Relation-algebraic specification and solution of special university timetabling problems

Abstract In this paper, we are concerned with a special timetabling problem. It was posed to us by the administration of our university and stems from the adoption of the British-American system of university education in Germany. This change led to the concrete task of constructing a timetable that enables the undergraduate education of secondary school teachers within three years in the “normal case” and within four years in the case of exceptional combinations of subjects. We develop two relation-algebraic models of the timetabling problem and in each case algorithms for computing solutions. The latter easily can be implemented in the Kiel RelView tool showing that RelView can be used for timetabling.

[1]  Alfred Tarski,et al.  Relational selves as self-affirmational resources , 2008 .

[2]  Thomas Ströhlein,et al.  A Boolean matrix iteration in timetable construction , 1976 .

[3]  J. van Leeuwen,et al.  Theory and Applications of Relational Structures as Knowledge Instruments , 2003, Lecture Notes in Computer Science.

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  Gunther Schmidt,et al.  Some Aspects in the Construction of Timetables , 1974, IFIP Congress.

[6]  Andrea Schaerf,et al.  A Survey of Automated Timetabling , 1999, Artificial Intelligence Review.

[7]  Frank Neumann,et al.  RelView - An OBDD-Based Computer Algebra System for Relations , 2005, CASC.

[8]  Rudolf Berghammer Relation-algebraic computation of fixed points with applications , 2006, J. Log. Algebraic Methods Program..

[9]  Gunther Schmidt,et al.  Relational Methods in Computer Science , 1999, Inf. Sci..

[10]  Gunther Schmidt,et al.  Theory and Applications of Relational Structures as Knowledge Instruments II , 2006 .

[11]  Gunther Schmidt,et al.  Relationen und Graphen , 1989, Mathematik für Informatiker.

[12]  Ralf Behnke,et al.  RELVIEW - A System for Calculating With Relations and Relational Programming , 1998, FASE.

[13]  Britta Kehden,et al.  Evaluating Sets of Search Points Using Relational Algebra , 2006, RelMiCS.

[14]  Rudolf Berghammer,et al.  Implementation of Relational Algebra Using Binary Decision Diagrams , 2001, RelMiCS.

[15]  Jonathan L. Gross,et al.  Handbook of graph theory , 2007, Discrete mathematics and its applications.