NP NP -completeness of generalized multi-Skolem sequences
A Skolem sequence is a sequence a1,a2,,a2n a 1 , a 2 ,  , a 2 n (where ai?A={1,,n}) a i ? A = { 1 ,  , n } ) , each ai a i occurs exactly twice in the sequence and the two occurrences are exactly ai a i positions apart. A set A 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} A = { 1 ,  , n } are Skolem sets was solved by Skolem [On certain distributions of integers in pairs with given differences, Math. Scand. 5 (1957) 5768] 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 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.
skolem sequence design theory np np -completeness np np np np np