An Optimal Cache-Oblivious Priority Queue and Its Application to Graph Algorithms

We develop an optimal cache-oblivious priority queue data structure, supporting insertion, deletion, and delete-min operations in O( 1 B logM/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. Our structure is as efficient as several previously developed external memory (cache-aware) priority queue data structures, 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.