Topics in Distributed Algorithms: On TDMA for Ad Hoc Networks and Coded Atomic Storage Algorithms

Abstract: Distributed algorithms run on a network of nodes. The nodes are running concurrently and are independent from each other. Furthermore, they have their own instructions and information. In this context, the challenges are to show that the algorithm is correct, regardless of computational, or communication delays. Furthermore, the behavior after transient faults and under the existence of Byzantine nodes is of our interest. This thesis discusses fundamental communication models for distributed algorithms. These models are implementing abstract communication methods. First we address medium access control for a wireless medium with guarantees on the communication delay. We discuss time division multiple access protocols for ad-hoc networks and we introduce an algorithm that creates a TDMA schedule without using external references for localization, or time. This algorithm recovers from transient faults and is self-stabilizing. The TDMA schedule provides guarantees on the delivery time. This enables the use of this algorithm as MAC layer for safety critical applications. Furthermore, we provide bounds for the convergence. The second topic is the emulation of shared memory on message passing networks. Both, shared memory and message passing are basic interprocessor communication models for distributed algorithms. We are providing a way of emulating shared memory on top of an existing message passing network under the presence of data corruption and stop-failed nodes. Additionally, we ensure the privacy of the data that is stored in the shared memory.