On the number of solutions of the discretizable molecular distance geometry problem

Authors:
Leo Liberti;Benoît Masson;Jon Lee;Carlile Lavor;Antonio Mucherino
Affiliations:
LIX, École Polytechnique, Palaiseau, France;IRISA, INRIA, Rennes, France;Dept. of Mathematical Sciences, IBM T.J. Watson Research Center, Yorktown Heights, NY;Department of Applied Mathematics, IMECC-UNICAMP, SP, Brazil;CERFACS, Toulouse, France
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

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Abstract

The Discretizable Molecular Distance Geometry Problem is a subset of instances of the distance geometry problem that can be solved by a combinatorial algorithm called "Branch-and-Prune". It was observed empirically that the number of solutions of YES instances is always a power of two. We perform an extensive theoretical analysis of the number of solutions for these instances and we prove that this number is a power of two with probability one.