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