Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally-Iterative Distributed (Delta + 1)-Coloring below
  Szegedy-Vishwanathan Barrier, and Applications to Self-Stabilization and to
  Restricted-Bandwidth Models   We consider graph coloring and related problems in the distributed
message-passing model. {Locally-iterative algorithms} are especially important
in this setting. These are algorithms in which each vertex decides about its
next color only as a function of the current colors in its 1-hop neighborhood.
In STOC'93 Szegedy and Vishwanathan showed that any locally-iterative
(Delta+1)-coloring algorithm requires Omega(Delta log Delta + log^* n) rounds,
unless there is "a very special type of coloring that can be very efficiently
reduced" \cite{SV93}. In this paper we obtain this special type of coloring.
Specifically, we devise a locally-iterative (Delta+1)-coloring algorithm with
running time O(Delta + log^* n), i.e., {below} Szegedy-Vishwanathan barrier.
This demonstrates that this barrier is not an inherent limitation for
locally-iterative algorithms. As a result, we also achieve significant
improvements for dynamic, self-stabilizing and bandwidth-restricted settings:
  - We obtain self-stabilizing distributed algorithms for
(Delta+1)-vertex-coloring, (2Delta-1)-edge-coloring, maximal independent set
and maximal matching with O(Delta+log^* n) time. This significantly improves
previously-known results that have O(n) or larger running times \cite{GK10}.
  - We devise a (2Delta-1)-edge-coloring algorithm in the CONGEST model with
O(Delta + log^* n) time and in the Bit-Round model with O(Delta + log n) time.
Previously-known algorithms had superlinear dependency on Delta for
(2Delta-1)-edge-coloring in these models.
  - We obtain an arbdefective coloring algorithm with running time O(\sqrt
Delta + log^* n). We employ it in order to compute proper colorings that
improve the recent state-of-the-art bounds of Barenboim from PODC'15 \cite{B15}
and Fraigniaud et al. from FOCS'16 \cite{FHK16} by polylogarithmic factors.
  - Our algorithms are applicable to the SET-LOCAL model of \cite{HKMS15}.

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex