6.851: Advanced Data Structures (Spring'12)

Prof. Erik Demaine TAs: Tom Morgan, Justin Zhang

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[+] Integer: sorting in linear time for w = Ω(lg^2+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(lg^2+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 lg^2+ε remains unsolved. The best algorithm so far runs in O(n √lg lg n) expected time.

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Lecture notes, page 1/7 • [previous page] • [next page] • [PDF]

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