1,051 research outputs found
Convex Graph Invariant Relaxations For Graph Edit Distance
The edit distance between two graphs is a widely used measure of similarity
that evaluates the smallest number of vertex and edge deletions/insertions
required to transform one graph to another. It is NP-hard to compute in
general, and a large number of heuristics have been proposed for approximating
this quantity. With few exceptions, these methods generally provide upper
bounds on the edit distance between two graphs. In this paper, we propose a new
family of computationally tractable convex relaxations for obtaining lower
bounds on graph edit distance. These relaxations can be tailored to the
structural properties of the particular graphs via convex graph invariants.
Specific examples that we highlight in this paper include constraints on the
graph spectrum as well as (tractable approximations of) the stability number
and the maximum-cut values of graphs. We prove under suitable conditions that
our relaxations are tight (i.e., exactly compute the graph edit distance) when
one of the graphs consists of few eigenvalues. We also validate the utility of
our framework on synthetic problems as well as real applications involving
molecular structure comparison problems in chemistry.Comment: 27 pages, 7 figure
Discrete torsion in non-geometric orbifolds and their open-string descendants
We discuss some Z_N^L x Z_N^R orbifold compactifications of the type IIB
superstring to D= 4,6 dimensions and their type I descendants. Although the
Z_N^L x Z_N^R generators act asymmetrically on the chiral string modes, they
result into left-right symmetric models that admit sensible unorientable
reductions. We carefully work out the phases that appear in the modular
transformations of the chiral amplitudes and identify the possibility of
introducing discrete torsion. We propose a simplifying ansatz for the
construction of the open-string descendants in which the transverse-channel
Klein-bottle, annulus and Moebius-strip amplitudes are numerically identical in
the proper parametrization of the world-sheet. A simple variant of the ansatz
for the Z_2^L x Z_2^R orbifold gives rise to models with supersymmetry breaking
in the open-string sector.Comment: 21 pages, Latex, minor typos corrected, references added, version to
appear in Nuclear Physics
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