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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Algorithms & Randomness Center (ARC)
Monday, February 1, 20116
Klaus 1116 West - 1:00 pm
(Refreshments will be served in Klaus 2222 at 2 pm)
Title:
Optimal Search Trees with 2-way Comparisons
Abstract:
This talk is about finding a polynomial time algorithm that you probably thought was known almost a half century ago, but it wasn’t. The polynomial time algorithm is still rather slow and requires a lot of space to solve, so we also look at extremely good and fast approximate solutions. More specifically …
In 1971, Knuth gave an O(n2)-time algorithm for the now classic problem of finding an optimal binary search tree. Knuth’s algorithm works only for search trees based on 3-way comparisons, but most modern programming languages and computers support only 2-way comparisons (<, = and >). Until this work, the problem of finding an optimal search tree using 2-way comparisons remained open — polynomial time algorithms were known only for restricted variants. We solve the general case, giving
(i) an O(n4)-time algorithm and
(ii) a linear time algorithm that gives a tree with expected search cost within 2 comparisons of the optimal.
This is joint work with Marek Chrobak, Mordecai Golin, and Neal E. Young.
