Cache-oblivious data structures for orthogonal range searching

We develop cache-oblivious data structures for orthogonal range searching, the problem of finding all T points in a set of N points in Rd lying in a query hyper-rectangle. Cacheoblivious data structures are designed to be efficient in arbitrary memory hierarchies. We describe a dynamic linear-size data structure that answers d-dimensional queries in O((N/B)1-1/d + T/B) memory transfers, where B is the block size of any two levels of a multilevel memory hierarchy. A point can be inserted into or deleted from this data structure in O(log2B N) memory transfers. We also develop a static structure for the twodimensional case that answers queries in O(logB N + T /B) memory transfers using O(N log22 N) space. The analysis of the latter structure requires that B = 22 c for some nonnegative integer constant c

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 logM/B N) amortized memory B 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 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 cacheoblivious graph algorithms

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 $O(\frac{1}{B}\log_{M/B}\frac{N}{B})$ 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