Algorithmic Approaches to the Steiner Problem in Networks

Das Steinerproblem in Netzwerken ist das Problem, in einem gewichteten Graphen eine gegebene Menge von Knoten kostenminimal zu verbinden. Es ist ein klassisches NP-schweres Problem und ein fundamentales Problem bei der Netzwerkoptimierung mit vielen praktischen Anwendungen. Wir nehmen dieses Problem mit verschiedenen Mitteln in Angriff: Relaxationen, die die Zulässigkeitsbedingungen lockern, um eine optimale Lösung annähern zu können; Heuristiken, um gute, aber nicht garantiert optimale Lösungen zu finden; und Reduktionen, um die Probleminstanzen zu vereinfachen, ohne eine optimale Lösung zu zerstören. In allen Fällen untersuchen und verbessern wir bestehende Methoden, stellen neue vor und evaluieren sie experimentell. Wir integrieren diese Bausteine in einen exakten Algorithmus, der den Stand der Algorithmik für die optimale Lösung dieses Problems darstellt. Viele der vorgestellten Methoden können auch für verwandte Probleme von Nutzen sein

Combinatorial Optimization

This report summarizes the meeting on Combinatorial Optimization where new and promising developments in the field were discussed. Th

Design of Overlay Networks for Internet Multicast - Doctoral Dissertation, August 2002

Multicast is an efficient transmission scheme for supporting group communication in networks. Contrasted with unicast, where multiple point-to-point connections must be used to support communications among a group of users, multicast is more efficient because each data packet is replicated in the network – at the branching points leading to distinguished destinations, thus reducing the transmission load on the data sources and traffic load on the network links. To implement multicast, networks need to incorporate new routing and forwarding mechanisms in addition to the existing are not adequately supported in the current networks. The IP multicast are not adequately supported in the current networks. The IP multicast solution has serious scaling and deployment limitations, and cannot be easily extended to provide more enhanced data services. Furthermore, and perhaps most importantly, IP multicast has ignored the economic nature of the problem, lacking incentives for service providers to deploy the service in wide area networks. Overlay multicast holds promise for the realization of large scale Internet multicast services. An overlay network is a virtual topology constructed on top of the Internet infrastructure. The concept of overlay networks enables multicast to be deployed as a service network rather than a network primitive mechanism, allowing deployment over heterogeneous networks without the need of universal network support. This dissertation addresses the network design aspects of overlay networks to provide scalable multicast services in the Internet. The resources and the network cost in the context of overlay networks are different from that in conventional networks, presenting new challenges and new problems to solve. Our design goal are the maximization of network utility and improved service quality. As the overall network design problem is extremely complex, we divide the problem into three components: the efficient management of session traffic (multicast routing), the provisioning of overlay network resources (bandwidth dimensioning) and overlay topology optimization (service placement). The combined solution provides a comprehensive procedure for planning and managing an overlay multicast network. We also consider a complementary form of overlay multicast called application-level multicast (ALMI). ALMI allows end systems to directly create an overlay multicast session among themselves. This gives applications the flexibility to communicate without relying on service provides. The tradeoff is that users do not have direct control on the topology and data paths taken by the session flows and will typically get lower quality of service due to the best effort nature of the Internet environment. ALMI is therefore suitable for sessions of small size or sessions where all members are well connected to the network. Furthermore, the ALMI framework allows us to experiment with application specific components such as data reliability, in order to identify a useful set of communication semantic for enhanced data services

Well-solvable special cases of the TSP : a survey

The Traveling Salesman Problem belongs to the most important and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently. We survey these special cases with emphasis on results obtained during the decade 1985-1995. This survey complements an earlier survey from 1985 compiled by Gilmore, Lawler and Shmoys. Keywords: Traveling Salesman Problem, Combinatorial optimization, Polynomial time algorithm, Computational complexity