On the intractability of preemptive single-machine job scheduling with release times, deadlines, and family setup times

Abstract

When building secure safety-critical software systems upon modern processors, a system designer may wish to thwart cache side-channel attacks while ensuring that no process misses its deadline. If the side-channel attacks are prevented in a uniprocessor environment by flushing the cache whenever context is switched from a process with a high security level to a process with a low security level then the problem of scheduling processes while meeting deadlines can be modeled as a single-machine job scheduling problem with release times, deadlines, preemption, and family setup times, which is known to be NP-hard. Since we expect the number of security levels and the worst-case cache flush time in practical applications to be “small”, the number of families, F, and the largest setup time, S, are natural parameters for the problem. We show that the problem, when parameterized by (F,S), is not fixed-parameter tractable by proving that the single-machine job scheduling problem with release times, deadlines, preemption, and two families with setup times picked from the set {0,1} is NP-hard. We also develop an O(nlog⁡n) algorithm for the single-machine job scheduling problem with deadlines and two families with setup times.