Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Non-Degenerate Perturbation of the Assignment Polytope and its
  Application to Graph Matching   We consider maximizing a continuous convex function over the assignment
polytope. Such problems arise in Graph Matching (the optimization version of
Graph Isomorphism) and Quadratic Assignment problems. In the typical case of
maximizing a convex function over a polytope the problem can be solved by using
a simplicial algorithm such as Tuy's method or the Falk-Hoffman method, but
these algorithms require that the underlying polytope be non-degenerate, which
is not the case for the assignment polytope. In this note we show how a simple
perturbation scheme can be used to create a "surrogate problem" that is both
non-degenerate and combinatorially equivalent to the original problem. We
further provide an explicit construction of a surrogate problem that is
non-degenerate and combinatorially equivalent to the Graph Matching problem,
when the latter is posed as a convex maximization problem. By constructing a
surrogate problem that is known a priori to be non-degenerate and
combinatorially equivalent to Graph Matching we resolve an "open issue" of
solving Graph Matching via convex maximization first raised by Maciel.

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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int