Year: 1989
Type: dissertation
Abstract: In distributed computing, often several processors need to perform some action, but two simultaneous actions might produce unacceptable interactions. Preventing these interactions is the symmetry breaking problem. Processes must cooperate to determine the order in which they will proceed, subject to additional rules that depend on the particular problem. Three problems are considered.
The first problem is electing a leader in a ring. Solutions to this problem are well-known for the case that all processors have distinct identifiers. Election is not always possible if identifiers are not distinct. Those cases which can be solved are delineated and algorithms are given for the solvable cases. Several of the algorithms are shown to be optimal in terms of messages sent and total information sent (measured by counting how many identifiers are sent).
The distributed resource allocation problem is a generalized form of Dining Philosophers. Each process needs a predetermined set of resources before it can enter its critical section, but two processes cannot simultaneously use a resource. Processes can communicate directly only if they have a resource in common. Access to resources must be controlled so that each process quickly obtains the resources it needs. We show an algorithm that has a waiting time that is a polynomial function of the number of nearby processes. Extensions of the problem where not all resources are necessary, or where many processes might require the same resource are considered.
The final problem is to determine the number of variables needed for symmetric mutual exclusion type problems. In symmetric mutual exclusion, processes are identical except for an identifier, and processes can distinguish themselves only by comparing identifiers. Some bounds for the asymmetric case were known, but we give tight bounds for symmetric lockout-free and deadlock-free mutual exclusion. The lower bounds hold even if comparisons between unequal identifiers can provide an arbitrary amount of information about identifiers. A tight bound for symmetric leader election is given, even if asymmetric solutions are allowed. Other problems such as synchronous election, systems with memory and process numbering are also considered.
Authors: Eugene Styer, Gary L. Peterson
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2565249478