An efficient parallel termination detection algorithm

An assumed partition algorithm for determining processor inter-communication

“…Without this requirement, we would need at least four traversals of the spanning tree instead of the two required for this algorithm (for example, see [1]). The cost of this algorithm in terms of P is O(log(P )) for the two sweeps of the virtual spanning tree.…”

An efficient delay-optimal distributed termination detection algorithm

“…Some of these algorithms are efficient in terms of the number of secondary messages used [4,17,28], but may take a long time to detect termination [4]. Similarly, some of the algorithms are either less compute intensive [15] or require less memory [14], but are vulnerable to underflow [15] or overflow [14,3] problems. 2 Although the system model described in Section 1.1 is most commonly used, there are algorithms meant for other system characteristics: those that rely on a common clock [9,25,31], or assume a specific target system topology [11], or require first-in first-out (FIFO) communication between PEs [39], 3 or are designed to tolerate PE or link failures [9,18,22,32,37,38].…”

“…Although DTD is a long-standing problem, new algorithms for it with different performance characteristics and varying assumptions regarding the target computing system model appear regularly [2][3][4]9,11,14,15,17,18,22,24,25,28,27,29,31,32,[36][37][38][39]. Some of these algorithms are efficient in terms of the number of secondary messages used [4,17,28], but may take a long time to detect termination [4].…”

“…The advantage of using this approach is that the complexity of the DTD algorithm then depends not on the total number of primary messages M, but rather on the number of primary messages M M sent out after the DTD computation begins. The other advantage is that 2 In these algorithms, underflow [15] or overflow [14,3] may occur in counters used to keep track of how primary-computation load at a PE gets distributed to other PEs because of dynamic load balancing [15] or the number of messages sent and received by a PE [14,3]. 3 That is, messages sent out by any PE i to another PE j are processed by the latter in the same order as they were issued by i.…”

“…Similarly, some of the algorithms are either less compute intensive [15] or require less memory [14], but are vulnerable to underflow [15] or overflow [14,3] problems. 2 Although the system model described in Section 1.1 is most commonly used, there are algorithms meant for other system characteristics: those that rely on a common clock [9,25,31], or assume a specific target system topology [11], or require first-in first-out (FIFO) communication between PEs [39], 3 or are designed to tolerate PE or link failures [9,18,22,32,37,38]. A general approach to transform a DTD algorithm meant for a fault-free system into that for a system with PE failures (assuming the non-faulty system graph remains connected) is given in [27].…”