Note: A note on the hardness of Skolem-type sequences

Authors:
Gustav Nordh
Affiliations:
Department of Computer and Information Science, Linköpings Universitet, S-581 83 Linköping, Sweden
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

The purpose of this note is to give upper bounds (assuming P different from NP) on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. We prove that the existence questions for both multi-Skolem sequences and generalized Skolem sequences are strongly NP-complete. These results are significant strengthenings and simplifications of the recent NP-completeness result for generalized multi-Skolem sequences.