Scheduling with Bully Selfish Jobs

Abstract

In job scheduling with precedence constraints, i ≺ j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedenceconstraint where i ≺ s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa.The work of our hero teacher, Ms. Schedule, was initiated due to an arrival of bully jobs to her kindergarten. Bully jobs bypass all other nice jobs, but respect each other. This natural environment corresponds to the case where the selfish precedence-constraints graph is a complete bipartite graph. Ms. Schedule analyzed the minimum makespan and the minimum total flow-time problems for this setting. She then extended her interest to other topologies of the precedence constraints graph and other special instances with uniform length jobs and/or release times.

Minimizing Tardiness in a Scheduling Environment with Jobs' Hierarchy

“…Dominant jobs can be processed after less dominant ones, if their performance is not harmed. An environment in which some jobs are aggressive is studied in [20], where a new notion of selfish precedence constraint is defined. The paper presents algorithms for scheduling jobs on parallel machines, where some of the jobs are aggressive.…”