Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Search Trees with 2-Way Comparisons   In 1971, Knuth gave an $O(n^2)$-time algorithm for the classic problem of
finding an optimal binary search tree. Knuth's algorithm works only for search
trees based on 3-way comparisons, while most modern computers support only
2-way comparisons (e.g., $<, \le, =, \ge$, and $>$). Until this paper, the
problem of finding an optimal search tree using 2-way comparisons remained open
-- poly-time algorithms were known only for restricted variants. We solve the
general case, giving (i) an $O(n^4)$-time algorithm and (ii) an $O(n \log
n)$-time additive-3 approximation algorithm. Also, for finding optimal binary
split trees, we (iii) obtain a linear speedup and (iv) prove some previous work
incorrect.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org