Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $D$-ary Bounded-Length Huffman Coding   Efficient optimal prefix coding has long been accomplished via the Huffman
algorithm. However, there is still room for improvement and exploration
regarding variants of the Huffman problem. Length-limited Huffman coding,
useful for many practical applications, is one such variant, in which codes are
restricted to the set of codes in which none of the $n$ codewords is longer
than a given length, $l_{\max}$. Binary length-limited coding can be done in
$O(n l_{\max})$ time and O(n) space via the widely used Package-Merge
algorithm. In this paper the Package-Merge approach is generalized without
increasing complexity in order to introduce a minimum codeword length,
$l_{\min}$, to allow for objective functions other than the minimization of
expected codeword length, and to be applicable to both binary and nonbinary
codes; nonbinary codes were previously addressed using a slower dynamic
programming approach. These extensions have various applications -- including
faster decompression -- and can be used to solve the problem of finding an
optimal code with limited fringe, that is, finding the best code among codes
with a maximum difference between the longest and shortest codewords. The
previously proposed method for solving this problem was nonpolynomial time,
whereas solving this using the novel algorithm requires only $O(n (l_{\max}-
l_{\min})^2)$ time and O(n) space.

37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
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
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex