Dekker's algorithm

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 fast mutual exclusion algorithm where only five accesses to the shared memory are needed in order to enter a critical section in the absence of contention is presented. In the presence of contention, the winning process may need to delay itself for 3* Delta time units, where Delta is an upper bound on the time taken by the slowest process to execute a statement involving an access to the shared memory. It is also proven that there is not two (or more) process mutual exclusion algorithm with an upper bound on the number of times a winning process needs to access the shared memory in order to enter its critical section in the presence of contention. However, under the assumption that busy-waiting counts as just one step, the authors present, for every fixed parameter k, an algorithm with the property that from a state where no process tries to enter its critical section, as long as the number of contenders does not exceed k, the time complexity of the winning process is a linear function of k. Finally, the ideas from the mutual exclusion algorithm are used to implement a fast and simple consensus algorithm. >

Abstract: We present an adaptive algorithm for N-process mutual exclusion under read/write atomicity in which all busy waiting is by local spinning. In our algorithm, each process p performs O(k) remote memory references to enter and exit its critical section, where k is the maximum "point contention" experienced by p. The space complexity of our algorithm is Θ (N), which is clearly optimal. Our algorithm is the first mutual exclusion algorithm under read/write atomicity that is adaptive when time complexity is measured by counting remote memory references.

Abstract: A new solution to the concurrent programming control (mutual exclusion) problem that is immune to process failures and restarts is presented. The algorithm uses just four values of shared memory per process, which is within one value of the known lower bound. The algorithm is implemented using two binary variables tha t make it immune to read errors occurring during writes, tha t is, "flickering bits."