Ranganath Atreya

A Quorum-Based Group Mutual Exclusion Algorithm for a Distributed System with Dynamic Group Set

The group mutual exclusion problem extends the traditional mutual exclusion problem by associating a type (or a group) with each critical section. In this problem, processes requesting critical sections of the same type can execute their critical sections concurrently. However, processes requesting critical sections of different types must execute their critical sections in a mutually exclusive manner. We present a distributed algorithm for solving the group mutual exclusion problem based on the notion of surrogate-quorum. Intuitively, our algorithm uses the quorum that has been successfully locked by a request as a surrogate to service other compatible requests for the same type of critical section. Unlike the existing quorum-based algorithms for group mutual exclusion, our algorithm achieves a low message complexity of O(q) and a low (amortized) bit-message complexity of O(bqr), where q is the maximum size of a quorum, b is the maximum number of processes from which a node can receive critical section requests, and r is the maximum size of a request while maintaining both synchronization delay and waiting time at two message hops. As opposed to some existing quorum-based algorithms, our algorithm can adapt without performance penalties to dynamic changes in the set of groups. Our simulation results indicate that our algorithm outperforms the existing quorum-based algorithms for group mutual exclusion by as much as 45 percent in some cases. We also discuss how our algorithm can be extended to satisfy certain desirable properties such as concurrent entry and unnecessary blocking freedom.

A Dynamic Group Mutual Exclusion Algorithm Using Surrogate-Quorums

The group mutual exclusion problem extends the traditional mutual exclusion problem by associating a type with each critical section. In this problem, processes requesting critical sections of the same type can execute their critical sections concurrently. However, processes requesting critical sections of different types must execute their critical sections in a mutually exclusive manner. In this paper, we provide a distributed algorithm for solving the group mutual exclusion problem based on the notion of surrogate-quorum. Intuitively, the algorithm uses the quorum that has been successfully locked by a request as a surrogate to service other compatible requests for the same type of critical section. Unlike the existing quorum-based algorithms for group mutual exclusion, the algorithm achieves a low message complexity of O(q), where q is the maximum size of a quorum, while maintaining both synchronization delay and waiting time at two message hops. Moreover, like the existing quorum-based algorithms, the algorithm has high maximum concurrency of n, where n is the number of processes in the system. The existing quorum-based algorithms assume that the number of groups is static and does not change during runtime. However, the algorithm can adapt without performance penalties to dynamic changes in the number of groups. Simulation results indicate that our algorithm outperforms the existing quorum-based algorithms for group mutual exclusion by as much as 50% in some cases

Efficient detection of a locally stable predicate in a distributed system

We present an efficient approach to detect a locally stable predicate in a distributed computation. Examples of properties that can be formulated as locally stable predicates include termination and deadlock of a subset of processes. Our algorithm does not require application messages to be modified to carry control information (e.g., vector timestamps), nor does it inhibit events (or actions) of the underlying computation. The worst-case message complexity of our algorithm is O(n(m+1)), where n is the number of processes in the system and m is the number of events executed by the underlying computation. We show that, in practice, its message complexity should be much lower than its worst-case message complexity. The detection latency of our algorithm is O(d) time units, where d is the diameter of communication topology. Our approach also unifies several known algorithms for detecting termination and deadlock. We also show that our algorithm for detecting a locally stable predicate can be used to efficiently detect a stable predicate that is a monotonic function of other locally stable predicates.

Detecting Locally Stable Predicates Without Modifying Application Messages

In this paper, we give an efficient algorithm to determine whether a locally stable predicate has become true in an underlying computation. Examples of locally stable predicates include termination and deadlock. Our algorithm does not require application messages to be modified to carry control information (e.g., vector timestamps), nor does it inhibit events (or actions) of the underlying computation. Once the predicate becomes true, the detection latency (or delay) of our algorithm is proportional to the time-complexity of computing a (possibly inconsistent) snapshot of the system. Moreover, only O(n) control messages are required to detect the predicate once it holds, where n is the number of processes.