A more efficient message-optimal algorithm for distributed termination detection

Abstract

Termination detection is a fundamental problem in distributed computing. Many algorithms have been proposed, but only the Chandrasekaran and Venkatesan ( C V ) algorithm [l]is known to be optimal in worst-case message complexity. This optimal algorithm, however, has several undesirable properties. First, it always requires M' + 2 * IEl+ n -1 control messages, whether it is worst case o r best case, where M' is the number of basic messages issued b y the underlying computation after the algorithm starts, IEl is the number of channels in the system, and n is the number of processes. Second, ita worst-case detection delay is O(M'). In a message-intensive computation, that might not be tolerable. Third, the maximum amount of space needed b y each process is O(M'), a quantity not known at compile time, making it necessary t o use the more expensive dynamic memory allocation. Last, it works only for FIFO channels.The purpose of this paper is to remedy these drawbacks, while keeping its strength. W e propose an algorithm that requires M' + 2(n -1) control messages in the word case, but much fewer on the average, and in the best case, it uses only 2(n -1) control messages, no matter how large M' is. The worst-case detection delay is O(n), as compared to the CValgorithm's O(M'); and the space Complexity is e(n) for each process, a compile-time known quantity. The algorithm works equally well for both FIFO and Non-FIFO channels.

Tiered Algorithm for Distributed Process Quiescence and Termination Detection

“…To be consistent with existing literature, every terminating process is said to send one internal notification message to indicate completion of a process on that same PE in the PE's local queue [10]. Hence the algorithms eventually require T tasks in the epoch.…”

“…A wide range of termination detection algorithms have been proposed both as software-only [2,9,10] and hardware-specific [3,4,6,7] [21]. The most general of these algorithms support a dynamic environment in which processes are created and destroyed as the underlying computation progresses [8,12,16,21,22].…”

“…The best performing previous algorithms which support dynamic execution and do not impose message ordering nor topology constraints include the Credit Algorithm [2] which is a parental responsibility-based approach, and the CV Algorithm [9] and LTD Algorithm [10] which are wave-based approaches.…”

“…Hence the algorithms eventually require T tasks in the epoch. Since there are E events in the epoch, E quantity of external notification messages are required from one physical PE to another [10]. In the case of the Tiered Algorithm as depicted in Figure 4(a), a PE is allocated r tasks, but only one message is transmitted containing the DIFF value at nesting level i to the controller C. Thus, (T + E) messages are required for internal and external messages overall.…”

“…However, the Tiered Algorithm developed herein belongs to a class of more capable termination detection schemes [2,4,[9][10][11] that support more general diffusing models of distributed computation which allow dynamic process creation [12,13]. Applications in which processes are created and destroyed based on run-time conditions, such as distributed garbage collection [14,15], network multicasting [16], parallel marker-passing [17], and parallel polygon rendering in real time scientific visualization [18], explicitly require such capabilities.…”