On the Connectedness of Clash-free Timetables

TL;DR

This paper studies the connectedness of clash-free timetables using Kempe-exchange operations, enhancing understanding of search space properties crucial for optimization algorithms in timetabling problems.

Contribution

It extends the theoretical framework of reconfiguration graphs by incorporating timeslot availability, providing improved conditions for connectedness in clash-free timetables.

Findings

Established connectedness for several benchmark instances.

Derived new conditions for timetable connectedness.

Enhanced the theoretical understanding of search space structure.

Abstract

We investigate the connectedness of clash-free timetables with respect to the Kempe-exchange operation. This investigation is related to the connectedness of the search space of timetabling problem instances, which is a desirable property, for example for two-step algorithms using the Kempe-exchange during the optimization step. The theoretical framework for our investigations is based on the study of reconfiguration graphs, which model the search space of timetabling problems. We contribute to this framework by including timeslot availability requirements in the analysis and we derive improved conditions for the connectedness of clash-free timetables in this setting. We apply the theoretical insights to establish the connectedness of clash-free timetables for a number of benchmark instances.