Abstract
We introduce a natural but seemingly yet unstudied generalization of the
problem of scheduling jobs on a single machine so as to minimize the
number of tardy jobs. Our generalization lies in simultaneously
considering several instances of the problem at once. In particular, we
have $n$ clients over a period of $m$ days, where each client has a
single job with its own processing time and deadline per day. Our goal
is to provide a schedule for each of the $m$ days, so that each client
is guaranteed to have their job meet its deadline in at least $k \le m$
days. This corresponds to an equitable schedule where each client is
guaranteed a minimal level of service throughout the period of $m$ days.
We provide a thorough analysis of the computational complexity of three
main variants of this problem, identifying both efficient algorithms and
worst-case intractability results.
Original language | English |
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Publisher | arXiv:2010.04643 [cs.DM] |
State | Published - 2020 |
Keywords
- Computer Science - Discrete Mathematics
- Computer Science - Data Structures and Algorithms