One of the biggest open problems in external memory data structures is the priority queue problem with DecreaseKey operations. If only Insert and ExtractMin operations need to be supported, one can design a comparison-based priority queue performing O ((N /B) lg M /B N ) I/Os over a sequence of N operations, where B is the disk block size in number of words and M is the main memory size in number of words. This matches the lower bound for comparison-based sorting and is hence optimal for comparisonbased priority queues. However, if we also need to support De-creaseKeys, the performance of the best known priority queue is only O ((N /B) lg 2 N ) I/Os. The big open question is whether a degradation in performance really is necessary. We answer this question a rmatively by proving a lower bound of Ω((N /B) lg lg N B) I/Os for processing a sequence of N intermixed Insert, ExtraxtMin and DecreaseKey operations. Our lower bound is proved in the cell probe model and thus holds also for non-comparison-based priority queues. • Theory of computation → Communication complexity; Cell probe models and lower bounds; KEYWORDS Priority queues, external memory, communication complexity, lower bound ACM Reference format:
Their upper bound almost matches an unconditional lower bound by Eenberg et al. REF (also proved in the cell probe model).
DecreaseKeys are expensive for external memory priority queues
STOC 2017
Mathematics Computer Science