Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: SDP-based bounds for graph partition via extended ADMM   We study two NP-complete graph partition problems, $k$-equipartition problems
and graph partition problems with knapsack constraints (GPKC). We introduce
tight SDP relaxations with nonnegativity constraints to get lower bounds, the
SDP relaxations are solved by an extended alternating direction method of
multipliers (ADMM). In this way, we obtain high quality lower bounds for
$k$-equipartition on large instances up to $n =1000$ vertices within as few as
five minutes and for GPKC problems up to $n=500$ vertices within as little as
one hour. On the other hand, interior point methods fail to solve instances
from $n=300$ due to memory requirements. We also design heuristics to generate
upper bounds from the SDP solutions, giving us tighter upper bounds than other
methods proposed in the literature with low computational expense.

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The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
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The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn