# 6.851: Advanced Data Structures (Spring'21)

## Prof. Erik Demaine     TAs: Josh Brunner, Yevhenii Diomidov, Dylan Hendrickson

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## Lecture 14 Video     [previous] [next]

 [+] Integer: sorting in linear time for w = Ω(lg2+ε n), priority queues This lecture is about the state-of-the-art in sorting and priority queues on a word RAM. An equivalence by Thorup shows that any sorting algorithm can be transformed into a priority queue with operations taking 1/nth the time to sort. So these are really one and the same problem. The best results we know for sorting in linear time (and thus for constant-time priority queues) is when w = O(lg n) and when w = Ω(lg2+ε n). The first result is just radix sort. The second result is the main topic of the lecture: a fancy word-RAM algorithm called signature sorting. It uses a combination of hashing, merge sort, and parallel sorting networks. The range of w in between lg and lg2+ε remains unsolved. The best algorithm so far runs in O(n √lg lg n) expected time.
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