Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomized contractions meet lean decompositions   We show an algorithm that, given an $n$-vertex graph $G$ and a parameter $k$,
in time $2^{O(k \log k)} n^{O(1)}$ finds a tree decomposition of $G$ with the
following properties:
  * every adhesion of the tree decomposition is of size at most $k$, and
  * every bag of the tree decomposition is $(i,i)$-unbreakable in $G$ for every
$1 \leq i \leq k$.
  Here, a set $X \subseteq V(G)$ is $(a,b)$-unbreakable in $G$ if for every
separation $(A,B)$ of order at most $b$ in $G$, we have $|A \cap X| \leq a$ or
$|B \cap X| \leq a$. The resulting tree decomposition has arguably best
possible adhesion size boundsand unbreakability guarantees. Furthermore, the
parametric factor in the running time bound is significantly smaller than in
previous similar constructions. These improvements allow us to present
parameterized algorithms for Minimum Bisection, Steiner Cut, and Steiner
Multicut with improved parameteric factor in the running time bound.
  The main technical insight is to adapt the notion of lean decompositions of
Thomas and the subsequent construction algorithm of Bellenbaum and Diestel to
the parameterized setting.

37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
17
The categories of this paper are: q-fin