|[+] Memory hierarchy: ordered-file maintenance, list labeling, order queries, cache-oblivious priority queues||Scribe Notes [src]|
This lecture continues our theme of cache-oblivious data structures.
First we'll finally cover the black box we used last lecture to obtain cache-oblivious B-trees: maintain an ordered file with O(1)-size gaps in O(lg2 N) moves per insert/delete in the middle of the file. As an extra bonus, we'll see how to maintain a linked list subject to order queries in O(1) time per insert/delete, which is a black box we used back in Lecture 1 to linearize the version tree when implementing full persistence.
Second we'll cover cache-oblivious priority queues, supporting insert and delete-min in what's usually subconstant time per operation (!), O((1/B) logM/B (N/B)). This will be the first time we see how to adapt to the cache size M, not just the block size B, in a cache-oblivious data structure.
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