Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributed Strong Diameter Network Decomposition   For a pair of positive parameters $D,\chi$, a partition ${\cal P}$ of the
vertex set $V$ of an $n$-vertex graph $G = (V,E)$ into disjoint clusters of
diameter at most $D$ each is called a $(D,\chi)$ network decomposition, if the
supergraph ${\cal G}({\cal P})$, obtained by contracting each of the clusters
of ${\cal P}$, can be properly $\chi$-colored. The decomposition ${\cal P}$ is
said to be strong (resp., weak) if each of the clusters has strong (resp.,
weak) diameter at most $D$, i.e., if for every cluster $C \in {\cal P}$ and
every two vertices $u,v \in C$, the distance between them in the induced graph
$G(C)$ of $C$ (resp., in $G$) is at most $D$.
  Network decomposition is a powerful construct, very useful in distributed
computing and beyond. It was shown by Awerbuch \etal \cite{AGLP89} and
Panconesi and Srinivasan \cite{PS92}, that strong $(2^{O(\sqrt{\log
n})},2^{O(\sqrt{\log n})})$ network decompositions can be computed in
$2^{O(\sqrt{\log n})}$ distributed time. Linial and Saks \cite{LS93} devised an
ingenious randomized algorithm that constructs {\em weak} $(O(\log n),O(\log
n))$ network decompositions in $O(\log^2 n)$ time. It was however open till now
if {\em strong} network decompositions with both parameters $2^{o(\sqrt{\log
n})}$ can be constructed in distributed $2^{o(\sqrt{\log n})}$ time.
  In this paper we answer this long-standing open question in the affirmative,
and show that strong $(O(\log n),O(\log n))$ network decompositions can be
computed in $O(\log^2 n)$ time. We also present a tradeoff between parameters
of our network decomposition. Our work is inspired by and relies on the
"shifted shortest path approach", due to Blelloch \etal \cite{BGKMPT11}, and
Miller \etal \cite{MPX13}. These authors developed this approach for PRAM
algorithms for padded partitions. We adapt their approach to network
decompositions in the distributed model of computation.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas