During the last five years a peak of interest has been observed in the problems related to computer-aided timetabling. The most recent works in this area are based on the application of modern information technologies. Here the main directions of modern research and design are reviewed. A classification is proposed for academic timetabling problems, requirements for the timetables, mathematical models, solution methods, data representation, and interface design. Modern problem solution and software design approaches are represented in connection with the theoretical background and world experience of 35 years. The integration of several algorithmic and interactive tools is discussed. Criticisms of timetabling computer support practicability and related myths are also reviewed. Related topics, like sport scheduling and scheduling sport, are represented. Some unsolved matters are outlined.

Computer-Aided School and University Timetabling: The New Wave

An XML format for benchmarks in high school timetabling II

The High School Timetabling Problem is amongst the most widely used timetabling problems. This problem has varying structures in different high schools even within the same country or educational system. Due to lack of standard benchmarks and data formats this problem has been studied less than other timetabling problems in the literature. In this paper we describe the High School Timetabling Problem in several countries in order to find a common set of constraints and objectives. Our main goal is to provide exchangeable benchmarks for this problem. To achieve this we propose a standard data format suitable for different countries and educational systems, defined by an XML schema. The schema and datasets are available online.

/pdf/an-xml-format-for-benchmarks-in-high-school-timetabling-1uh5s251bw.pdf

An XML format for benchmarks in High School Timetabling

https://org.uib.no/iirapporter/2004-271.pdf

Equitable colorings of bounded treewidth graphs

In this paper, we consider the mutual exclusion scheduling problem for comparability graphs. Given an undirected graph G and a fixed constant m, the problem is to find a minimum coloring of G such that each color is used at most m times. The complexity of this problem for comparability graphs was mentioned as an open problem by Mohring [Problem 9.10, in: I. Rival (Ed.), Graphs and Orders, Reidel, Dordrecht, 1985, p. 583] and for permutation graphs (a subclass of comparability graphs) as an open problem by Lonc [On complexity of some chain and antichain partition problem, in: G. Schmidt, R. Berghammer (Eds.), Graph Theoretical Concepts in Computer Science, WG 91, Lecture Notes in Computer Science, vol. 570, 1999, pp. 97-104]. We prove that this problem is already NP-complete for permutation graphs and for each fixed constant m ≥ 6.

H. Ikeda

Papers

An existential problem of a weight-controlled subset and its application to school timetable construction