Abstract: Example aspects of the present disclosure provide for an example computer-implemented method for generating alternative network paths, the example method including obtaining a network graph; determining flows respectively for edges of the network graph by: resolving a linear system of weights associated with the edges, the linear system resolved over a reduced network graph, and propagating a solution of the linear system into a respective partition of a plurality of partitions of the network graph to determine at least one of the flows within the respective partition; and determining a plurality of alternative paths across the network graph.

Abstract: The scheduling of a processing job to be performed by at least a portion of a cluster of processing resources distributed across multiple machines. The processing job is associated with a certain entity having a certain amount of guaranteed processing resources on the cluster. If there are enough processing resources to perform the job, then the job may be initiated. On the other hand, if there are not enough processing resources to perform the job, and there are yet some remaining processing resources that are guaranteed to the certain entity, then one or more other jobs that are associated with other entities are at least partially preempted until there are enough processing resources to perform the processing job.