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 OðqÞ and a low (amortized) bit-message complexity of OðbqrÞ, 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.Index Terms-Message-passing system, resource management, mutual exclusion, group mutual exclusion, quorum-based algorithm.

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Given a distributed computation and a global predicate, predicate detection involves determining whether there exists at least one consistent cut (or global state) of the computation that satisfies the predicate. On the other hand, computation slicing is concerned with computing the smallest sub-computation-with the least number of consistent cuts-that contains all consistent cuts of the computation satisfying the predicate. In this paper, we investigate the relationship between predicate detection and computation slicing and show that the two problems are equivalent. Specifically, given an algorithm to detect a predicate in a computation , we derive an algorithm to compute the slice of with respect to . The time-complexity of the (derived) slicing algorithm is Ç´Ò µ times the time-complexity of the detection algorithm, where Ò is the number of processes and is the set of events. We discuss how the "equivalence" result of this paper can be utilized to derive a faster algorithm for solving the general predicate detection problem.Slicing algorithms described in our earlier papers are all off-line in nature. In this paper, we also give an on-line algorithm for computing the slice for a predicate that can be detected efficiently. The amortized time-complexity of the algorithm is Ç´Ò´ · Òµµ times the time-complexity of the detection algorithm, where is the average concurrency in the computation.

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.