Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parameterization of tensor network contraction   We present a conceptually clear and algorithmically useful framework for
parameterizing the costs of tensor network contraction. Our framework is
completely general, applying to tensor networks with arbitrary bond dimensions,
open legs, and hyperedges. The fundamental objects of our framework are rooted
and unrooted contraction trees, which represent classes of contraction orders.
Properties of a contraction tree correspond directly and precisely to the time
and space costs of tensor network contraction. The properties of rooted
contraction trees give the costs of parallelized contraction algorithms. We
show how contraction trees relate to existing tree-like objects in the graph
theory literature, bringing to bear a wide range of graph algorithms and tools
to tensor network contraction. Independent of tensor networks, we show that the
edge congestion of a graph is almost equal to the branchwidth of its line
graph.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con