Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Representation of Iterative Approximate Byzantine Consensus in
  Directed Graphs   This paper presents a proof of correctness of an iterative approximate
Byzantine consensus (IABC) algorithm for directed graphs. The iterative
algorithm allows fault- free nodes to reach approximate conensus despite the
presence of up to f Byzantine faults. Necessary conditions on the underlying
network graph for the existence of a correct IABC algorithm were shown in our
recent work [15, 16]. [15] also analyzed a specific IABC algorithm and showed
that it performs correctly in any network graph that satisfies the necessary
condition, proving that the necessary condition is also sufficient. In this
paper, we present an alternate proof of correctness of the IABC algorithm,
using a familiar technique based on transition matrices [9, 3, 17, 19].
  The key contribution of this paper is to exploit the following observation:
for a given evolution of the state vector corresponding to the state of the
fault-free nodes, many alternate state transition matrices may be chosen to
model that evolution cor- rectly. For a given state evolution, we identify one
approach to suitably "design" the transition matrices so that the standard
tools for proving convergence can be applied to the Byzantine fault-tolerant
algorithm as well. In particular, the transition matrix for each iteration is
designed such that each row of the matrix contains a large enough number of
elements that are bounded away from 0.

20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin