Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite-time and Asymptotic Convergence of Distributed Averaging and
  Maximizing Algorithms   In this paper, we formulate and investigate a generalized consensus algorithm
which makes an attempt to unify distributed averaging and maximizing algorithms
considered in the literature. Each node iteratively updates its state as a
time-varying weighted average of its own state, the minimal state, and the
maximal state of its neighbors. We prove that finite-time consensus is almost
impossible for averaging under this uniform model. Both time-dependent and
state-dependent graphs are considered, and various necessary and/or sufficient
conditions are presented on the consensus convergence. For time-dependent
graphs, we show that quasi-strong connectivity is critical for averaging, as is
strong connectivity for maximizing. For state-dependent graphs defined by a
$\mu$-nearest-neighbor rule, where each node interacts with its $\mu$ nearest
smaller neighbors and the $\mu$ nearest larger neighbors, we show that $\mu+1$
is a critical threshold on the total number of nodes for the transit from
finite-time to asymptotic convergence for averaging, in the absence of node
self-confidence. The threshold is $2\mu$ if each node chooses to connect only
to neighbors with unique values. Numerical examples illustrate the tightness of
the conditions. The results characterize some fundamental similarities and
differences between distributed averaging and maximizing algorithms.

4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ