Existing Global Data Computation (GDC) protocols for asynchronous systems are designed for fully connected networks. In this paper, we discuss GDC in a dedicated asynchronous chordal ring, a type of un-fully connected networks. The virtual links approach, which constructs t+1 (t<n) process-disjoint paths for each pair of processes without direct connection to tolerate failures (where t is the maximum number of processes that may crash and n is the total number of processes), can be applied to solve the GDC problem in the chordal but the virtual links approach incurs high message complexity. To reduce the high communication cost, we propose a non round-based GDC protocol for the asynchronous chordal ring with perfect failure detectors. The main advantage of our approach is that there is no notion of round, processes only send messages via direct connections and the implementation of failure detectors does not require process-disjoint paths. Analysis and comparison with the virtual links approach shows that our protocol reduces the message complexity significantly. / Singapore-MIT Alliance (SMA)

This dissertation explores the necessary and sufficient conditions to solve a variant of the dining philosophers problem. This dining variant is defined by three properties: wait-freedom, eventual weak exclusion, and eventual bounded fairness. Wait-freedom guarantees that every correct hungry process eventually enters its critical section, regardless of process crashes. Eventual weak exclusion guarantees that every execution has an infinite suffix during which no two live neighbors execute overlapping critical sections. Eventual bounded fairness guarantees that there exists a fairness bound k such that every execution has an infinite suffix during which no correct hungry process is overtaken more than k times by any neighbor. This dining variant (WF-EBF dining for short) is important for synchronization tasks where eventual safety (i.e., eventual weak exclusion) is sufficient for correctness (e.g., duty-cycle scheduling, self-stabilizing daemons, and contention managers). Unfortunately, it is known that wait-free dining is unsolvable in asynchronous message-passing systems subject to crash faults. To circumvent this impossibility result, it is necessary to assume the existence of bounds on timing properties, such as relative process speeds and message delivery time. As such, it is of interest to characterize the necessary and sufficient timing assumptions to solve WF-EBF dining. We focus on implicit timing assumptions, which can be encapsulated by failure detectors. Failure detectors can be viewed as distributed oracles that can be queried for potentially unreliable information about crash faults. The weakest detector D for WF-EBF dining means that D is both necessary and sufficient. Necessity means that every failure detector that solves WF-EBF dining is at least as strong as D. Sufficiency means that there exists at least one algorithm that solves WF-EBF dining using D. As such, our research goal is to characterize the weakest failure detector to solve WF-EBF dining. We prove that the eventually perfect failure detector 3P is the weakest failure detector for solving WF-EBF dining. 3P eventually suspects crashed processes permanently, but may make mistakes by wrongfully suspecting correct processes finitely many times during any execution. As such, 3P eventually stops suspecting correct processes.