TY - UNPB

T1 - Equitable Scheduling for the Total Completion Time Objective.

AU - Hermelin, Danny

AU - Molter, Hendrik

AU - Niedermeier, Rolf

AU - Shabtay, Dvir

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2021/12/27

Y1 - 2021/12/27

N2 - We investigate a novel scheduling problem where we have n clients, each associated with a single job on each of a set of m different days. On each day, a single machine is available to process the n jobs non-preemptively. The goal is provide an equitable set of schedules for all m days such that the sum of completion times of each client over all days is not greater than some specified equability parameter k. The 1∣∣maxj∑iCi,j problem, as we refer to it in this paper, fits nicely into a new model introduced by Heeger et al. [AAAI '21] that aims at capturing a generic notion of fairness in scheduling settings where the same set of clients repeatedly submit scheduling requests over a fixed period of time. We show that the 1∣∣maxj∑iCi,j problem is NP-hard even under quite severe restrictions. This leads us to investigating two natural special cases: One where we assume the number of days to be small and one where we consider the number of clients to be small. We present several tractability results for both cases.

AB - We investigate a novel scheduling problem where we have n clients, each associated with a single job on each of a set of m different days. On each day, a single machine is available to process the n jobs non-preemptively. The goal is provide an equitable set of schedules for all m days such that the sum of completion times of each client over all days is not greater than some specified equability parameter k. The 1∣∣maxj∑iCi,j problem, as we refer to it in this paper, fits nicely into a new model introduced by Heeger et al. [AAAI '21] that aims at capturing a generic notion of fairness in scheduling settings where the same set of clients repeatedly submit scheduling requests over a fixed period of time. We show that the 1∣∣maxj∑iCi,j problem is NP-hard even under quite severe restrictions. This leads us to investigating two natural special cases: One where we assume the number of days to be small and one where we consider the number of clients to be small. We present several tractability results for both cases.

M3 - Preprint

BT - Equitable Scheduling for the Total Completion Time Objective.

ER -