Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice Agreement in Message Passing Systems   This paper studies the lattice agreement problem and the generalized lattice
agreement problem in distributed message passing systems. In the lattice
agreement problem, given input values from a lattice, processes have to
non-trivially decide output values that lie on a chain. We consider the lattice
agreement problem in both synchronous and asynchronous systems. For synchronous
lattice agreement, we present two algorithms which run in $\log f$ and $\min
\{O(\log^2 h(L)), O(\log^2 f)\}$ rounds, respectively, where $h(L)$ denotes the
height of the {\em input sublattice} $L$, $f < n$ is the number of crash
failures the system can tolerate, and $n$ is the number of processes in the
system. These algorithms have significant better round complexity than
previously known algorithms. The algorithm by Attiya et al.
\cite{attiya1995atomic} takes $\log n$ synchronous rounds, and the algorithm by
Mavronicolasa \cite{mavronicolasabound} takes $\min \{O(h(L)), O(\sqrt{f})\}$
rounds. For asynchronous lattice agreement, we propose an algorithm which has
time complexity of $2 \cdot \min \{h(L), f + 1\}$ message delays which improves
on the previously known time complexity of $O(n)$ message delays.
  The generalized lattice agreement problem defined by Faleiro et al in
\cite{faleiro2012generalized} is a generalization of the lattice agreement
problem where it is applied for the replicated state machine. We propose an
algorithm which guarantees liveness when a majority of the processes are
correct in asynchronous systems. Our algorithm requires $\min \{O(h(L)),
O(f)\}$ units of time in the worst case which is better than $O(n)$ units of
time required by the algorithm of Faleiro et al. \cite{faleiro2012generalized}.

2
The categories of this paper are: math
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th