Maekawa's algorithm

Abstract: An algorithm is presented that uses only c√N messages to create mutual exclusion in a computernetwork, where N is the number of nodes and c a constant between 3 and 5. The algorithm issymmetric and allows fully parallel operation.

Abstract: An algorithm is proposed that creates mutual exclusion in a computer network whose nodes communicate only by messages and do not share memory. The algorithm sends only 2*(N - 1) messages, where N is the number of nodes in the network per critical section invocation. This number of messages is at a minimum if parallel, distributed, symmetric control is used; hence, the algorithm is optimal in this respect. The time needed to achieve mutual exclusion is also minimal under some general assumptions. As in Lamport's "bakery algorithm," unbounded sequence numbers are used to provide first-come firstserved priority into the critical section. It is shown that the number can be contained in a fixed amount of memory by storing it as the residue of a modulus. The number of messages required to implement the exclusion can be reduced by using sequential node-by-node processing, by using broadcast message techniques, or by sending information through timing channels. The "readers and writers" problem is solved by a simple modification of the algorithm and the modifications necessary to make the algorithm robust are described.

Abstract: A distributed algorithm is presented that realizes mutual exclusion among N nodes in a computer network. The algorithm requires at most N message exchanges for one mutual exclusion invocation. Accordingly, the delay to invoke mutual exclusion is smaller than in an algorithm of Ricart and Agrawala, which requires 2*(N - 1) message exchanges per invocation. A drawback of the algorithm is that the sequence numbers contained in the messages are unbounded. It is shown that this problem can be overcome by slightly increasing the number of message exchanges.

Abstract: In this paper, we present an efficient and fault-tolerant algorithm for generating quorums to solve the distributed mutual exclusion problem. The algorithm uses a logical tree organization of the network to generate tree quorums, which are logarithmic in the size of the network in the best case. Our approach is resilient to both site and communication failures, even when such failures lead to network partitioning. Furthermore, the algorithm exhibits a property of graceful degradation, i.e., it requires more messages only as the number of failures increase in the network. We describe how tree quorums can be used for various distributed applications for providing mutually exclusive access to a distributed resource, managing replicated objects, and atomically commiting a distributed transaction.