The set union problem with dynamic weighted backtracking

We consider an extension of the set union problem, in which dynamic weighted backtracking over sequences of unions is permitted. We present a new data structure which can support each operation inO(logn) time in the worst case. We prove that this bound is tight for pointer based algorithms. Furthermore, we design a different data structure to achieve better amortized bounds. The space complexity of both our data structures isO(n). Motivations for studying this problem arise in logic programming memory management.Work partially supported by NSF Grant CCR-88-14977, by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (Project ALCOM), and by the Italian MURST Project Algoritmi e Strutture di Calcolo.Partially supported by an IBM Graduate Fellowship.