Distributed Algorithms For Resource Allocation And Routing
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Distributed Algorithms for Resource Allocation and Routing
In this thesis, we study distributed algorithms in the context of two fundamental problems in distributed systems, resource allocation and routing. Resource allocation studies how to distribute workload evenly to resources. We consider two different resource allocation models, the diffusive load balancing and the weighted balls-into-bins games. Routing studies how to deliver messages from source to destination efficiently. We design routing algorithms for broadcasting and gossiping in ad hoc networks. Diffusive load balancing studies how nodes with initial tasks in a network balance their loads concurrently with all their neighbours. We propose a novel analytical method to deal with the concurrent load balancing actions, which are the major obstacle for the analysis. The idea is to first sequentialize the concurrent load balancing actions, analyze this sequential system instead, and then bound the gap between both. We analyze various diffusive load balancing algorithms using this idea. The weighted balls-into-bins game studies how to evenly allocate a set of independent weighted balls into a set of bins. In particular, we consider two different scenarios, the static sequential game and the selfish reallocation game. In the static sequential game, balls come one after another and need to be allocated in such order. We study how the outcome of the game, the expected maximum load of any bin, is influenced by the game parameters such as the distribution of ball weights and the order that balls are allocated. In the selfish reallocation game, every ball has its own initial location. An iterative, selfish distributed reallocation algorithm is applied to balance the workload. We show bounds for the convergence time of the algorithm, which is the number of steps to reach (or get close to) some equilibrium state. We study routing algorithms for broadcasting and gossiping in ad hoc networks. We consider the so-called "energy efficient" ad hoc network model. Our goal is to minimize not only broadcasting/gossiping time, but also energy consumption, which is measured by the total number of sent messages. We present and analyze several energy efficient broadcasting/gossiping algorithms for both random and general ad hoc networks.
Link Reversal Algorithms
Link reversal is a versatile algorithm design technique that has been used in numerous distributed algorithms for a variety of problems. The common thread in these algorithms is that the distributed system is viewed as a graph, with vertices representing the computing nodes and edges representing some other feature of the system (for instance, point-to-point communication channels or a conflict relationship). Each algorithm assigns a virtual direction to the edges of the graph, producing a directed version of the original graph. As the algorithm proceeds, the virtual directions of some of the links in the graph change in order to accomplish some algorithm-specific goal. The criterion for changing link directions is based on information that is local to a node (such as the node having no outgoing links) and thus this approach scales well, a feature that is desirable for distributed algorithms. This monograph presents, in a tutorial way, a representative sampling of the work on link-reversal-based distributed algorithms. The algorithms considered solve routing, leader election, mutual exclusion, distributed queueing, scheduling, and resource allocation. The algorithms can be roughly divided into two types, those that assume a more abstract graph model of the networks, and those that take into account more realistic details of the system. In particular, these more realistic details include the communication between nodes, which may be through asynchronous message passing, and possible changes in the graph, for instance, due to movement of the nodes. We have not attempted to provide a comprehensive survey of all the literature on these topics. Instead, we have focused in depth on a smaller number of fundamental papers, whose common thread is that link reversal provides a way for nodes in the system to observe their local neighborhoods, take only local actions, and yet cause global problems to be solved. We conjecture that future interesting uses of link reversal are yet to be discovered. Table of Contents: Introduction / Routing in a Graph: Correctness / Routing in a Graph: Complexity / Routing and Leader Election in a Distributed System / Mutual Exclusion in a Distributed System / Distributed Queueing / Scheduling in a Graph / Resource Allocation in a Distributed System / Conclusion
Resource Allocation and Performance Optimization in Communication Networks and the Internet
This book provides a comprehensive introduction to the underlying theory, design techniques and analytical results of wireless communication networks, focusing on the core principles of wireless network design. It elaborates the network utility maximization (NUM) theory with applications in resource allocation of wireless networks, with a central aim of design and the QoS guarantee. It presents and discusses state-of-the-art developments in resource allocation and performance optimization in wireless communication networks. It provides an overview of the general background including the basic wireless communication networks and the relevant protocols, architectures, methods and algorithms.