsledkom je, že pre tieto tri konkrétne haldy, očakávaný čas operácií ``Zníž prioritu'' a ``Zvýš prioritu'' je obmedzený konštantou.There are several approaches for creating double-ended heaps from the single-ended heaps. We build on one of them, the leaf correspondence heap, to create a generic double ended heap scheme called L-correspondence heap. This will broaden the class of eligible base single-ended heaps (e.g. by Fibonacci heap, Rank-pairing heap) and make the operations Decrease and Increase possible. We show this approach on specific examples for three different single-ended base heaps and give time complexity bounds for all operations. Another result is that for these three examples, the expected amortized time for Decrease and Increase operations in the L-correspondence heap is bounded by a constant.Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Distributed control architecture for multiservice networks

The research focuses in devising decentralised and distributed control system architecture for the management of internetworking systems to provide improved service delivery and network control. The theoretical basis, results of simulation and implementation in a real-network are presented. It is demonstrated that better performance, utilisation and fairness can be achieved for network customers as well as network/service operators with a value based control system. A decentralised control system framework for analysing networked and shared resources is developed and demonstrated. This fits in with the fundamental principles of the Internet. It is demonstrated that distributed, multiple control loops can be run on shared resources and achieve proportional fairness in their allocation, without a central control. Some of the specific characteristic behaviours of the service and network layers are identified. The network and service layers are isolated such that each layer can evolve independently to fulfil their functions better. A common architecture pattern is devised to serve the different layers independently. The decision processes require no co-ordination between peers and hence improves scalability of the solution. The proposed architecture can readily fit into a clearinghouse mechanism for integration with business logic. This architecture can provide improved QoS and better revenue from both reservation-less and reservation-based networks. The limits on resource usage for different types of flows are analysed. A method that can sense and modify user utilities and support dynamic price offers is devised. An optimal control system (within the given conditions), automated provisioning, a packet scheduler to enforce the control and a measurement system etc are developed. The model can be extended to enhance the autonomicity of the computer communication networks in both client-server and P2P networks and can be introduced on the Internet in an incremental fashion. The ideas presented in the model built with the model-view-controller and electronic enterprise architecture frameworks are now independently developed elsewhere into common service delivery platforms for converged networks. Four US/EU patents were granted based on the work carried out for this thesis, for the cross-layer architecture, multi-layer scheme, measurement system and scheduler. Four conference papers were published and presented

Relevanzbasierte Nachrichtenselektion für die serientaugliche Integration von Fahrzeug-zu-Fahrzeug-Kommunikation

Die Fahrzeug-zu-Fahrzeug-Kommunikation ermöglicht neue Anwendungen durch den direkten Austausch von Informationen zwischen Fahrzeugen. In den vergangenen Jahrzehnten wurde dazu intensiv geforscht und eine standardisierte Technologie auf der Grundlage von WLAN geschaffen. Die Fahrzeuge erfassen damit andere Verkehrsteilnehmer in ihrem Umfeld, auch über Sichthindernisse hinweg. Bei der Umsetzung von Seriensystemen stehen die Fahrzeughersteller vor der Herausforderung, dass unter Umständen höhere Raten an Nachrichten empfangen werden als von den Fahrzeugsystemen verarbeitet werden können. Diese Arbeit betrachtet diese Problemstellung erstmals umfänglich und schlägt eine Lösung vor, um auch in Überlastsituationen die Funktionalität sicherheitsrelevanter Anwendungen zu gewährleisten. Zunächst werden die auftretenden Nachrichtenraten anhand einer gekoppelten Verkehrs-, Kommunikations- und Anwendungssimulation quantifiziert. Es bestätigt sich, dass auch unter alltäglichen Bedingungen Überlast auftreten kann. Daher wird vorgeschlagen, die Verarbeitung empfangener Nachrichten um zwei Module zu ergänzen, eine Relevanzschätzung und einen Selektionsmechanismus. Die Relevanzschätzung hat die Aufgabe, jede Nachricht nach ihrer Relevanz zu bewerten und mit einem Relevanzwert zu versehen. Je früher sich der Sender und Empfänger einer Nachricht begegnen, desto höher wird die Relevanz bewertet. Der Selektionsmechanismus wählt auf Basis dieser Relevanzwerte die jeweils relevanteste Nachricht zur Weiterverarbeitung aus und verwirft bei Überlast weniger relevante Nachrichten. Sowohl die Relevanzschätzung als auch der Selektionsmechanismus sollten möglichst effizient implementierbar sein. Die Evaluation beider Module zeigt auf, dass die vorgeschlagenen Konzepte für einen Serieneinsatz geeignet sind und die Entwicklung stabiler Gesamtfahrzeugsysteme ermöglichen

A comparative analysis of three different priority deques

Abstract. In this project we compare the practical effectiveness of three different algorithms for “priority deques”, namely MinMax-heaps, The Deap and Interval Heaps. By implementing the algorithms and running benchmarks we find that interval heaps are the most effective, mainly due to its simplicity and similarity to standard heaps. We also discover some crucial shortcomings of Svante Carlsson’s deap algorithm and propose solutions for these. Our code is targeted towards submission to the Copenhagen STL project so we implement a “PriorityDeque”-class, in which the programmer can choose the underlying algorithm