Citation
Algorithms and Complexity of Student Sectioning for Existing Timetables. In proceedings of the 6th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2013), 27 - 30 Aug 2013, Ghent, Belgium, pages 218-229, 2013.
Paper
Abstract
We show that the following fundamental question in student sectioning can be e?ciently decided in polynomial time: Is it possible to assign m students to k sectioned courses w.r.t. a given timetable with l timeslots, such that the individual capacities of all sections are not exceeded and no student has more than one appointment per timeslot? Our result opens the possibility to check feasibility of candidate-timetables w.r.t. this question as part of timetabling algorithms e?ciently. Based on a succinct representation of solutions, we also provide an algorithm to compute optimal assignments in O(k2l2 log(sumA)) where sumA is the sum of all speci?ed section capacities. On the other hand, we prove that adding any single of the following constraints turns the above question into an NP-complete problem: Course-selection constraint: Student’s course-selections must be respected. Timeslot-constraint: Students have individual timeslot restrictions. Multiple-event constraint: Sections may have multiple events in the timetable, and there must be no timeslot clashes between all section-events for each student. Hence our investigation gives insight into the location of the borderline between e?ciently solvable and computational hard problem variations
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Bibtex
@INPROCEEDINGS{2013-218-229-P, author = {M. Dostert and A. Politz and H. Schmitz },
title = {Algorithms and Complexity of Student Sectioning for Existing Timetables },
booktitle = {In proceedings of the 6th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2013), 27 - 30 Aug 2013, Ghent, Belgium},
year = {2013},
editor = {G. Kendall and B. McCollum and G. {Venden Berghe}},
pages = {218--229},
note = {Paper},
abstract = {We show that the following fundamental question in student sectioning can be e?ciently decided in polynomial time: Is it possible to assign m students to k sectioned courses w.r.t. a given timetable with l timeslots, such that the individual capacities of all sections are not exceeded and no student has more than one appointment per timeslot? Our result opens the possibility to check feasibility of candidate-timetables w.r.t. this question as part of timetabling algorithms e?ciently. Based on a succinct representation of solutions, we also provide an algorithm to compute optimal assignments in O(k2l2 log(sumA)) where sumA is the sum of all speci?ed section capacities. On the other hand, we prove that adding any single of the following constraints turns the above question into an NP-complete problem: Course-selection constraint: Student’s course-selections must be respected. Timeslot-constraint: Students have individual timeslot restrictions. Multiple-event constraint: Sections may have multiple events in the timetable, and there must be no timeslot clashes between all section-events for each student. Hence our investigation gives insight into the location of the borderline between e?ciently solvable and computational hard problem variations},
owner = {Graham},
timestamp = {2017.01.16},
webpdf = {2013-218-229-P.pdf} }