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Optimal Scheduling for Disconnected Cooperation
, 2001
"... We consider a distributed environment consisting of n processors that need to perform t tasks. We assume that communication is initially unavailable and that processors begin work in isolation. At some unknown point of time an unknown collection of processors may establish communication. Before proc ..."
Abstract

Cited by 9 (3 self)
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We consider a distributed environment consisting of n processors that need to perform t tasks. We assume that communication is initially unavailable and that processors begin work in isolation. At some unknown point of time an unknown collection of processors may establish communication. Before processors begin communication they execute tasks in the order given by their schedules. Our goal is to schedule work of isolated processors so that when communication is established for the rst time, the number of redundantly executed tasks is controlled. We quantify worst case redundancy as a function of processor advancements through their schedules. In this work we rene and simplify an extant deterministic construction for schedules with n t, and we develop a new analysis of its waste. The new analysis shows that for any pair of schedules, the number of redundant tasks can be controlled for the entire range of t tasks. Our new result is asymptotically optimal: the tails of these schedules are within a 1 +O(n 1 4 ) factor of the lower bound. We also present two new deterministic constructions one for t n, and the other for t n 3=2 , which substantially improve pairwise waste for all prexes of length t= p n, and oer near optimal waste for the tails of the schedules. Finally, we present bounds for waste of any collection of k 2 processors for both deterministic and randomized constructions. 1
Dynamic Load Balancing with Group Communication ⋆
"... This work considers the problem of efficiently performing a set of tasks using a network of processors in the setting where the network is subject to dynamic reconfigurations, including partitions and merges. A key challenge for this setting is the implementation of dynamic load balancing that reduc ..."
Abstract
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This work considers the problem of efficiently performing a set of tasks using a network of processors in the setting where the network is subject to dynamic reconfigurations, including partitions and merges. A key challenge for this setting is the implementation of dynamic load balancing that reduces the number of tasks that are performed redundantly because of the reconfigurations. We explore new approaches for load balancing in dynamic networks that can be employed by applications using a group communication service. The group communication services that we consider include a membership service (establishing new groups to reflect dynamic changes) but does not include maintenance of a primary component. For the nprocessor, ntask load balancing problem defined in this work, the following specific results are obtained. For the case of fully dynamic changes including fragmentation and merges we show that the termination time of any online task assignment algorithm is greater than the termination time of an offline task assignment algorithm by a factor greater than n/12. We present a load balancing algorithm that guarantees completion of all tasks in all fragments caused by partitions with work O(n + f · n) inthepresenceoff fragmentation failures. We develop an effective scheduling strategy for minimizing the task execution redundancy and we prove that our strategy provides each of the n processors with a schedule of Θ(n 1/3) tasks such that at most one task is performed redundantly by any two processors.