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NP-completeness of generalized multi-Skolem sequences
Linköping University, The Institute of Technology. Linköping University, Department of Computer and Information Science, TCSLAB - Theoretical Computer Science Laboratory.
2007 (English)In: Discrete Applied Mathematics, ISSN 0166-218X, Vol. 155, no 16, 2061-2068 p.Article in journal (Refereed) Published
Abstract [en]

A Skolem sequence is a sequence a1, a2, ..., a2 n (where ai ? A = { 1, ..., n }), each ai occurs exactly twice in the sequence and the two occurrences are exactly ai positions apart. A set A that can be used to construct Skolem sequences is called a Skolem set. The existence question of deciding which sets of the form A = { 1, ..., n } are Skolem sets was solved by Skolem [On certain distributions of integers in pairs with given differences, Math. Scand. 5 (1957) 57-68] in 1957. Many generalizations of Skolem sequences have been studied. In this paper we prove that the existence question for generalized multi-Skolem sequences is NP-complete. This can be seen as an upper bound on how far the generalizations of Skolem sequences can be taken while still hoping to resolve the existence question. © 2007 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2007. Vol. 155, no 16, 2061-2068 p.
Keyword [en]
Design theory, NP-completeness, Skolem sequence
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-48388DOI: 10.1016/j.dam.2007.05.007OAI: oai:DiVA.org:liu-48388DiVA: diva2:269284
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-11

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Nordh, Gustav

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