Target-based Distributionally Robust Minimum Spanning Tree Problem

Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been proposed. Meanwhile, motivated by realistic applications, the minimum spanning tree problem in stochastic network has attracted considerable attention of researchers, with respect to which stochastic and robust spanning tree models and related algorithms have been continuingly developed. However, all of them would be either too restricted by the types of the edge weight random variables or computationally intractable, especially in large-scale networks. In this paper, we introduce a target-based distributionally robust optimization framework to solve the minimum spanning tree problem in stochastic graphs where the probability distribution function of the edge weight is unknown but some statistical information could be utilized to prevent the optimal solution from being too conservative. We propose two exact algorithms to solve it, based on Benders decomposition framework and a modified classical greedy algorithm of MST problem (Prim algorithm),respectively. Compared with the NP-hard stochastic and robust spanning tree problems,The proposed target-based distributionally robust minimum spanning tree problem enjoys more satisfactory algorithmic aspect and robustness, when faced with uncertainty in input data

Minimum Cuts in Near-Linear Time

We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques. We give a randomized algorithm that finds a minimum cut in an m-edge, n-vertex graph with high probability in O(m log^3 n) time. We also give a simpler randomized algorithm that finds all minimum cuts with high probability in O(n^2 log n) time. This variant has an optimal RNC parallelization. Both variants improve on the previous best time bound of O(n^2 log^3 n). Other applications of the tree-packing approach are new, nearly tight bounds on the number of near minimum cuts a graph may have and a new data structure for representing them in a space-efficient manner

Low Cost Quality of Service Multicast Routing in High Speed Networks

Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.

Performance optimization of wireless sensor networks for remote monitoring

Wireless sensor networks (WSNs) have gained worldwide attention in recent years because of their great potential for a variety of applications such as hazardous environment exploration, military surveillance, habitat monitoring, seismic sensing, and so on. In this thesis we study the use of WSNs for remote monitoring, where a wireless sensor network is deployed in a remote region for sensing phenomena of interest while its data monitoring center is located in a metropolitan area that is geographically distant from the monitored region. This application scenario poses great challenges since such kind of monitoring is typically large scale and expected to be operational for a prolonged period without human involvement. Also, the long distance between the monitored region and the data monitoring center requires that the sensed data must be transferred by the employment of a third-party communication service, which incurs service costs. Existing methodologies for performance optimization of WSNs base on that both the sensor network and its data monitoring center are co-located, and therefore are no longer applicable to the remote monitoring scenario. Thus, developing new techniques and approaches for severely resource-constrained WSNs is desperately needed to maintain sustainable, unattended remote monitoring with low cost. Specifically, this thesis addresses the key issues and tackles problems in the deployment of WSNs for remote monitoring from the following aspects. To maximize the lifetime of large-scale monitoring, we deal with the energy consumption imbalance issue by exploring multiple sinks. We develop scalable algorithms which determine the optimal number of sinks needed and their locations, thereby dynamically identifying the energy bottlenecks and balancing the data relay workload throughout the network. We conduct experiments and the experimental results demonstrate that the proposed algorithms significantly prolong the network lifetime. To eliminate imbalance of energy consumption among sensor nodes, a complementary strategy is to introduce a mobile sink for data gathering. However, the limited communication time between the mobile sink and nodes results in that only part of sensed data will be collected and the rest will be lost, for which we propose the concept of monitoring quality with the exploration of sensed data correlation among nodes. We devise a heuristic for monitoring quality maximization, which schedules the sink to collect data from selected nodes, and uses the collected data to recover the missing ones. We study the performance of the proposed heuristic and validate its effectiveness in improving the monitoring quality. To strive for the fine trade-off between two performance metrics: throughput and cost, we investigate novel problems of minimizing cost with guaranteed throughput, and maximizing throughput with minimal cost. We develop approximation algorithms which find reliable data routing in the WSN and strategically balance workload on the sinks. We prove that the delivered solutions are fractional of the optimum. We finally conclude our work and discuss potential research topics which derive from the studies of this thesis

Multipath routing for video delivery over bandwidth-limited networks

The delivery of quality video service often requires high bandwidth with low delay or cost in network transmission. Current routing protocols such as those used in the Internet are mainly based on the single-path approach (e.g., the shortest-path routing). This approach cannot meet the end-to-end bandwidth requirement when the video is streamed over bandwidth-limited networks. In order to overcome this limitation, we propose multipath routing, where the video takes multiple paths to reach its destination(s), thereby increasing the aggregate throughput. We consider both unicast (point-to-point) and multicast scenarios. For unicast, we present an efficient multipath heuristic (of complexity O(|V|3)), which achieves high bandwidth with low delay. Given a set of path lengths, we then present and prove a simple data scheduling algorithm as implemented at the server, which achieves the theoretical minimum end-to-end delay. For a network with unit-capacity links, the algorithm, when combined with disjoint-path routing, offers an exact and efficient solution to meet a bandwidth requirement with minimum delay. For multicast, we study the construction of multiple trees for layered video to satisfy the user bandwidth requirements. We propose two efficient heuristics on how such trees can be constructed so as to minimize the cost of their aggregation subject to a delay constraint.published_or_final_versio