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

Abstract

We develop an optimal cache-oblivious priority queue data structure, supporting insertion, deletion, and delete-min operations in $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ 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.