Cache-oblivious priority queue and graph algorithm applications

In this paper we develop an optimal cache-oblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O(1/B log_M/B N/B) amortized memory transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cache-oblivious data structure, M and B are not used in the description of the structure. The bounds match the bounds of several previously developed external-memory (cache-aware) priority queue data structure, which all rely crucially on knowledge about M and B. Priority queues are a critical component in many of the best known external-memory graph algorithms, and using our cache-oblivious priority queue we develop several cache-oblivious graph algorithms.