Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Dominating Set problem studied by simulated annealing and cavity
  method: Analytics and population dynamics   The minimal dominating Set (MDS) problem is a prototypical hard combinatorial
optimization problem. Two years ago we studied this problem by cavity method.
Although we get the solution of a given graph, which gives very good estimation
of minimal dominating size, but we don't know whether we get the ground state
solution and how many solutions exist in the ground state. For this purpose,
last year we continue to develop the one step replica symmetry breaking (RSB)
theory to find the ground state energy of the MDS problem. Finally we find that
1) The MDS problem solution space has both condensation transition and cluster
transition on regular Random (RR) graph and we prove this by simulated
annealing dynamical process. 2) We developed zero temperature Survey
Propagation (SP) algorithm on ER graph to estimate the ground state energy and
to get Survey Propagation Decimation (SPD) algorithm with good results same as
BPD algorithm.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys