Consider a parallel program with n processes and a synchronization granularity z. Consider also two parallel architectures: an SMP with q processors and run-time reallocation of processes to processors, and a distributed system (or cluster) with k processors and no run-time reallocation. There is an inter-processor communication delay of t time units for the system with no run-time reallocation. In this paper we define a function H(n,k,q,t,z) such that the minimum completion time for all programs with n processes and a granularity z is at most H(n,k,q,t,z) times longer using the system with no reallocation and k processors compared to using the system with q processors and run-time reallocation. We assume optimal allocation and scheduling of processes to processors. The function H(n,k,q,t,z)is optimal in the sense that there is at least one program, with n processes and a granularity z, such that the ratio is exactly H(n,k,q,t,z). We also validate our results using measurements on distributed and multiprocessor Sun/Solaris environments. The function H(n,k,q,t,z) provides important insights regarding the performance implications of the fundamental design decision of whether to allow run-time reallocation of processes or not. These insights can be used when doing the proper cost/benefit trade-offs when designing parallel execution platforms.

Vi betraktar ett parallellt program med n processer och synkroniseringsgranularitet z, samt två parallella arkitekturer. Det första har q processorer och full allokering av processerna är tillåten, och det andra har k processorer och ingen reallokering under körningen. Varje reallokering tar t sekunder. Vi definierar en funktion H(n,k,q,t,z) så att körtiden för ett program med n processer och granularitet z är högst en faktor H(n,k,q,t,z) längre för systemet utan reallokering än för systemed med. Vi antar optimal allokering av processer i de två systemen. Funktionen är optimal - det finns program där körtiden är exakt H(n,k,q,t,z) gånger längre. Resultaten valideras med mätningar på multiprocessorer i Sun/Solaris miljö.

We consider the optimal makespan C(P, m, i) of an arbitrary set P of independent jobs scheduled with i preemptions on a multiprocessor with m identical processors. We compare the ratio for such makespans for i and j preemptions, respectively, where i < j. This ratio depends on P, but we are interested in the P that maximizes this ratio, i. e. we calculate a formula for the worst case ratio G(m, i, j) defined as G(m, i, j) = max C(P, m, i)/C(P, m, j), where the maximum is taken over all sets P of independent jobs.

Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. In this paper we define recovery schemes, which are optimal for a number of important cases. We also show that the problem of finding optimal recovery schemes corresponds to the mathematical problem called Golomb rulers. These provide optimal recovery schemes for up to 373 computers in the cluster.

Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. We define recovery schemes, which are optimal for a larger number of computers down than in previous results. We also show that the problem of finding optimal recovery schemes for a cluster with n computers corresponds to the mathematical problem of finding the longest sequence of positive integers for which the sum of the sequence and the sums of all subsequences modulo n are unique.

Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down the load on these computers must be redistributed to other computers in the cluster. The redistribution is determined by the recovery scheme. The recovery scheme should keep the load as evenly distributed as possible even when the most unfavorable combinations of computers break down, i.e. we want to optimize the worst-case behavior. We have previously defined recovery schemes that are optimal for some limited cases. In this paper we find a new recovery schemes that are based on so called Golomb rulers. They are optimal for a much larger number of cases than the previous results.

Clusters and distributed systems offer fault tolerance and high performance through load sharing. When all n computers are up and running, we would like the load to be evenly distributed among the computers. When one or more computers break down, the load on these computers must be redistributed to other computers in the system. The redistribution is determined by the recovery scheme. The recovery scheme is governed by a sequence of integers modulo n. Each sequence guarantees minimal load on the computer that has maximal load even when the most unfavorable combinations of computers go down. We calculate the best possible such recovery schemes for any number of crashed computers by an exhaustive search, where brute force testing is avoided by a mathematical reformulation of the problem and a branch-and-bound algorithm. The search nevertheless has a high complexity. Optimal sequences, and thus a corresponding optimal bound, are presented for a maximum of twenty one computers in the distributed system or cluster.