On Optimal k-linear Scheduling of Tree-Like Graphs for LogP-Machines

A k-linear schedule may map up to k directed paths of a task graph onto one processor. We consider k-linear scheduling algorithms for the communication cost model of the LogP-machine, i.e. without assumption on processor bounds. The main result of this paper is that optimal k-linear schedules of trees and tree-like task graphs G with n tasks can be computed in time O(n k+2 log n) and O(n k+3 log n), respectively, if o ≥ g. These schedules satisfy a capacity constraint, i.e., there are at most ⌈L/g⌋ messages in transit from any or to any processor at any time.

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