A method is provided for prioritizing jobs in a computing environment having a plurality of nodes sharing one or more resources. Such method includes, given a job A to be scheduled having certain resource requirements, generating a list P of already scheduled jobs which utilize resources required by job A and which can be preempted by job A. For each resource requirement of job A, an ordered list of jobs which can be preempted by job A is created which is ranked by the applicability of each job in the list relative to resource requirements of job A, so as to provide a plurality of ordered lists, one for each resource requirement. An ordered list L is generated by selecting one of the ordered lists, adding the top-ranked job from that ordered list to list L, then adding the top-ranked job from another one of the ordered lists to list L and so on, by repetitively selecting the top-ranked job from individual ones of all the ordered lists. Finally, a set of jobs to be preempted by job A is selected based on the list L of jobs.