Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Two LZ78-style Grammars: Compression Bounds and Compressed-Space
  Computation   We investigate two closely related LZ78-based compression schemes: LZMW (an
old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.).
Both LZD and LZMW naturally produce a grammar for a string of length $n$; we
show that the size of this grammar can be larger than the size of the smallest
grammar by a factor $\Omega(n^{\frac{1}3})$ but is always within a factor
$O((\frac{n}{\log n})^{\frac{2}{3}})$. In addition, we show that the standard
algorithms using $\Theta(z)$ working space to construct the LZD and LZMW
parsings, where $z$ is the size of the parsing, work in $\Omega(n^{\frac{5}4})$
time in the worst case. We then describe a new Las Vegas LZD/LZMW parsing
algorithm that uses $O (z \log n)$ space and $O(n + z \log^2 n)$ time w.h.p..

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat