The musical all-interval series have a certain prominence in serial composition; they can be traced back to Alban Berg and have been extensively studied and used by Ernst Krenek, for example, in his orchestral piece op.170, “Quaestio temporis” (A Question of Time).

Hoos describes the generalization of the problem and its formulation as a CSP and SAT problem in his PhD thesis: Stochastic Local Search - Methods, Models, Applications (PhD thesis, TU Darmstadt, 1998)

Simonis and Beldiceanu have shown that, using global constraints, CHIP can find one solution without search. A note on CSPLIB prob007, by Simonis and Beldiceanu.

A followup note by Puget and Regin shows that all solutions can be found in ILOG’s Solver with reasonable efficiency.

Gent, McDonald and Smith have shown, in a paper (Conditional Symmetry in the All-Interval Series Problem) in the proceedings of SymCon03, that a reformulation of the problem yields all solutions 50 times faster than previous techniques.

File	Type	Notes
gmsSymCon03.pdf	pdf
helmut.pdf	pdf
puget.pdf	pdf