A constrained steiner tree approach for reconstructions of multicast trees.

Sun Tong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 77-81).Abstracts in English and Chinese.Chinese Abstract --- p.IAbstract --- p.IIAcknowledgements --- p.IIIList of Contents --- p.IVList of Figures --- p.VIIChapter Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Multicast Routing Problem --- p.1Chapter 1.2 --- Constrained multicast routing problem and SSRA algorithm --- p.4Chapter 1.3 --- Thesis organization --- p.7Chapter Chapter 2 --- Constrained Multicast Routing Algorithms --- p.8Chapter 2.1 --- Steiner tree heuristic --- p.8Chapter 2.1.1 --- Shortest Paths Heuristic --- p.9Chapter 2.1.2 --- Distance Network Heuristic --- p.10Chapter 2.2 --- Review of existing constrained multicast routing algorithms --- p.10Chapter 2.2.1 --- Static group member --- p.10Chapter 2.2.2 --- Dynamic group member --- p.14Chapter 2.2.2.1 --- Non-rearrangeable --- p.15Chapter 2.2.2.2 --- Rearrangeable --- p.23Chapter Chapter 3 --- Small Scale Rearrangement Algorithm for Multicast Routing --- p.32Chapter 3.1 --- Problem formulation --- p.32Chapter 3.1.1 --- Network Model --- p.32Chapter 3.1.2 --- Problem Specification --- p.33Chapter 3.1.3 --- Definitions and Notations --- p.36Chapter 3.2 --- Local Checking Scheme (LCS) --- p.37Chapter 3.3 --- Small Scale Rearrangement Algorithm (SSRA) for Multicast Routing --- p.41Chapter 3.3.1 --- Static group membership --- p.42Chapter 3.3.2 --- Dynamic group membership --- p.43Chapter 3.3.2.1 --- Node addition --- p.44Chapter 3.3.2.2 --- Node removal --- p.44Chapter 3.3.2.3 --- General steps --- p.45Chapter 3.3.2.4 --- Example --- p.47Chapter Chapter 4 --- Analysis --- p.50Chapter Chapter 5 --- Simulations --- p.54Chapter 5.1 --- Simulation Model --- p.54Chapter 5.2 --- Simulation Parameters Parameter Default Value/Generating Method --- p.56Chapter 5.3 --- Performance Metrics --- p.58Chapter 5.4 --- Discussion of Results --- p.59Chapter 5.4.1 --- Group 1: static group membership --- p.59Chapter 5.4.2 --- Group 2: dynamic group membership --- p.63Chapter 5.4.3 --- Comparison --- p.69Chapter 5.5 --- Implementation Issue --- p.73Chapter Chapter 6 --- Conclusion --- p.75Reference --- p.7

An Efficient Multicast Routing Algorithm for Delay-Sensitive Applications with Dynamic Membership

We propose an algorithm for finding a multicast tree in packet-switched networks. The objective is to minimize total cost incurred at the multicast path. The routing model is based on the minimum cost Steiner tree problem. The Steiner problem is extended to incorporate two additional requirements. First, the delay experienced along the path from the source to each destination is bounded. Second, the destinations are allowed to join and leave multicasting anytime during a session. To minimize the disruption to on-going multicasting the algorithm adopts the idea of connecting a new destination to the current multicasting by a minimum cost path satisfying the delay bound. To find such a path is an NP-hard problem and an enumerative method relying on generation of delay bounded paths between node pairs is not likely to find a good routing path in acceptable computation time when network size is large. To cope with such difficulty, the proposed algorithm utilizes an optimization technique called Lagrangian relaxation method. A computational experiment is done on relatively dense and large Waxman's networks. The results seem to be promising. For sparse networks, the algorithm can find near-optimal multicast trees. Also the quality of multicast trees does not seem to deteriorate even when the network size grows. Furthermore, the experimental results shows that the computational efforts for each addition of node to the call are fairly moderate, namely the same as to solve a few shortest path problems.The research is partially supported by a UTA grant 96163-CT-1-1 of Ministry of Information and Communications of Korea. Research also partially supported by Korea Telecom under contract 96-29

The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set $S \subseteq V$, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear $o(n)$ time, and keep the approximation factor of the algorithm as small as possible. We show that we can maintain a $(6+\varepsilon)$-approximate Steiner tree of a general graph in $\tilde{O}(\sqrt{n} \log D)$ time per terminal addition or removal. Here, $D$ denotes the stretch of the metric induced by $G$. For planar graphs we achieve the same running time and the approximation ratio of $(2+\varepsilon)$. Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time $(4+\varepsilon)$-approximate algorithm for planar graphs. One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.Comment: Full version of the paper accepted to STOC'1

Learning algorithms for the control of routing in integrated service communication networks

There is a high degree of uncertainty regarding the nature of traffic on future integrated service networks. This uncertainty motivates the use of adaptive resource allocation policies that can take advantage of the statistical fluctuations in the traffic demands. The adaptive control mechanisms must be 'lightweight', in terms of their overheads, and scale to potentially large networks with many traffic flows. Adaptive routing is one form of adaptive resource allocation, and this thesis considers the application of Stochastic Learning Automata (SLA) for distributed, lightweight adaptive routing in future integrated service communication networks. The thesis begins with a broad critical review of the use of Artificial Intelligence (AI) techniques applied to the control of communication networks. Detailed simulation models of integrated service networks are then constructed, and learning automata based routing is compared with traditional techniques on large scale networks. Learning automata are examined for the 'Quality-of-Service' (QoS) routing problem in realistic network topologies, where flows may be routed in the network subject to multiple QoS metrics, such as bandwidth and delay. It is found that learning automata based routing gives considerable blocking probability improvements over shortest path routing, despite only using local connectivity information and a simple probabilistic updating strategy. Furthermore, automata are considered for routing in more complex environments spanning issues such as multi-rate traffic, trunk reservation, routing over multiple domains, routing in high bandwidth-delay product networks and the use of learning automata as a background learning process. Automata are also examined for routing of both 'real-time' and 'non-real-time' traffics in an integrated traffic environment, where the non-real-time traffic has access to the bandwidth 'left over' by the real-time traffic. It is found that adopting learning automata for the routing of the real-time traffic may improve the performance to both real and non-real-time traffics under certain conditions. In addition, it is found that one set of learning automata may route both traffic types satisfactorily. Automata are considered for the routing of multicast connections in receiver-oriented, dynamic environments, where receivers may join and leave the multicast sessions dynamically. Automata are shown to be able to minimise the average delay or the total cost of the resulting trees using the appropriate feedback from the environment. Automata provide a distributed solution to the dynamic multicast problem, requiring purely local connectivity information and a simple updating strategy. Finally, automata are considered for the routing of multicast connections that require QoS guarantees, again in receiver-oriented dynamic environments. It is found that the distributed application of learning automata leads to considerably lower blocking probabilities than a shortest path tree approach, due to a combination of load balancing and minimum cost behaviour